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.

%B IEEE TRANSACTIONS ON INFORMATION THEORY %V 63 %P 7832–7844 %8 dec %R 10.1109/TIT.2017.2754268 %0 Journal Article %J Physical Review X %D 2017 %T Autonomous Quantum Clocks: Does Thermodynamics Limit Our Ability to Measure Time? %A Erker, Paul %A Mitchison, Mark T. %A Silva, Ralph %A Woods, Mischa P. %A Brunner, Nicolas %A Huber, Marcus %XTime remains one of the least well-understood concepts in physics, most notably in quantum mechanics. A central goal is to find the fundamental limits of measuring time. One of the main obstacles is the fact that time is not an observable and thus has to be measured indirectly. Here, we explore these questions by introducing a model of time measurements that is complete and autonomous. Specifically, our autonomous quantum clock consists of a system out of thermal equilibrium—a prerequisite for any system to function as a clock—powered by minimal resources, namely, two thermal baths at different temperatures. Through a detailed analysis of this specific clock model, we find that the laws of thermodynamics dictate a trade-off between the amount of dissipated heat and the clock’s performance in terms of its accuracy and resolution. Our results furthermore imply that a fundamental entropy production is associated with the operation of any autonomous quantum clock, assuming that quantum machines cannot achieve perfect efficiency at finite power. More generally, autonomous clocks provide a natural framework for the exploration of fundamental questions about time in quantum theory and beyond.

%B Physical Review X %V 7 %P 031022 %U https://link.aps.org/doi/10.1103/PhysRevX.7.031022 %R 10.1103/PhysRevX.7.031022 %0 Journal Article %J Physical Review A %D 2016 %T Achieving sub-shot-noise sensing at finite temperatures %A Mehboudi, Mohammad %A Correa, Luis A. %A Sanpera, Anna %B Physical Review A %V 94 %8 10/2016 %N 4 %! Phys. Rev. A %R 10.1103/PhysRevA.94.042121 %0 Journal Article %J Physical Review B %D 2016 %T Autonomous {Quantum} {Refrigerator} in a {Circuit}-{QED} {Architecture} {Based} on a {Josephson} {Junction} %A Hofer, Patrick P. %A Perarnau-Llobet, Marti %A Brask, Jonatan Bohr %A Silva, Ralph %A Huber, Marcus %A Brunner, Nicolas %K Condensed Matter - Mesoscale and Nanoscale Physics %K Quantum Physics %X An implementation of a small quantum absorption refrigerator in a circuit QED architecture is proposed. The setup consists of three harmonic oscillators coupled to a Josephson unction. The refrigerator is autonomous in the sense that it does not require any external control for cooling, but only thermal contact between the oscillators and heat baths at different temperatures. In addition, the setup features a built-in switch, which allows the cooling to be turned on and off. If timing control is available, this enables the possibility for coherence-enhanced cooling. Finally, we show that significant cooling can be achieved with experimentally realistic parameters and that our setup should be within reach of current technology. %B Physical Review B %V 94 %U http://arxiv.org/abs/1607.05218 %R 10.1103/PhysRevB.94.235420 %0 Journal Article %J New Journal of Physics %D 2015 %T Autonomous quantum thermal machine for generating steady-state entanglement %A Bohr Brask, Jonatan %A Haack, Géraldine %A Nicolas Brunner %A Huber, Marcus %B New Journal of Physics %V 17 %P 113029 %8 nov %G eng %U http://stacks.iop.org/1367-2630/17/i=11/a=113029?key=crossref.0c6a75cb628f113c6cbd2a7b0d092f0d %R 10.1088/1367-2630/17/11/113029 %0 Journal Article %J Phys. Rev. Lett. %D 2011 %T All Nonclassical Correlations Can Be Activated into Distillable Entanglement %A Piani, Marco %A Gharibian, Sevag %A Adesso, Gerardo %A Calsamiglia, John %A Horodecki, Paweł %A Winter, Andreas %B Phys. Rev. Lett. %I American Physical Society %V 106 %P 220403 %8 Jun %U http://prl.aps.org/abstract/PRL/v106/i22/e220403 %) http://arxiv.org/abs/1103.4032 %R 10.1103/PhysRevLett.106.220403 %0 Journal Article %J Phys. Rev. Lett. %D 2010 %T Adiabatic Markovian Dynamics %A Oreshkov, Ognyan %A Calsamiglia, John %K Quantum Physics %X We propose a theory of adiabaticity in quantum Markovian dynamics based on a structural decomposition of the Hilbert space induced by the asymptotic behavior of the Lindblad semigroup. A central idea of our approach is that the natural generalization of the concept of eigenspace of the Hamiltonian in the case of Markovian dynamics is a noiseless subsystem with a minimal noisy cofactor. Unlike previous attempts to define adiabaticity for open systems, our approach deals exclusively with physical entities and provides a simple, intuitive picture at the underlying Hilbert-space level, linking the notion of adiabaticity to the theory of noiseless subsystems. As an application of our theory, we propose a framework for decoherence-assisted computation in noiseless codes under general Markovian noise. We also formulate a dissipation-driven approach to holonomic computation based on adiabatic dragging of subsystems that is generally not achievable by non-dissipative means. %B Phys. Rev. Lett. %V 105 %P 050503 %U http://arxiv.org/abs/1002.2219 %R 10.1103/PhysRevLett.105.050503 %0 Journal Article %J International Journal of Quantum Information %D 2006 %T Aligning spatial frames through quantum channels %A Bagan, Emili %A Muñoz-Tapia, Ramon %B International Journal of Quantum Information %V 4 %P 5 %G eng %0 Journal Article %J Physical Review A %D 2004 %T Active and passive quantum erasers for neutral kaons %A Bramon, A. %A Garbarino, G. %A Hiesmayr, B. %B Physical Review A %V 69 %G eng %U http://pra.aps.org/abstract/PRA/v69/i6/e062111 %R 10.1103/PhysRevA.69.062111 %0 Journal Article %J Physical Review Letters %D 2004 %T Atomic Fermi-Bose Mixtures in Inhomogeneous and Random Lattices: From Fermi Glass to Quantum Spin Glass and Quantum Percolation %A Sanpera, A. %A Kantian, A. %A Sanchez-Palencia, L. %A Zakrzewski, J. %A Lewenstein, M. %B Physical Review Letters %V 93 %G eng %U http://prl.aps.org/abstract/PRL/v93/i4/e040401 %R 10.1103/PhysRevLett.93.040401 %0 Journal Article %J arXiv %D 2001 %T Aligning Reference Frames with Quantum States %A Bagan, Emili %A Baig, Marià %A Muñoz-Tapia, Ramon %B arXiv %G eng %U http://arxiv.org/abs/quant-ph/0106155 %0 Journal Article %J Physical Review Letters %D 2001 %T Aligning Reference Frames with Quantum States %A E. Bagan %A Baig, M. %A Muñoz-Tapia, R. %B Physical Review Letters %V 87 %G eng %U http://prl.aps.org/abstract/PRL/v87/i25/e257903 %R 10.1103/PhysRevLett.87.257903