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.

%B PHYSICAL REVIEW X %V 7 %8 apr %R 10.1103/PhysRevX.7.021006 %0 Conference Paper %B 2017 {INTERNATIONAL} {SYMPOSIUM} {ON} {WIRELESS} {COMMUNICATION} {SYSTEMS} ({ISWCS}) %D 2017 %T Information Theoretic Principles of Universal Discrete Denoising %A Noetzel, Janis %A Winter, Andreas %XSocial 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).

%B 2017 {INTERNATIONAL} {SYMPOSIUM} {ON} {WIRELESS} {COMMUNICATION} {SYSTEMS} ({ISWCS}) %S International {Symposium} on {Wireless} {Communication} {Systems} %P 205–210 %@ 978-1-5386-2913-0 %0 Journal Article %J JOURNAL OF MATHEMATICAL PHYSICS %D 2017 %T Unitary 2-designs from random X- and Z-diagonal unitaries %A Nakata, Yoshifumi %A Hirche, Christoph %A Morgan, Ciara %A Winter, Andreas %XUnitary 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.

%B JOURNAL OF MATHEMATICAL PHYSICS %V 58 %R 10.1063/1.4983266 %0 Web Page %D 2015 %T Decoupling with random diagonal-unitary matrices %A Yoshifumi Nakata %A Christoph Hirche %A Ciara Morgan %A Winter, Andreas %U http://arxiv.org/abs/1509.05155 %0 Web Page %D 2015 %T Implementing unitary 2-designs using random diagonal-unitary matrices %A Yoshifumi Nakata %A Christoph Hirche %A Ciara Morgan %A Winter, Andreas %U http://arxiv.org/abs/1502.07514 %0 Journal Article %J New Journal of Physics %D 2014 %T Quantumness of correlations, quantumness of ensembles and quantum data hiding %A Piani, M %A Narasimhachar, V %A Calsamiglia, John %B New Journal of Physics %V 16 %P 113001 %G eng %U http://stacks.iop.org/1367-2630/16/i=11/a=113001?key=crossref.9f5154f8c85e7f9471e2931d9a02df88 %R 10.1088/1367-2630/16/11/113001 %0 Journal Article %J Physical Review A (Atomic, Molecular, and Optical Physics) %D 2008 %T Multipartite continuous-variable solution for the Byzantine agreement problem %A Neigovzen, Rodion %A Rodó, Carles %A Adesso, Gerardo %A Sanpera, Anna %K Gaussian processes %K homodyne detection %K quantum cryptography %K quantum entanglement %B Physical Review A (Atomic, Molecular, and Optical Physics) %V 77 %P 062307–11 %8 06/2008 %G eng %U http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PLRAAN000077000006062307000001&idtype=cvips&prog=normal %R 10.1103/PhysRevA.77.062307 %0 Journal Article %J arXiv %D 2005 %T Continuous Variable Solution for Byzantine Agreement %A Neigovzen, Rodion %A Sanpera, Anna %B arXiv %G eng %U http://arxiv.org/abs/quant-ph/0507249 %0 Journal Article %J Physical Review Letters %D 2005 %T Quantum Key Distillation from Gaussian States by Gaussian Operations %A Navascués, M. %A Bae, J. %A Cirac, J. Ignacio %A Lewenstein, Maciej %A Sanpera, Anna %A Acín, Antonio %X We study the secrecy properties of Gaussian states under Gaussian operations. Although such operations are useless for quantum distillation, we prove that it is possible to distill a secret key secure against any attack from sufficiently entangled Gaussian states with nonpositive partial transposition. Moreover, all such states allow for key distillation, when Eve is assumed to perform finite-size coherent attacks before the reconciliation process. %B Physical Review Letters %I American Physical Society %V 94 %P 010502 %8 01/2005 %G eng %U http://link.aps.org/doi/10.1103/PhysRevLett.94.010502 %R 10.1103/PhysRevLett.94.010502 %0 Conference Paper %B {2018 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)} %D 0 %T {Fully Quantum Arbitrarily Varying Channels: Random Coding Capacity and Capacity Dichotomy} %A Boche, Holger %A Deppe, Christian %A Noetzel, Janis %A Winter, Andreas %X {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.} %B {2018 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT)} %S {IEEE International Symposium on Information Theory} %I {IEEE; IEEE Informat Theory Soc; NSF; Huawei; Qualcomm} %P {2012-2016} %@ {978-1-5386-4781-3}