Coherence manipulation under incoherent operations

Du, Shuanping; Bai, Zhaofang; Qi, Xiaofei

doi:10.1103/physreva.100.032313

Cited by 27 publications

(27 citation statements)

References 32 publications

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“…based on Ref. [80], shows that |ψ l can be converted into ρ l by IO. According to the definition of C m , we have…”

Section: The Coherence Monotone Via Pure-state Coherencementioning

confidence: 98%

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Quantifying coherence in terms of the pure-state coherence

Yu,

Zhang,

2020

Preprint

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Quantifying quantum coherence is a key task in the resource theory of coherence. Here we establish a good coherence monotone in terms of a state conversion process, which automatically endows the coherence monotone with an operational meaning. We show that any state can be produced from some input pure states via the corresponding incoherent channels. It is especially found that the coherence of a given state can be well characterized by the least coherence of the input pure states, so a coherence monotone is established by only effectively quantifying the input pure states. In particular, we show that our proposed coherence monotone is the supremum of all the coherence monotones that give the same coherence for any given pure state. Considering the convexity, we prove that our proposed coherence measure is a subset of the coherence measure based on the convex roof construction. As an application, we give a concrete expression of our coherence measure by employing the geometric coherence of a pure state. We also give a thorough analysis on the states of qubit and finally obtain series of analytic coherence measures.

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“…based on Ref. [80], shows that |ψ l can be converted into ρ l by IO. According to the definition of C m , we have…”

Section: The Coherence Monotone Via Pure-state Coherencementioning

confidence: 98%

“…In other words, |ψ can be converted into {t i q il , |φ il } by IO, which, based on Ref. [80], is equivalent to…”

Section: The Coherence Monotone Via Pure-state Coherencementioning

confidence: 99%

Quantifying coherence in terms of the pure-state coherence

Yu,

Zhang,

2020

Preprint

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“…[5][6][7][8][9] or Lemma 4), as well as for transformations from pure to mixed states (see Refs. [9,10] or Prop. 5 for this more general case).…”

Section: Introductionmentioning

confidence: 99%

“…5 (see Refs. [9,10]) to the general case of initial mixed states, which is also given in terms of the majorization relation of the corresponding coherence vectors. This result is an step forward on the characterization of conversions between general quantum states under incoherent operations, whose complete solution is only known for the single qubit system [16,17].…”

Section: Introductionmentioning

confidence: 99%

Generalized coherence vector applied to coherence transformations and quantifiers

Bosyk,

Losada,

Massri

et al. 2020

Preprint

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“…Given two coherent states ρ and σ, the question of coherence manipulation is to study whether there exists some free operation Φ such that Φ(ρ) = σ. Attempts have been made to uncover the fundamental laws of its behaviour under free operations [8,12,14,15,22,[40][41][42][43]. In [22], it is proved that, for qubit states ρ, σ with Bloch vector r = (r x , r y , r z ) t and s = (s x , s y , s z ) t , ρ can be converted into σ by stochastic SIO if and only if the following inequalities are fulfilled…”

mentioning

confidence: 99%

Strictly incoherent operations for one-qubit systems

Du,

Bai

2020

Preprint

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Strictly incoherent operations (SIO) proposed in [Phys. Rev. Lett. 116, 120404 (2016)] are promising to be a good candidate of free operations in the resource theory of quantum coherence, setting against the central role of local operations and classical communication in the resource theory of quantum entanglement. An important open problem is an efficient description for strictly incoherent operations in physical region. Such a description plays key role for axiomatic study of resource theory of quantum coherence. We are aimed to give a structural characterization of bistochastic SIOs in terms of Pauli operators and the Phase operator for one-qubit systems. Some applications of our results are also sketched in reconstructing quantum thermal averages via a quantum computer and in coherence manipulation.

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Coherence manipulation under incoherent operations

Cited by 27 publications

References 32 publications

Quantifying coherence in terms of the pure-state coherence

Quantifying coherence in terms of the pure-state coherence

Generalized coherence vector applied to coherence transformations and quantifiers

Strictly incoherent operations for one-qubit systems

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