Trace-distance measure of coherence

Rana, Swapan; Parashar, Preeti; Lewenstein, Maciej

doi:10.1103/physreva.93.012110

Cited by 307 publications

(247 citation statements)

References 32 publications

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“…First, it supports the claim in [15,16] that C l1 is analogous to entanglement negativity. Indeed, considering C c is equal to C l1 for pure states, we have…”

Section: Comparison Of C (2) Csupporting

confidence: 82%

Generalized coherence concurrence and path distinguishability

Chin¹

2017

J. Phys. A: Math. Theor.

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We propose a new family of coherence monotones, named the generalized coherence concurrence (or coherence k-concurrence), which is an analogous concept to the generalized entanglement concurrence. The coherence k-concurrence of a state is nonzero if and only if the coherence number (a recently introduced discrete coherence monotone) of the state is not smaller than k, and a state can be converted to a state with nonzero entanglement k-concurrence via incoherent operations if and only if the state has nonzero coherence k-concurrence. We apply the coherence concurrence family to the problem of wave-particle duality in multi-path interference phenomena. We obtain a sharper equation for path distinguishability (which witness the duality) than the known value and show that the amount of each concurrence for the quanton state determines the number of slits which are identified unambiguously.

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“…First, it supports the claim in [15,16] that C l1 is analogous to entanglement negativity. Indeed, considering C c is equal to C l1 for pure states, we have…”

Section: Comparison Of C (2) Csupporting

confidence: 82%

Generalized coherence concurrence and path distinguishability

Chin¹

2017

J. Phys. A: Math. Theor.

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“…Based on this framework, one can define suitable measures with respect to the prescribed orthonormal basis, including the relative entropy of coherence and the l 1 norm of coherence [9]. In addition, various other coherence measures were discussed [10][11][12][13][14][15][16][17]. Many further discussions about quantum coherence were aroused [18][19][20][21][22][23][24][25][26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Ordering states with Tsallis relative $$\alpha $$ α -entropies of coherence

Zhang

Shao

Luo

et al. 2016

Quantum Inf Process

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In this paper, we study the ordering states with Tsallis relative α-entropies of coherence and l1 norm of coherence for single-qubit states. We show that any Tsallis relative α-entropies of coherence and l1 norm of coherence give the same ordering for single-qubit pure states. However, they don't generate the same ordering for some high dimensional pure states, even though these states are pure. We also consider three special Tsallis relative α-entropies of coherence, such as C1 ,C2 and C 1 2 , and show any one of these three measures and C l 1 will not generate the same ordering for single-qubit mixed states. Furthermore, we find that any two of these three special measures generate different ordering for single-qubit mixed states.

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“…As proved in [16], C l1 (ρ) = C tr (ρ) if the density matrix ρ is in a block diagonal form on the incoherent basis, where the dimension of each block is at most 2.…”

Section: Quantum Coherence Measuresmentioning

confidence: 99%

Channels that do not generate coherence

2016

Phys. Rev. A

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We define the coherence non-generating channel as the completely positive trace-preserving map which does not generate quantum coherence from an incoherent state. The incoherent operations are the strict subset of the non-coherence-generating channels. Although the relative entropy of coherence is monotonically decreasing under the non-coherence-generating channels, we prove that the coherence of formation may increase under such channels. Interestingly, by building a mathematical relation between the coherence of formation and the entanglement of formation, we show that the coherence of formation of a single-qubit state is never increased by a non-coherence-generating channel. This leads to the superadditivity property for the coherence increasing power of quantum channels, namely, while two channels can not increase coherence individually, they may increase the quantum coherence of a composed system. Further, we derive the general form of the rank-2 coherence non-generating qubit channels. Our results contribute to the resource theory of quantum coherence.

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Trace-distance measure of coherence

Cited by 307 publications

References 32 publications

Generalized coherence concurrence and path distinguishability

Generalized coherence concurrence and path distinguishability

Ordering states with Tsallis relative $$\alpha $$ α -entropies of coherence

Channels that do not generate coherence

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