Catalyst-assisted probabilistic coherence distillation for mixed states

Liu, C. L.; Zhou, D. L.

doi:10.1103/physreva.101.012313

Cited by 26 publications

(8 citation statements)

References 46 publications

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“…These results tell us that when we want to deterministically transform a pure state into another one, IO and SIO have the same set of accessible pure states. After that, the probabilistic transformation between pure coherent states under SIO was studied in [20,21]. The results of [17,22,23] showed that the set of accessible states through IO and SIO are still the same when qubit states are deterministically transformed.…”

Section: Introductionmentioning

confidence: 99%

Transformation protocols of pure-coherent states under incoherent operation

Li¹,

Li²

2023

Laser Phys.

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It is well known that the majorization condition is the necessary and sufficient for the deterministic transformations of pure-coherent states under incoherent operation (IO). In this paper, we present the protocol 1 (product-form) which provides a method for the pure-coherent transformation under IO and overcomes the restriction of the number of Kraus operators of Protocol I (Torun and Yildiz 2018 Phys. Rev. A 97 052331). Then, we show that the corresponding uncorrelated-catalytic protocol (discarding the catalytic state) is not incoherent-preserving. We construct the protocol 2 such that the uncorrelated-catalytic transformation with four-dimensional catalyst state can be implemented probabilistically under dephasing-covariant IO. Especially, the protocol 2 provides the target state from the catalyst-assisted transformation and its equivalent states with respect to Pauli operators X , Z .

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Section: Introductionmentioning

confidence: 99%

Transformation protocols of pure-coherent states under incoherent operation

Li¹,

Li²

2023

Laser Phys.

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“…Based on this theory, many other coherence measures were also proposed, see [8,10] for a detailed review of them. Recently, coherence was analyzed in a number of contexts, for example, its distillation and dilution [11][12][13][14][15][16], its basis dependency [17][18][19], its role in interpreting the wave-particle duality [20,21], and its applications in certain practical tasks [22][23][24][25][26][27][28]. Besides, there are also evidences that the coherence provides an indicator of quantum phase transitions in spin systems [29][30][31][32][33][34].…”

Section: Introductionmentioning

confidence: 99%

Enhancing steered coherence in the Heisenberg model using Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions

Xie¹,

Liu²

2022

Laser Phys. Lett.

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Steered coherence characterizes the ability of one party to steer the coherence of another when they share a bipartite state. It is crucial to control its strength so as to use it as a resource for practical applications. We investigate average steered coherence (ASC) in the Heisenberg XXZ model. It is found that for the thermal state at finite temperature, the ASC can always be noticeably enhanced by adjusting the Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions. There are also parameter regions in which the ASC approaches to its maximum. This result suggests an alternative for manipulating ASC in a spin system.

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“…Thus, a critical issue is to investigate coherence manipulations via free operations. Many protocols of coherence manipulation have been proposed based on various physical scenarios [16,[42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58], and some have been demonstrated in the experiment [59][60][61][62].…”

Section: Introductionmentioning

confidence: 99%

No-go theorems for deterministic purification and probabilistic enhancement of coherence

Ding¹,

Liu²

2022

J. Phys. A: Math. Theor.

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The manipulation of quantum coherence is one of the principal issues in the resource theory of coherence, with two critical topics being the purification and enhancement of coherence. Here, we present two no-go theorems for the deterministic purification of coherence and the probabilistic enhancement of coherence, respectively. Specifically, we prove that a quantum state cannot be deterministically purified if it can be expressed as a convex combination of an incoherent state and a coherent state. Besides, we give an easy-to-verified sufficient and necessary condition to determine whether a state can be probabilistically enhanced via a stochastic strictly incoherent operation (sSIO). Our findings provide two feasibility criteria for the deterministic purification and the probabilistic enhancement of coherence, respectively. These results have repercussions on the understanding of quantum coherence in real quantum systems.

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Catalyst-assisted probabilistic coherence distillation for mixed states

Cited by 26 publications

References 46 publications

Transformation protocols of pure-coherent states under incoherent operation

Transformation protocols of pure-coherent states under incoherent operation

Enhancing steered coherence in the Heisenberg model using Dzyaloshinsky–Moriya and Kaplan–Shekhtman–Entin-Wohlman–Aharony interactions

No-go theorems for deterministic purification and probabilistic enhancement of coherence

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