Witnessing incompatibility of quantum channels

Carmeli, Claudio; Heinosaari, Teiko; Miyadera, Takayuki; Toigo, Alessandro

doi:10.1063/1.5126496

Cited by 34 publications

(38 citation statements)

References 42 publications

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“…This question has been studied from various different angles in [11,12,13,14,15] and important findings have been reported. Extensions to the detection of incompatibility of quantum channels have also been developed [16,17]. One statement is the following (see Theorem 2 in [11]).…”

Section: Guessing Games With Prior Information and Detection Of Incom...mentioning

confidence: 99%

Quantum guessing games with posterior information

Carmeli,

Heinosaari,

Toigo

2021

Preprint

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Quantum guessing games form a versatile framework for studying different tasks of information processing. A quantum guessing game with posterior information uses quantum systems to encode messages and classical communication to give partial information after quantum measurement has been performed. We present a general framework for quantum guessing games with posterior information and derive structure and reduction theorems that enable to analyze any such game. We formalize symmetry of guessing games and characterize the optimal measurements in cases where the symmetry is related to an irreducible representation. The application of guessing games to incompatibility detection is reviewed and clarified. All the presented main concepts and results are demonstrated with examples.

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Section: Guessing Games With Prior Information and Detection Of Incom...mentioning

confidence: 99%

Quantum guessing games with posterior information

Carmeli,

Heinosaari,

Toigo

2021

Preprint

Self Cite

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“…Recently, we have become aware of independent works related to our Theorem 1 by R. Uola et al [22] and by C. Carmeli et al [23].…”

Section: Note Addedmentioning

confidence: 99%

Operational characterization of incompatibility of quantum channels with quantum state discrimination

Mori

2020

Phys. Rev. A

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A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection of incompatible channels can be more useful than compatible ones as preprocessings in a state discrimination task with multiple ensembles of states. This is done by showing that the robustness of channel incompatibility which is a measure for incompatibility of channels exactly quantifies the maximum advantage in the state discrimination. We also show that incompatibility of quantum measurement and channel has a similar operational interpretation. Finally, we demonstrate that our result with respect to channel incompatibility includes all other kinds of incompatibility as special cases.

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“…The incompatibility in one family of POVMs/channels/instruments can then be quantitatively compared to another. Resource theories also provide tools for detecting or "witnessing" the incompatibility present in general measurement devices [27,[29][30][31][32]. This certification can also be done in a semi-device-independent way [12,18,19,23,[33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Incompatibility as a resource for programmable quantum instruments

Ji¹,

Chitambar²

2021

Preprint

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Quantum instruments represent the most general type of quantum measurement, as they incorporate processes with both classical and quantum outputs. In many scenarios, it may be desirable to have some "on-demand" device that is capable of implementing one of many possible instruments whenever the experimenter desires. We refer to such objects as programmable instrument devices (PIDs), and this paper studies PIDs from a resource-theoretic perspective. A physically important class of PIDs are those that do not require quantum memory to implement, and these are naturally "free" in this resource theory. The traditional notion of measurement incompatibility emerges as a resource in this theory since any PID controlling an incompatible family of instruments requires quantum memory to build. We identify an incompatibility partial ordering of PIDs based on whether one can be transformed into another using processes that do not require additional quantum memory. Necessary and sufficient conditions are derived for when such transformations are possible based on how well certain guessing games can be played using a given PID. Ultimately our results provide an operational characterization of incompatibility, and they offer tests for incompatibility in the most general types of quantum instruments. Since channel steerability is equivalent to PID incompatibility, this work can also be seen as a resource theory of channel steering.

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Witnessing incompatibility of quantum channels

Cited by 34 publications

References 42 publications

Quantum guessing games with posterior information

Quantum guessing games with posterior information

Operational characterization of incompatibility of quantum channels with quantum state discrimination

Incompatibility as a resource for programmable quantum instruments

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