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arXiv:1603.01124 · Physical Review A

Measure-independent freezing of quantum coherence

Xiao‐Dong Yu, Da-Jian Zhang, C. L. Liu, D. M. Tong

Published Jun 27, 2016• 125 citations
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Abstract

We find that all measures of coherence are frozen for an initial state in a strictly incoherent channel if and only if the relative entropy of coherence is frozen for the state. Our finding reveals the existence of measure-independent freezing of coherence, and provides an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.

DOI
10.1103/physreva.93.060303

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We find that all measures of coherence are frozen for an initial state in a strictly incoherent channel if and only if the relative entropy of coherence is frozen for the state. Our finding reveals the existence of measure-independent freezing of coherence, and provides an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.
We analyze under which dynamical conditions the coherence of an open quantum system is totally unaffected by noise. For a single qubit, specific measures of coherence are found to freeze under different conditions, with no general agreement between them. Conversely, for an N-qubit system with even N, we identify universal conditions in terms of initial states and local incoherent channels such that all bona fide distance-based coherence monotones are left invariant during the entire evolution. This finding also provides an insightful physical interpretation for the freezing phenomenon of quantum correlations beyond entanglement. We further obtain analytical results for distance-based measures of coherence in two-qubit states with maximally mixed marginals.
Abstract Quantum coherence as an important physical resource plays the key role in implementing various quantum tasks, whereas quantum coherence is generally nonincreasing under incoherent operations. In this paper, we analyse under which dynamical conditions the l 1-norm or the relative entropy of coherence can remain unchanged under strictly incoherent operations (freezing coherence). We provide a detailed analysis of their structure together with exact geometric conditions of freezing coherence. It reveals a remarkable feature: any strictly incoherent operation freezing coherence can be decomposed as a convex combination of unitary operations. This partially answers an open question named unitary decomposition of doubly-stochastic quantum operations [M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information, (Cambridge University Press, Cambridge, 2000)]. Based on this analysis, we also give a complete classification of coherent states from operational coherence theory. This builds the counterpart of entanglement classification under LOCC.
Asymmetry of quantum states is a useful resource in applications such as quantum metrology, quantum communication, and reference frame alignment. However, asymmetry of a state tends to be degraded in physical scenarios where environment-induced noise is described by covariant operations, e.g., open systems constrained by superselection rules, and such degradations weaken the abilities of the state to implement quantum information processing tasks. In this paper, we investigate under which dynamical conditions asymmetry of a state is totally unaffected by the noise described by covariant operations. We find that all asymmetry measures are frozen for a state under a covariant operation if and only if the relative entropy of asymmetry is frozen for the state. Our finding reveals the existence of universal freezing of asymmetry, and provides a necessary and sufficient condition under which asymmetry is totally unaffected by the noise.
Necessary and sufficient conditions for arbitrary multimode (pure or mixed) Gaussian states to be equivalent under incoherent Gaussian operations are derived. We show that two Gaussian states are incoherent equivalence if and only if they are related by incoherent unitaries. This builds the counterpart of the celebrated result that two pure entangled states are equivalent under local operations and classical communication (LOCC) if and only if they are related by local unitaries. Furthermore, incoherent equivalence of Gaussian states is equivalent to frozen coherence [Phys. Rev. Lett. 114, 210401 (2015)]. Basing this as foundation, we find all measures of coherence are frozen for an initial Gaussian state under strongly incoherent Gaussian operations if and only if the relative entropy measure of coherence is frozen for the state. This gives an entropy-based dynamical condition in which the coherence of an open quantum system is totally unaffected by noise.