Constructing monotones for quantum phase references in totally dephasing channels

Toloui, Borzu; Gour, Gilad; Sanders, Barry C.

doi:10.1103/physreva.84.022322

Cited by 29 publications

(37 citation statements)

References 21 publications

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“…Also, note that for closed-system dynamics under Hamiltonian H , any measure of asymmetry (relative to time translation) remains constant, i.e., [20,21,26,29,30,[36][37][38][39][40][41]). In particular, Refs.…”

Section: A Coherence As Asymmetry Relative To Translationsmentioning

confidence: 99%

Quantum speed limits, coherence, and asymmetry

2016

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The resource theory of asymmetry is a framework for classifying and quantifying the symmetry-breaking properties of both states and operations relative to a given symmetry. In the special case where the symmetry is the set of translations generated by a fixed observable, asymmetry can be interpreted as coherence relative to the observable eigenbasis, and the resource theory of asymmetry provides a framework to study this notion of coherence. We here show that this notion of coherence naturally arises in the context of quantum speed limits. Indeed, the very concept of speed of evolution, i.e., the inverse of the minimum time it takes the system to evolve to another (partially) distinguishable state, is a measure of asymmetry relative to the time translations generated by the system Hamiltonian. Furthermore, the celebrated Mandelstam-Tamm and Margolus-Levitin speed limits can be interpreted as upper bounds on this measure of asymmetry by functions which are themselves measures of asymmetry in the special case of pure states. Using measures of asymmetry that are not restricted to pure states, such as the Wigner-Yanase skew information, we obtain extensions of the Mandelstam-Tamm bound which are significantly tighter in the case of mixed states. We also clarify some confusions in the literature about coherence and asymmetry, and show that measures of coherence are a proper subset of measures of asymmetry.

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Section: A Coherence As Asymmetry Relative To Translationsmentioning

confidence: 99%

Quantum speed limits, coherence, and asymmetry

2016

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“…The latter is the ability of a state to act as a reference frame under a superselection rule, being widely investigated in recent years [13,14,[31][32][33][34][35][36][37][38][39][40][41][42][43][44]. One can observe that asymmetry is the quantum coherence lost by applying a phase shift w.r.t.…”

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confidence: 99%

Observable Measure of Quantum Coherence in Finite Dimensional Systems

2014

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Quantum coherence is the key resource for quantum technology, with applications in quantum optics, information processing, metrology and cryptography. Yet, there is no universally efficient method for quantifying coherence either in theoretical or in experimental practice. I introduce a framework for measuring quantum coherence in finite dimensional systems. I define a theoretical measure which satisfies the reliability criteria established in the context of quantum resource theories. Then, I present an experimental scheme implementable with current technology which evaluates the quantum coherence of an unknown state of a d-dimensional system by performing two programmable measurements on an ancillary qubit, in place of the O(d 2 ) direct measurements required by full state reconstruction. The result yields a benchmark for monitoring quantum effects in complex systems, e.g. certifying non-classicality in quantum protocols and probing the quantum behaviour of biological complexes. Introduction -While harnessing quantum coherence is matter of routine in delivering quantum technology [1][2][3][4][5], and the quantum optics rationale rests on creation and manipulation of coherence [6], there is no universally efficient route to measure the amount of quantum coherence carried by the state of a system in dimension d > 2. It is customary to employ quantifiers tailored to the scenario of interest, i.e. of not general employability, expressed in terms of ad hoc entropic functions, correlators, or functions of the off-diagonal density matrix coefficients (if available) [7][8][9]. Quantum information theory provides the framework to address the problem. Physical laws are interpreted as restrictions on the accessible quantum states and operations, while the properties of physical systems are the resources that one must consume to perform a task under such laws [10]. An algorithmic characterization of quantum coherence as a resource and a set of bona fide criteria for coherence monotones have been identified [7, 11, 12]. Also, coherence has been shown to be related to the asymmetry of a quantum state [13, 14]. On the experimental side, the scalability of the detection scheme is a major criterion in developing witnesses and measures of coherence, as we are interested in exploring the quantum features of highly complex macrosystems, e.g. multipartite quantum registers and networks. Therefore, it is desirable to have a coherence measure which is both theoretically sound and experimentally appealing.

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“…An asymmetry measure quantifies how much the symmetry in question is broken by a given state. More precisely, a function f from states to real numbers is an asymmetry measure [5][6][7][8][9][10][11] if the existence of symmetric dynamics taking r to s implies f(r)Zf(s). A measure for rotational asymmetry, for instance, is a function over states that is non-increasing under rotationally invariant dynamics.…”

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confidence: 99%

Extending Noether’s theorem by quantifying the asymmetry of quantum states

2014

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Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: for one, it is not applicable to dynamics wherein the system interacts with an environment; furthermore, even in the case where the system is isolated, if the quantum state is mixed then the Noether conservation laws do not capture all of the consequences of the symmetries. Here we address these deficiencies by introducing measures of the extent to which a quantum state breaks a symmetry. Such measures yield novel constraints on state transitions: for nonisolated systems they cannot increase, whereas for isolated systems they are conserved. We demonstrate that the problem of finding non-trivial asymmetry measures can be solved using the tools of quantum information theory. Applications include deriving model-independent bounds on the quantum noise in amplifiers and assessing quantum schemes for achieving high-precision metrology.

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Constructing monotones for quantum phase references in totally dephasing channels

Cited by 29 publications

References 21 publications

Quantum speed limits, coherence, and asymmetry

Quantum speed limits, coherence, and asymmetry

Observable Measure of Quantum Coherence in Finite Dimensional Systems

Extending Noether’s theorem by quantifying the asymmetry of quantum states

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