One-Shot Coherence Distillation

Regula, Bartosz; Fang, Kun; Wang, Xin; Adesso, Gerardo

doi:10.1103/physrevlett.121.010401

Cited by 142 publications

(177 citation statements)

References 69 publications

(136 reference statements)

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“…, and  is the set of all unit-trace diagonal Hermitian operators (see [61] for the rightmost equality). Therefore, the one-shot distillable entanglement of a maximally correlated state under the largest set of free operations in the resource theory of entanglement (SEPP) can be strictly larger than the distillable coherence of the corresponding single-partite state under the largest set of free operations in the resource theory of coherence (MIO).…”

Section: Isotropic Statesmentioning

confidence: 99%

One-shot entanglement distillation beyond local operations and classical communication

et al. 2019

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We study the task of entanglement distillation in the one-shot setting under different classes of quantum operations which extend the set of local operations and classical communication (LOCC). Establishing a general formalism which allows for a straightforward comparison of their exact achievable performance, we relate the fidelity of distillation under these classes of operations with a family of entanglement monotones and the rates of distillation with a class of smoothed entropic quantities based on the hypothesis testing relative entropy. We then characterise exactly the one-shot distillable entanglement of several classes of quantum states and reveal many simplifications in their manipulation. We show in particular that the ε-error one-shot distillable entanglement of any pure state is the same under all sets of operations ranging from one-way LOCC to separability-preserving operations or operations preserving the set of states with positive partial transpose, and can be computed exactly as a quadratically constrained linear program. We establish similar operational equivalences in the distillation of isotropic and maximally correlated states, reducing the computation of the relevant quantities to linear or semidefinite programs. We also show that all considered sets of operations achieve the same performance in environment-assisted entanglement distillation from any state.

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Section: Isotropic Statesmentioning

confidence: 99%

One-shot entanglement distillation beyond local operations and classical communication

et al. 2019

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“…Many other quantities related to coherence may be phrased as a semidefinite program. For examples, see [6,7,[34][35][36][37].…”

Section: A Semidefinite Program For Computing Coherence Measuresmentioning

confidence: 99%

“…Another example that falls under our framework is the fidelity of coherence distillation, which is discussed in greater detail in [34]. The fidelity of coherence is defined as the maximum overlap with the maximally coherent state optimized over some set of operations , which may be MIO or IO.…”

Section: Examplesmentioning

confidence: 99%

Optimizing nontrivial quantum observables using coherence

2019

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In this paper we consider the quantum resources required to maximize the mean values of any nontrivial quantum observable. We show that the task of maximizing the mean value of an observable is equivalent to maximizing some form of coherence, up to the application of an incoherent operation. For any nontrivial observable, there always exists a set of preferred basis states where the superposition between such states is always useful for optimizing the mean value of a quantum observable. The usefulness of such states is expressed in terms of an infinitely large family of valid coherence measures which is then shown to be efficiently computable via a semidefinite program. We also show that these coherence measures respect a hierarchy that gives the robustness of coherence and the l 1 norm of coherence additional operational significance in terms of such optimization tasks.

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“…In the resource theory of coherence, the relative entropy of coherence and the coherence of formation measures the asymptotic coherence distillation and dilution rates, respectively . The coherence distillation and dilution problems are then extended into the non‐asymptotical scenario using other coherence measures . We refer to refs.…”

Section: Introductionmentioning

confidence: 99%

“…[9] The coherence distillation and dilution problems are then extended into the non-asymptotical scenario using other coherence measures. [10][11][12][13] We refer to refs. [14,15] for reviews of the resource theory of coherence.…”

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confidence: 99%

Quantum Coherence and Intrinsic Randomness

et al. 2019

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The peculiar uncertainty or randomness of quantum measurements stems from quantum coherence, whose information‐theoretic characterization is currently under investigation. The resource theory of coherence investigates interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as a resource for generating intrinsic randomness by measuring a state in the computational basis. It is observed in a previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a correlated party (classical system) about the system measurement outcome. In this work, the result is re‐derived from a quantum point of view, and then the intrinsic randomness is connected to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there do not exist bound coherent states, these two coherence measures—intrinsic randomness quantified by coherence of formation and by relative entropy of coherence—are different. Interestingly, it is shown that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system.

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One-Shot Coherence Distillation

Cited by 142 publications

References 69 publications

One-shot entanglement distillation beyond local operations and classical communication

One-shot entanglement distillation beyond local operations and classical communication

Optimizing nontrivial quantum observables using coherence

Quantum Coherence and Intrinsic Randomness

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