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-norm coherence of assistance

Zhao, Ming‐Jing; Ma, Teng; Quan, Quan; Fan, Heng; Pereira, Rajesh

doi:10.1103/physreva.100.012315

Cited by 32 publications

(26 citation statements)

References 28 publications

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“…If for in the probability simplex, becomes the entanglement of formation of assistance 13 – 15 , and becomes the relative entropy coherence of assistance 12 . If for in the probability simplex, then becomes the half convex-roof extended negativity of assistance 17 and becomes the norm coherence of assistance 16 . Analogously, one can also define various other types of entanglement of assistance and coherence of assistance based on other real symmetric concave functions f .…”

Section: Resultsmentioning

confidence: 99%

“…As with other measures of coherence and entanglement, the coherence of assistance and the entanglement of assistance are also closely related. In fact, the relative entropy coherence of assistance corresponds to the entanglement formation of assistance 12 – 15 and the norm coherence of assistance corresponds to the convex-roof extended negativity entanglement of assistance 16 – 18 . As intrinsic characteristics of quantum physics, the inextricable relationship between quantum coherence and quantum entanglement is not limited to specific quantum coherence measures and entanglement measures as well as the coherence of assistance and the entanglement of assistance.…”

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confidence: 99%

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Coherence of assistance and assisted maximally coherent states

Zhao

Pereira

et al. 2021

Sci Rep

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Coherence and entanglement are fundamental concepts in resource theory. The coherence (entanglement) of assistance is the coherence (entanglement) that can be extracted assisted by another party with local measurement and classical communication. We introduce and study the general coherence of assistance. First, in terms of real symmetric concave functions on the probability simplex, the coherence of assistance and the entanglement of assistance are shown to be in one-to-one correspondence. We then introduce two classes of quantum states: the assisted maximally coherent states and the assisted maximally entangled states. They can be transformed into maximally coherent or entangled pure states with the help of another party using local measurement and classical communication. We give necessary conditions for states to be assisted maximally coherent or assisted maximally entangled. Based on these, a unified framework between coherence and entanglement including coherence (entanglement) measures, coherence (entanglement) of assistance, coherence (entanglement) resources is proposed. Then we show that the coherence of assistance as well as entanglement of assistance are strictly larger than the coherence of convex roof and entanglement of convex roof for all full rank density matrices. So all full rank quantum states are distillable in the assisted coherence distillation.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Coherence of assistance and assisted maximally coherent states

Zhao

Pereira

et al. 2021

Sci Rep

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“…Dual to the definition of coherence concurrence, the l 1 -norm coherence of assistance is the maximal average l 1 -norm coherence C a l 1 (ρ) = max k p k C l 1 (|ψ k ψ k |), where the maximization is taken over all pure state decompositions of ρ = k p k |ψ k ψ k | [13]. Employing the physical illustration of the coherence of assistance, the coherence concurrence C c l 1 has the following operational interpretation.…”

Section: The Coherence Concurrence For X Statesmentioning

confidence: 99%

Coherence concurrence for X states

Zhao

Wang

et al. 2020

Quantum Inf Process

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We study the properties of coherence concurrence and present a physical explanation analogous to the coherence of assistance. We give an optimal pure state decomposition which attains the coherence concurrence for qubit states. We prove the additivity of coherence concurrence under direct sum operations in another way. Using these results, we calculate analytically the coherence concurrence for X states and show its optimal decompositions. Moreover, we show that the coherence concurrence is exactly twice the convex roof extended negativity of the Schmidt correlated states, thus establishing a direct relation between coherence concurrence and quantum entanglement.

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“…This is called the assisted coherence distillation. For the average coherence, its maximum which quantifies a one way coherence distillation rate is called the coherence of assistance [16,17] and its minimum is identified as a coherence measure [14,15].…”

Section: Introductionmentioning

confidence: 99%

The Average Quantum Coherence of Pure State Decomposition

Zhao,

Ma,

Pereira

2021

Preprint

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We study the average quantum coherence over the pure state decompositions of a mixed quantum state. An upper bound of the average quantum coherence is provided and sufficient conditions for the saturation of the upper bound are shown. These sufficient conditions always hold for two and three dimensional systems. This provides a tool to estimate the average coherence experimentally by measuring only the diagonal elements, which remarkably requires less measurements compared with state tomography. We then describe the pure state decompositions of qubit state in Bloch sphere geometrically. For any given qubit state, the optimal pure state decomposition achieving the maximal average quantum coherence as well as three other pure state decompositions are shown in the Bloch sphere. The order relations among their average quantum coherence are invariant for any coherence measure. The results presented in this paper are universal and suitable for all coherence measures.

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l1 -norm coherence of assistance

Cited by 32 publications

References 28 publications

Coherence of assistance and assisted maximally coherent states

Coherence of assistance and assisted maximally coherent states

Coherence concurrence for X states

The Average Quantum Coherence of Pure State Decomposition

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