The theoretical measuring of information was famously initiated by Shannon in his mathematical theory of communication, in which he proposed a now widely used quantity, the entropy, measured in bits. Yet, in the same paper, Shannon also chose to measure the information in continuous systems in nats, which differ from bits by the use of the natural rather than the binary logarithm.

We point out that there is nothing natural about the choice of logarithm basis, rather it is arbitrary. We remedy this problematic state of affairs by proposing a genuinely natural measure of information, which we dub gnats. We show that gnats have many advantages in information theory, and propose to adopt the underlying methodology throughout science, arts and everyday life.

UR - https://arxiv.org/abs/2103.16662 ER - TY - JOUR T1 - Infinite-Dimensional Programmable Quantum Processors JF - PRX Quantum Y1 - 2021 A1 - Gschwendtner, Martina A1 - Winter, Andreas VL - 2 UR - https://link.aps.org/doi/10.1103/PRXQuantum.2.030308http://harvest.aps.org/v2/journals/articles/10.1103/PRXQuantum.2.030308/fulltexthttps://link.aps.org/article/10.1103/PRXQuantum.2.030308 JO - PRX Quantum ER - TY - JOUR T1 - LOCC protocols with bounded width per round optimize convex functions JF - Reviews in Mathematical Physics Y1 - 2021 A1 - Leung, Debbie A1 - Winter, Andreas A1 - Yu, Nengkun VL - 33 UR - https://www.worldscientific.com/doi/abs/10.1142/S0129055X21500136 JO - Rev. Math. Phys. ER - TY - JOUR T1 - Programmability of covariant quantum channels JF - Quantum Y1 - 2021 A1 - Gschwendtner, Martina A1 - Bluhm, Andreas A1 - Winter, Andreas VL - 5 UR - https://quantum-journal.orghttps://quantum-journal.org/papers/q-2021-06-29-488/https://quantum-journal.org/papers/q-2021-06-29-488/pdf/ JO - Quantum ER - TY - JOUR T1 - Resource theory of unextendibility and nonasymptotic quantum capacity JF - Physical Review A Y1 - 2021 A1 - Kaur, Eneet A1 - Das, Siddhartha A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 104 UR - https://link.aps.org/doi/10.1103/PhysRevA.104.022401 JO - Phys. Rev. A ER - TY - JOUR T1 - Thermality versus Objectivity: Can They Peacefully Coexist? JF - Entropy Y1 - 2021 A1 - Le, Thao P. A1 - Winter, Andreas A1 - Adesso, Gerardo VL - 23 UR - https://www.mdpi.com/1099-4300/23/11/1506 JO - Entropy ER - TY - JOUR T1 - All tight correlation Bell inequalities have quantum violations JF - Physical Review Research Y1 - 2020 A1 - Escolà, Llorenç A1 - John Calsamiglia A1 - Winter, Andreas VL - 2 UR - https://link.aps.org/doi/10.1103/PhysRevResearch.2.012044http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevResearch.2.012044/fulltexthttps://link.aps.org/article/10.1103/PhysRevResearch.2.012044 JO - Phys. Rev. Research ER - TY - CONF T1 - An Alphabet-Size Bound for the Information Bottleneck Function T2 - 2020 IEEE International Symposium on Information Theory (ISIT) Y1 - 2020 A1 - Hirche, Christoph A1 - Winter, Andreas JF - 2020 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Los Angeles, CA, USA UR - https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=9166581 ER - TY - JOUR T1 - Distributed Compression of Correlated Classical-Quantum Sources or: The Price of Ignorance JF - IEEE Transactions on Information Theory Y1 - 2020 A1 - Baghali Khanian, Zahra A1 - Winter, Andreas VL - 66 UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18https://ieeexplore.ieee.org/document/9039682/http://xplorestaging.ieee.org/ielx7/18/9170933/09039682.pdf?arnumber=9039682 JO - IEEE Trans. Inform. Theory ER - TY - CONF T1 - General Mixed State Quantum Data Compression with and without Entanglement Assistance T2 - 2020 IEEE International Symposium on Information Theory (ISIT) Y1 - 2020 A1 - Khanian, Zahra Baghali A1 - Winter, Andreas JF - 2020 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Los Angeles, CA, USA UR - https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=9166581 ER - TY - JOUR T1 - Introduction to the Special Issue on Quantum Information Science JF - IEEE Journal on Selected Areas in Information Theory Y1 - 2020 A1 - Soljanin, Emina A1 - Winter, Andreas VL - 1 UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=8700143 JO - IEEE J. Sel. Areas Inf. Theory ER - TY - CONF T1 - Multi-User Distillation of Common Randomness and Entanglement from Quantum States T2 - 2020 IEEE International Symposium on Information Theory (ISIT) Y1 - 2020 A1 - Salek, Farzin A1 - Winter, Andreas JF - 2020 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Los Angeles, CA, USA UR - https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=9166581 ER - TY - BOOK T1 - A Quantum Leap in Information Theory Y1 - 2020 A1 - Mancini, Stefano A1 - Winter, Andreas PB - World Scientific ER - TY - CONF T1 - Quantum State Redistribution for Ensemble Sources T2 - 2020 IEEE International Symposium on Information Theory (ISIT) Y1 - 2020 A1 - Khanian, Zahra Baghali A1 - Winter, Andreas JF - 2020 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Los Angeles, CA, USA UR - https://ieeexplore.ieee.org/xpl/mostRecentIssue.jsp?punumber=9166581 ER - TY - JOUR T1 - Reference Frames Which Separately Store Noncommuting Conserved Quantities JF - Physical Review Letters Y1 - 2020 A1 - Popescu, Sandu A1 - Sainz, Ana Belén A1 - Short, Anthony J. A1 - Winter, Andreas VL - 125 UR - https://link.aps.org/doi/10.1103/PhysRevLett.125.090601 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Universal Gaps for XOR Games from Estimates on Tensor Norm Ratios JF - Communications in Mathematical Physics Y1 - 2020 A1 - Aubrun, Guillaume A1 - Lami, Ludovico A1 - Palazuelos, Carlos A1 - Szarek, Stanisław J. A1 - Winter, Andreas VL - 375 UR - http://link.springer.com/10.1007/s00220-020-03688-2 JO - Commun. Math. Phys. ER - TY - CONF T1 - Convexity and Operational Interpretation of the Quantum Information Bottleneck Function T2 - 2019 IEEE International Symposium on Information Theory (ISIT) Y1 - 2019 A1 - Datta, Nilanjana A1 - Hirche, Christoph A1 - Winter, Andreas JF - 2019 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Paris, France UR - https://ieeexplore.ieee.org/document/8849518/ ER - TY - CONF T1 - Distributed Compression of Correlated Classical-Quantum Sources T2 - 2019 IEEE International Symposium on Information Theory (ISIT) Y1 - 2019 A1 - Khanian, Zahra Baghali A1 - Winter, Andreas JF - 2019 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Paris, France UR - https://ieeexplore.ieee.org/document/8849794/ ER - TY - JOUR T1 - Distributed Private Randomness Distillation JF - Phys. Rev. Lett. Y1 - 2019 A1 - Yang, Dong A1 - Horodecki, Karol A1 - Winter, Andreas VL - 123 UR - https://link.aps.org/doi/10.1103/PhysRevLett.123.170501 ER - TY - CONF T1 - Entanglement-Assisted Quantum Data Compression T2 - 2019 IEEE International Symposium on Information Theory (ISIT) Y1 - 2019 A1 - Khanian, Zahra Baghali A1 - Winter, Andreas JF - 2019 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Paris, France UR - https://ieeexplore.ieee.org/document/8849352/ ER - TY - JOUR T1 - Extendibility Limits the Performance of Quantum Processors JF - Phys. Rev. Lett. Y1 - 2019 A1 - Kaur, Eneet A1 - Das, Siddhartha A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 123 UR - https://link.aps.org/doi/10.1103/PhysRevLett.123.070502 ER - TY - JOUR T1 - How to Quantify a Dynamical Quantum Resource JF - Phys. Rev. Lett. Y1 - 2019 A1 - Gour, Gilad A1 - Winter, Andreas VL - 123 UR - https://link.aps.org/doi/10.1103/PhysRevLett.123.150401 ER - TY - JOUR T1 - Indistinguishability-enabled coherence for quantum metrology JF - Phys. Rev. A Y1 - 2019 A1 - Castellini, Alessia A1 - Lo Franco, Rosario A1 - Lami, Ludovico A1 - Winter, Andreas A1 - Adesso, Gerardo A1 - Compagno, Giuseppe VL - 100 UR - https://link.aps.org/doi/10.1103/PhysRevA.100.012308 ER - TY - JOUR T1 - Intersection patterns of linear subspaces with the hypercube JF - Journal of Combinatorial Theory, Series A Y1 - 2019 A1 - Melo, Nolmar A1 - Winter, Andreas VL - 164 UR - https://www.sciencedirect.com/science/article/pii/S0097316518301705 JO - Journal of Combinatorial Theory, Series A ER - TY - JOUR T1 - One-Shot Coherence Distillation: Towards Completing the Picture JF - IEEE Transactions on Information Theory Y1 - 2019 A1 - Zhao, Qi A1 - Liu, Yunchao A1 - Yuan, Xiao A1 - Chitambar, Eric A1 - Winter, Andreas VL - 65 UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18https://ieeexplore.ieee.org/document/8691620/http://xplorestaging.ieee.org/ielx7/18/8836351/08691620.pdf?arnumber=8691620https://ieeexplore.ieee.org/ielaam/18/8836351/8691620-aam.pdf JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Secure and Robust Identification via Classical-Quantum Channels JF - IEEE Transactions on Information Theory Y1 - 2019 A1 - Boche, Holger A1 - Deppe, Christian A1 - Winter, Andreas VL - 65 UR - https://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=18https://ieeexplore.ieee.org/document/8731894/http://xplorestaging.ieee.org/ielx7/18/8836351/08731894.pdf?arnumber=8731894 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Stochastic thermodynamics with arbitrary interventions JF - Phys. Rev. E Y1 - 2019 A1 - Strasberg, Philipp A1 - Winter, Andreas VL - 100 UR - https://link.aps.org/doi/10.1103/PhysRevE.100.022135 ER - TY - JOUR T1 - Thermodynamics as a Consequence of Information Conservation JF - Quantum Y1 - 2019 A1 - Bera, Manabendra Nath A1 - Riera, Arnau A1 - Lewenstein, Maciej A1 - Khanian, Zahra Baghali A1 - Winter, Andreas VL - 3 UR - https://quantum-journal.orghttps://quantum-journal.org/papers/q-2019-02-14-121/https://quantum-journal.org/papers/q-2019-02-14-121/pdf/ JO - Quantum ER - TY - CHAP T1 - Thermodynamics from Information T2 - Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions Y1 - 2019 A1 - Bera, Manabendra Nath A1 - Winter, Andreas A1 - Lewenstein, Maciej ED - Binder, Felix ED - Correa, Luis A. ED - Gogolin, Christian ED - Anders, Janet ED - Adesso, Gerardo JF - Thermodynamics in the Quantum Regime: Fundamental Aspects and New Directions T3 - Fundamental Theories of Physics PB - Springer Verlag CY - Cham Newark Kuala Lumpur VL - 195 SN - 978-3-319-99045-3 UR - http://link.springer.com/10.1007/978-3-319-99046-0_33 ER - TY - JOUR T1 - All phase-space linear bosonic channels are approximately Gaussian dilatable JF - New Journal of Physics Y1 - 2018 A1 - Lami, Ludovico A1 - Sabapathy, Krishna Kumar A1 - Winter, Andreas VL - 20 JO - New J. Phys. ER - TY - CONF T1 - Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy T2 - 2018 IEEE International Symposium on Information Theory (ISIT) Y1 - 2018 A1 - Boche, Holger A1 - Deppe, Christian A1 - Noetzel, Janis A1 - Winter, Andreas AB -We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, via a quantum version of the ``elimination of of correlation{''} using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant.

JF - 2018 IEEE International Symposium on Information Theory (ISIT) T3 - {IEEE International Symposium on Information Theory} PB - IEEE SN - 978-1-5386-4781-3 N1 - {IEEE International Symposium on Information Theory (ISIT), Vail, CO, JUN 17-22, 2018} ER - TY - JOUR T1 - Gaussian quantum resource theories JF - Physical Review A Y1 - 2018 A1 - Lami, Ludovico A1 - Regula, Bartosz A1 - Wang, Xin A1 - Nichols, Rosanna A1 - Winter, Andreas A1 - Adesso, Gerardo VL - 987 UR - https://link.aps.org/doi/10.1103/PhysRevA.98.022335http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevA.98.022335/fulltexthttps://link.aps.org/article/10.1103/PhysRevA.98.022335 JO - Phys. Rev. A ER - TY - JOUR T1 - Quantum Enhancement of Randomness Distribution JF - IEEE Transactions on Information Theory Y1 - 2018 A1 - Garcia-Patron, Raul A1 - Matthews, William A1 - Winter, Andreas VL - 64 UR - https://ieeexplore.ieee.org/document/8328871/http://xplorestaging.ieee.org/ielx7/18/8361085/08328871.pdf?arnumber=8328871 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Quantum reference frames and their applications to thermodynamics JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences Y1 - 2018 A1 - Popescu, Sandu A1 - Sainz, Belén A1 - Short, Anthony J. A1 - Winter, Andreas VL - 376(2123) UR - http://rsta.royalsocietypublishing.org/lookup/doi/10.1098/rsta.2018.0111https://syndication.highwire.org/content/doi/10.1098/rsta.2018.0111 JO - Phil. Trans. R. Soc. A ER - TY - CONF T1 - Secure and Robust Identification via Classical-Quantum Channels T2 - 2018 IEEE International Symposium on Information Theory (ISIT) Y1 - 2018 A1 - Boche, Holger A1 - Deppe, Christian A1 - Winter, Andreas JF - 2018 IEEE International Symposium on Information Theory (ISIT) T3 - {IEEE International Symposium on Information Theory} PB - IEEE CY - Vail, CO SN - 978-1-5386-4781-3 N1 - {IEEE International Symposium on Information Theory (ISIT), Vail, CO, JUN 17-22, 2018} ER - TY - JOUR T1 - Squashed Entanglement,k-Extendibility, Quantum Markov Chains, and Recovery Maps JF - Foundations of Physics Y1 - 2018 A1 - Li, Ke A1 - Winter, Andreas VL - 48 UR - http://link.springer.com/10.1007/s10701-018-0143-6http://link.springer.com/content/pdf/10.1007/s10701-018-0143-6.pdfhttp://link.springer.com/article/10.1007/s10701-018-0143-6/fulltext.htmlhttp://link.springer.com/content/pdf/10.1007/s10701-018-0143-6.pdf JO - Found Phys ER - TY - JOUR T1 - Ultimate Data Hiding in Quantum Mechanics and Beyond JF - Communications in Mathematical Physics Y1 - 2018 A1 - Lami, Ludovico A1 - Palazuelos, Carlos A1 - Winter, Andreas VL - 361 UR - http://link.springer.com/10.1007/s00220-018-3154-4http://link.springer.com/content/pdf/10.1007/s00220-018-3154-4.pdfhttp://link.springer.com/article/10.1007/s00220-018-3154-4/fulltext.htmlhttp://link.springer.com/content/pdf/10.1007/s00220-018-3154-4.pdf JO - Commun. Math. Phys. ER - TY - JOUR T1 - Universal Recovery Maps and Approximate Sufficiency of Quantum Relative Entropy JF - Annales Henri Poincaré Y1 - 2018 A1 - Junge, Marius A1 - Renner, Renato A1 - Sutter, David A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 19 UR - http://link.springer.com/10.1007/s00023-018-0716-0 JO - Ann. Henri Poincaré ER - TY - JOUR T1 - Using and reusing coherence to realize quantum processes JF - Quantum Y1 - 2018 A1 - García-Díaz, María A1 - Fang, Kun A1 - Wang, Xin A1 - Rosati, Matteo A1 - Skotiniotis, Michalis A1 - John Calsamiglia A1 - Winter, Andreas VL - 2 UR - https://quantum-journal.orghttps://quantum-journal.org/papers/q-2018-10-19-100/https://quantum-journal.org/papers/q-2018-10-19-100/pdf/ JO - Quantum ER - TY - JOUR T1 - Approximate Degradable Quantum Channels JF - IEEE Transactions on Information Theory Y1 - 2017 A1 - Sutter, David A1 - Scholz, Volkher B. A1 - Winter, Andreas A1 - Renner, Renato AB -Degradable quantum channels are an important class of completely positive trace-preserving maps. Among other properties, they offer a single-letter formula for the quantum and the private classical capacity and are characterized by the fact that a complementary channel can be obtained from the channel by applying a degrading channel. In this paper, we introduce the concept of approximate degradable channels, which satisfy this condition up to some finite epsilon {\textgreater}= 0. That is, there exists a degrading channel which upon composition with the channel is e-close in the diamond norm to the complementary channel. We show that for any fixed channel the smallest such e can be efficiently determined via a semidefinite program. Moreover, these approximate degradable channels also approximately inherit all other properties of degradable channels. As an application, we derive improved upper bounds to the quantum and private classical capacity for certain channels of interest in quantum communication.

VL - 63 ER - TY - JOUR T1 - Constant Compositions in the Sphere Packing Bound for Classical-Quantum Channels JF - IEEE Transactions on Information Theory Y1 - 2017 A1 - Dalai, Marco A1 - Winter, Andreas VL - 63 UR - http://ieeexplore.ieee.org/document/7979569/ JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Decoupling with random diagonal unitaries JF - Quantum Y1 - 2017 A1 - Nakata, Yoshifumi A1 - Hirche, Christoph A1 - Morgan, Ciara A1 - Winter, Andreas AB - Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, and Andreas Winter, Quantum 1, 18 (2017). https://doi.org/10.22331/q-2017-07-21-18 We investigate decoupling, one of the most important primitives in quantum Shannon theory, by replacing the uniformly distributed random unitaries commonly used to achieve the protocol, with… VL - 1 UR - https://quantum-journal.org/papers/q-2017-07-21-18/ ER - TY - JOUR T1 - Efficient Quantum Pseudorandomness with Nearly Time-Independent Hamiltonian Dynamics JF - PHYSICAL REVIEW X Y1 - 2017 A1 - Nakata, Yoshifumi A1 - Hirche, Christoph A1 - Koashi, Masato A1 - Winter, Andreas AB -Quantum randomness is an essential key to understanding the dynamics of complex many-body systems and also a powerful tool for quantum engineering. However, exact realizations of quantum randomness take an extremely long time and are infeasible in many-body systems, leading to the notion of quantum pseudorandomness, also known as unitary designs. Here, to explore microscopic dynamics of generating quantum pseudorandomness in many-body systems, we provide new efficient constructions of unitary designs and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time. The new constructions are based on the alternate applications of random potentials in the generalized position and momentum spaces, and we provide explicit quantum circuits generating quantum pseudorandomness significantly more efficient than previous ones. We then provide a design Hamiltonian in disordered systems with periodically changing spin-glass-type interactions. The design Hamiltonian generates quantum pseudorandomness in a constant time even in the system composed of a large number of spins. We also point out the close relationship between the design Hamiltonian and quantum chaos.

VL - 7 ER - TY - JOUR T1 - Equilibration Time Scales of Physically Relevant Observables JF - Physical Review X Y1 - 2017 A1 - Garcia-Pintos, Luis Pedro A1 - Linden, Noah A1 - Malabarba, Artur S. L. A1 - Short, Anthony J. A1 - Winter, Andreas AB -We address the problem of understanding, from first principles, the conditions under which a quantum system equilibrates rapidly with respect to a concrete observable. On the one hand, previously known general upper bounds on the time scales of equilibration were unrealistically long, with times scaling linearly with the dimension of the Hilbert space. These bounds proved to be tight since particular constructions of observables scaling in this way were found. On the other hand, the computed equilibration time scales for certain classes of typical measurements, or under the evolution of typical Hamiltonians, are unrealistically short. However, most physically relevant situations fall outside these two classes. In this paper, we provide a new upper bound on the equilibration time scales which, under some physically reasonable conditions, give much more realistic results than previously known. In particular, we apply this result to the paradigmatic case of a system interacting with a thermal bath, where we obtain an upper bound for the equilibration time scale independent of the size of the bath. In this way, we find general conditions that single out observables with realistic equilibration times within a physically relevant setup.

VL - 7 ER - TY - JOUR T1 - Erratum: Resource theory of coherence: Beyond states [Phys. Rev. ASocial media platforms make tremendous amounts of data available. Often times, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, one may assume such a distorted image to be corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA).

JF - 2017 International Symposium on Wireless Communication Systems (ISWCS) T3 - International {Symposium} on {Wireless} {Communication} {Systems} PB - IEEE CY - Bologna SN - 978-1-5386-2913-0 ER - TY - JOUR T1 - Interferometric visibility and coherence JF - Proceedings of the Royal Society A London Y1 - 2017 A1 - Biswas, Tanmoy A1 - García-Díaz, María A1 - Winter, Andreas AB -Recently, the basic concept of quantum coherence (or superposition) has gained a lot of renewed attention, after Baumgratz et al. (Phys. Rev. Lett. 113, 140401. (doi: 10.1103/PhysRevLett.113.140401)), following Aberg (http://arxiv.org/abs/quant-ph/0612146), have proposed a resource theoretic approach to quantify it. This has resulted in a large number of papers and preprints exploring various coherence monotones, and debating possible forms for the resource theory. Here, we take the view that the operational foundation of coherence in a state, be it quantum or otherwise wave mechanical, lies in the observation of interference effects. Our approach here is to consider an idealized multi-path interferometer, with a suitable detector, in such a way that the visibility of the interference pattern provides a quantitative expression of the amount of coherence in a given probe state. We present a general framework of deriving coherence measures from visibility, and demonstrate it by analysing several concrete visibility parameters, recovering some known coherence measures and obtaining some new ones.

VL - 473 ER - TY - JOUR T1 - Logarithmic coherence: Operational interpretation of L1-norm coherence JF - Physical Review A Y1 - 2017 A1 - Rana, Swapan A1 - Parashar, Preeti A1 - Winter, Andreas A1 - Lewenstein, Maciej AB -We show that the distillable coherence-which is equal to the relative entropy of coherence-is, up to a constant factor, always bounded by the l(1)-norm measure of coherence (defined as the sum of absolute values of off diagonals). Thus the latter plays a similar role as logarithmic negativity plays in entanglement theory and this is the best operational interpretation from a resource-theoretic viewpoint. Consequently the two measures are intimately connected to another operational measure, the robustness of coherence. We find also relationships between these measures, which are tight for general states, and the tightest possible for pure and qubit states. For a given robustness, we construct a state having minimum distillable coherence.

VL - 96 ER - TY - JOUR T1 - Non-Gaussian operations on Bosonic modes of light: Photon-added Gaussian channels JF - Physical Review A Y1 - 2017 A1 - Sabapathy, Krishna Kumar A1 - Winter, Andreas AB -We present a framework for studying bosonic non-Gaussian channels of continuous-variable systems. Our emphasis is on a class of channels that we call photon-added Gaussian channels, which are experimentally viable with current quantum-optical technologies. A strong motivation for considering these channels is the fact that it is compulsory to go beyond the Gaussian domain for numerous tasks in continuous-variable quantum information processing such as entanglement distillation from Gaussian states and universal quantum computation. The single-mode photon-added channels we consider are obtained by using two-mode beam splitters and squeezing operators with photon addition applied to the ancilla ports giving rise to families of non-Gaussian channels. For each such channel, we derive its operator-sum representation, indispensable in the present context. We observe that these channels are Fock preserving (coherence nongenerating). We then report two examples of activation using our scheme of photon addition, that of quantum-optical nonclassicality at outputs of channels that would otherwise output only classical states and of both the quantum and private communication capacities, hinting at far-reaching applications for quantum-optical communication. Further, we see that noisy Gaussian channels can be expressed as a convex mixture of these non-Gaussian channels. We also present other physical and information-theoretic properties of these channels.

VL - 95 UR - https://link.aps.org/doi/10.1103/PhysRevA.95.062309 ER - TY - JOUR T1 - Resource theory of coherence: Beyond states JF - Physical Review A Y1 - 2017 A1 - Ben Dana, Khaled A1 - García-Díaz, María A1 - Mejatty, Mohamed A1 - Winter, Andreas AB -We generalize the recently proposed resource theory of coherence (or superposition) [T. Baumgratz et al., Phys. Rev. Lett. 113, 140401 (2014); A. Winter and D. Yang, Phys. Rev. Lett. 116, 120404 ( 2016)] to the setting where not just the free (”incoherent”) resources, but also the manipulated objects, are quantum operations rather than states. In particular, we discuss an information theoretic notion of the coherence capacity of a quantum channel and prove a single-letter formula for it in the case of unitaries. Then we move to the coherence cost of simulating a channel and prove achievability results for unitaries and general channels acting on a d-dimensional system; we show that a maximally coherent state of rank d is always sufficient as a resource if incoherent operations are allowed, and one of rank d(2) for “strictly incoherent” operations. We also show lower bounds on the simulation cost of channels that allow us to conclude that there exists bound coherence in operations, i.e., maps with nonzero cost of implementing them but zero coherence capacity; this is in contrast to states, which do not exhibit bound coherence.

VL - 95 ER - TY - JOUR T1 - Unitary 2-designs from random X- and Z-diagonal unitaries JF - Journal of Mathematical Physics Y1 - 2017 A1 - Nakata, Yoshifumi A1 - Hirche, Christoph A1 - Morgan, Ciara A1 - Winter, Andreas AB -Unitary 2-designs are random unitaries simulating up to the second order statistical moments of the uniformly distributed random unitaries, often referred to as Haar random unitaries. They are used in a wide variety of theoretical and practical quantum information protocols and also have been used to model the dynamics in complex quantum many-body systems. Here, we show that unitary 2-designs can be approximately implemented by alternately repeating random unitaries diagonal in the Pauli-Z basis and Pauli-X basis. We also provide a converse about the number of repetitions needed to achieve unitary 2-designs. These results imply that the process after l repetitions achieves a Theta(d(-l))-approximate unitary 2-design. Based on the construction, we further provide quantum circuits that efficiently implement approximate unitary 2-designs. Although a more efficient implementation of unitary 2-designs is known, our quantum circuit has its own merit that it is divided into a constant number of commuting parts, which enables us to apply all commuting gates simultaneously and leads to a possible reduction of an actual execution time. We finally interpret the result in terms of the dynamics generated by time-dependent Hamiltonians and provide for the first time a random disordered time-dependent Hamiltonian that generates a unitary 2-design after switching interactions only a few times. Published by AIP Publishing.

VL - 58 ER - TY - JOUR T1 - Weak Locking Capacity of Quantum Channels Can be Much Larger Than Private Capacity JF - Journal of Cryptology Y1 - 2017 A1 - Winter, Andreas VL - 30 UR - http://arxiv.org/abs/1403.6361 JO - J Cryptol ER - TY - JOUR T1 - Estimating quantum chromatic numbers JF - Journal of Functional Analysis Y1 - 2016 A1 - Paulsen, Vern I. A1 - Severini, Simone A1 - Stahlke, Daniel A1 - Todorov, Ivan G. A1 - Winter, Andreas VL - 270 IS - 6 JO - Journal of Functional Analysis ER - TY - JOUR T1 - Microcanonical and resource-theoretic derivations of the thermal state of a quantum system with noncommuting charges JF - Nature Communications Y1 - 2016 A1 - Yunger Halpern, Nicole A1 - Faist, Philippe A1 - Oppenheim, Jonathan A1 - Winter, Andreas VL - 77 UR - http://www.nature.com/doifinder/10.1038/ncomms12051 JO - Nat Comms ER - TY - JOUR T1 - No-Signalling-Assisted Zero-Error Capacity of Quantum Channels and an Information Theoretic Interpretation of the Lovász Number JF - IEEE Transactions on Information Theory Y1 - 2016 A1 - Duan, Runyao A1 - Winter, Andreas VL - 62 IS - 2 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Operational Resource Theory of Coherence JF - Physical Review Letters Y1 - 2016 A1 - Winter, Andreas A1 - Dong Yang VL - 116 IS - 12 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Potential Capacities of Quantum Channels JF - IEEE Transactions on Information Theory Y1 - 2016 A1 - Winter, Andreas A1 - Dong Yang VL - 62 IS - 3 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - The Private and Public Correlation Cost of Three Random Variables With Collaboration JF - IEEE Transactions on Information Theory Y1 - 2016 A1 - Eric Chitambar A1 - Hsieh, Min-Hsiu A1 - Winter, Andreas VL - 62 IS - 4 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Quantum Channel Capacities With Passive Environment Assistance JF - IEEE Transactions on Information Theory Y1 - 2016 A1 - Karumanchi, Siddharth A1 - Mancini, Stefano A1 - Winter, Andreas A1 - Dong Yang VL - 62 IS - 4 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Quantum learning of classical stochastic processes: The completely positive realization problem JF - Journal of Mathematical Physics Y1 - 2016 A1 - Monràs, Alex A1 - Winter, Andreas VL - 57 IS - 1 JO - J. Math. Phys. ER - TY - JOUR T1 - Schur Complement Inequalities for Covariance Matrices and Monogamy of Quantum Correlations JF - Physical Review Letters Y1 - 2016 A1 - Lami, Ludovico A1 - Hirche, Christoph A1 - Adesso, Gerardo A1 - Winter, Andreas VL - 117 UR - http://link.aps.org/doi/10.1103/PhysRevLett.117.220502http://harvest.aps.org/v2/journals/articles/10.1103/PhysRevLett.117.220502/fulltexthttp://link.aps.org/article/10.1103/PhysRevLett.117.220502 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Should Entanglement Measures be Monogamous or Faithful? JF - Physical Review Letters Y1 - 2016 A1 - Lancien, Cécilia A1 - Di Martino, Sara A1 - Huber, Marcus A1 - Piani, Marco A1 - Adesso, Gerardo A1 - Winter, Andreas VL - 117 IS - 6 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Tight Uniform Continuity Bounds for Quantum Entropies: Conditional Entropy, Relative Entropy Distance and Energy Constraints JF - Communications in Mathematical Physics Y1 - 2016 A1 - Winter, Andreas VL - 347 UR - http://arxiv.org/abs/1507.07775 JO - Commun. Math. Phys. ER - TY - JOUR T1 - Witnessing entanglement by proxy JF - New Journal of Physics Y1 - 2016 A1 - Bäuml, Stefan A1 - Bruß, Dagmar A1 - Huber, Marcus A1 - Kampermann, Hermann A1 - Winter, Andreas VL - 18 IS - 1 JO - New J. Phys. ER - TY - JOUR T1 - On Zero-Error Communication via Quantum Channels in the Presence of Noiseless Feedback JF - IEEE Transactions on Information Theory Y1 - 2016 A1 - Duan, Runyao A1 - Severini, Simone A1 - Winter, Andreas KW - bipartite equivocation graph KW - Bipartite graph KW - Capacity planning KW - Choi-Kraus operators KW - coding theorem KW - commutative bipartite graph KW - Electronic mail KW - encoding KW - entanglement-assisted capacity KW - feedback KW - feedback-assisted capacity KW - feedback-assisted zero-error capacity KW - information theory KW - noiseless feedback channel KW - quantum channels KW - quantum communication KW - quantum entanglement KW - Quantum information KW - Receivers KW - Shannon's zero-error communication KW - telecommunication channels KW - unlimited quantum capacity KW - zero-error capacity AB -We initiate the study of zero-error communication via quantum channels when the receiver and the sender have at their disposal a noiseless feedback channel of unlimited quantum capacity, generalizing Shannon's zero-error communication theory with instantaneous feedback. We first show that this capacity is only a function of the linear span of Choi-Kraus operators of the channel, which generalizes the bipartite equivocation graph of a classical channel, and which we dub non-commutative bipartite graph. Then, we go on to show that the feedback-assisted capacity is non-zero (allowing for a constant amount of activating noiseless communication) if and only if the non-commutative bipartite graph is non-trivial, and give a number of equivalent characterizations. This result involves a far-reaching extension of the conclusive exclusion of quantum states. We then present an upper bound on the feedback-assisted zero-error capacity, motivated by a conjecture originally made by Shannon and proved later by Ahlswede. We demonstrate that this bound to have many good properties, including being additive and given by a minimax formula. We also prove a coding theorem showing that this quantity is the entanglement-assisted capacity against an adversarially chosen channel from the set of all channels with the same Choi-Kraus span, which can also be interpreted as the feedback-assisted unambiguous capacity. The proof relies on a generalization of the Postselection Lemma (de Finetti reduction) that allows to reflect additional constraints, and which we believe to be of independent interest. This capacity is a relaxation of the feedback-assisted zero-error capacity; however, we have to leave open the question of whether they coincide in general. We illustrate our ideas with a number of examples, including classical-quantum channels and Weyl diagonal channels, and close with an extensive discussion of open questions.

VL - 62 ER - TY - JOUR T1 - Limitations on quantum key repeaters JF - Nature Communications Y1 - 2015 A1 - Bäuml, Stefan A1 - Christandl, Matthias A1 - Horodecki, Karol A1 - Winter, Andreas VL - 6 JO - Nat Comms ER - TY - JOUR T1 - Strong Converse for the Classical Capacity of Optical Quantum Communication Channels JF - IEEE Transactions on Information Theory Y1 - 2015 A1 - Bardhan, Bhaskar Roy A1 - Garcia-Patron, Raul A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 61 IS - 4 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Bounds on entanglement assisted source-channel coding via the Lovasz theta number and its variants JF - IEEE Transactions on Information Theory Y1 - 2014 A1 - Toby S. Cubitt A1 - Laura Mancinska A1 - David Roberson A1 - Stahlke, Daniel A1 - Winter, Andreas VL - 60 ER - TY - Generic T1 - Constant compositions in the sphere packing bound for classical-quantum channels T2 - 2014 IEEE International Symposium on Information Theory (ISIT) Y1 - 2014 A1 - Dalai, Marco A1 - Winter, Andreas JF - 2014 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Honolulu, HI, USA ER - TY - JOUR T1 - Everything You Always Wanted to Know About LOCC (But Were Afraid to Ask) JF - Communications in Mathematical Physics Y1 - 2014 A1 - Eric Chitambar A1 - Debbie Leung A1 - Mančinska, Laura A1 - Maris Ozols A1 - Winter, Andreas VL - 328 IS - 1 JO - Commun. Math. Phys. ER - TY - JOUR T1 - Full Security of Quantum Key Distribution From No-Signaling Constraints JF - IEEE Transactions on Information Theory Y1 - 2014 A1 - Masanes, Lluis A1 - Renner, Renato A1 - Christandl, Matthias A1 - Winter, Andreas A1 - Barrett, Jonathan VL - 60 IS - 8 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Graph-Theoretic Approach to Quantum Correlations JF - Physical Review Letters Y1 - 2014 A1 - Cabello, Adán A1 - Severini, Simone A1 - Winter, Andreas VL - 112 IS - 4 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Inequalities for the ranks of multipartite quantum states JF - Linear Algebra and its Applications Y1 - 2014 A1 - Josh Cadney A1 - Huber, Marcus A1 - Noah Linden A1 - Winter, Andreas AB - We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We show that there exist inequalities constraining the possible distribution of ranks. This is analogous to the case of von Neumann entropy (\alpha-R\'enyi entropy for \alpha=1), where nontrivial inequalities constraining the distribution of entropies (such as e.g. strong subadditivity) are known. It was also recently discovered that all other \alpha-R\'enyi entropies for α∈(0,1)∪(1,∞) satisfy only one trivial linear inequality (non-negativity) and the distribution of entropies for α∈(0,1) is completely unconstrained beyond non-negativity. Our result resolves an important open question by showing that also the case of \alpha=0 (logarithm of the rank) is restricted by nontrivial linear relations and thus the cases of von Neumann entropy (i.e., \alpha=1) and 0-R\'enyi entropy are exceptionally interesting measures of entanglement in the multipartite setting. VL - 452 JO - Linear Algebra and its Applications ER - TY - JOUR T1 - ‘Pretty strong’ converse for the quantum capacity of degradable channels JF - IEEE Transactions on Information Theory Y1 - 2014 A1 - Ciara Morgan A1 - Winter, Andreas VL - 60 ER - TY - JOUR T1 - The Quantum Reverse Shannon Theorem and Resource Tradeoffs for Simulating Quantum Channels JF - IEEE Transactions on Information Theory Y1 - 2014 A1 - Bennett, Charles H. A1 - Devetak, Igor A1 - Harrow, Aram W. A1 - Shor, Peter W. A1 - Winter, Andreas VL - 60 IS - 5 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Relative Entropy and Squashed Entanglement JF - Communications in Mathematical Physics Y1 - 2014 A1 - Ke Li A1 - Winter, Andreas VL - 326 IS - 1 JO - Commun. Math. Phys. ER - TY - JOUR T1 - Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy JF - Communications in Mathematical Physics Y1 - 2014 A1 - Wilde, Mark M. A1 - Winter, Andreas A1 - Dong Yang VL - 331 IS - 2 JO - Commun. Math. Phys. ER - TY - JOUR T1 - Strong converse for the classical capacity of the pure-loss bosonic channel JF - Problems of Information Transmission Y1 - 2014 A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 50 IS - 2 JO - Probl Inf Transm ER - TY - Generic T1 - Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes T2 - 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) Y1 - 2014 A1 - Wilde, Mark M. A1 - Winter, Andreas ED - Steve T Flammia ED - Harrow, Aram W. JF - 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014) PB - LIPICS CY - Singapore VL - 27 ER - TY - JOUR T1 - What does an experimental test of quantum contextuality prove or disprove? JF - Journal of Physics A: Mathematical and Theoretical Y1 - 2014 A1 - Winter, Andreas VL - 47 IS - 42 JO - J. Phys. A: Math. Theor. ER - TY - JOUR T1 - Distinguishing Multi-Partite States by Local Measurements JF - Communications in Mathematical Physics Y1 - 2013 A1 - Lancien, Cécilia A1 - Winter, Andreas VL - 323 IS - 2 JO - Commun. Math. Phys. ER - TY - CHAP T1 - Identification via Quantum Channels T2 - Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede Y1 - 2013 A1 - Winter, Andreas ED - Aydinian, Harout ED - Cicalese, Ferdinando ED - Deppe, Christian JF - Information Theory, Combinatorics, and Search Theory: In Memory of Rudolf Ahlswede T3 - Lecture Notes in Computer Science PB - Springer Berlin Heidelberg CY - Berlin, Heidelberg VL - LNCS 7777 SN - 978-3-642-36899-8 ER - TY - Generic T1 - The Quantum Entropy Cone of Stabiliser States T2 - Proc. 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) Y1 - 2013 A1 - Noah Linden A1 - Frantisek Matus A1 - Mary Beth Ruskai A1 - Winter, Andreas ED - Severini, Simone ED - Fernando Brandao JF - Proc. 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013) T3 - LIPICS PB - Leibniz International Proceedings in Informatics (LIPICS) CY - Guelph, ON VL - 22 ER - TY - JOUR T1 - Quantum Rate-Distortion Coding With Auxiliary Resources JF - IEEE Transactions on Information Theory Y1 - 2013 A1 - Wilde, Mark M. A1 - Datta, Nilanjana A1 - Hsieh, Min-Hsiu A1 - Winter, Andreas VL - 59 IS - 10 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - Quantum State Cloning Using Deutschian Closed Timelike Curves JF - Physical Review Letters Y1 - 2013 A1 - Brun, Todd A. A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 111 IS - 19 JO - Phys. Rev. Lett. ER - TY - JOUR T1 - Quantum-to-classical rate distortion coding JF - Journal of Mathematical Physics Y1 - 2013 A1 - Datta, Nilanjana A1 - Hsieh, Min-Hsiu A1 - Wilde, Mark M. A1 - Winter, Andreas VL - 54 IS - 4 JO - J. Math. Phys. ER - TY - JOUR T1 - The structure of Renyi entropic inequalities JF - Proceedings of the Royal Society A London Y1 - 2013 A1 - Linden, Noah A1 - Mosonyi, Milan A1 - Winter, Andreas VL - 469 IS - 2158472222 JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences ER - TY - CONF T1 - Towards a strong converse for the quantum capacity (of degradable channels) T2 - 2013 IEEE International Symposium on Information Theory (ISIT) Y1 - 2013 A1 - Morgan, Ciara A1 - Winter, Andreas JF - 2013 IEEE International Symposium on Information Theory (ISIT) PB - IEEE CY - Istanbul, Turkey UR - http://ieeexplore.ieee.org/document/6620210/ ER - TY - JOUR T1 - Zero-Error Communication via Quantum Channels, Noncommutative Graphs, and a Quantum Lovász Number JF - IEEE Transactions on Information Theory Y1 - 2013 A1 - Duan, Runyao A1 - Severini, Simone A1 - Winter, Andreas VL - 59 IS - 2 JO - IEEE Trans. Inform. Theory ER - TY - JOUR T1 - All Nonclassical Correlations Can Be Activated into Distillable Entanglement JF - Phys. Rev. Lett. Y1 - 2011 A1 - Piani, Marco A1 - Gharibian, Sevag A1 - Adesso, Gerardo A1 - John Calsamiglia A1 - Horodecki, Paweł A1 - Winter, Andreas PB - American Physical Society VL - 106 UR - http://prl.aps.org/abstract/PRL/v106/i22/e220403 ER -