Necessary and sufficient condition for joint measurability

Jae, Jeongwoo; Baek, Kyunghyun; Ryu, Junghee; Lee, Jinhyoung

doi:10.1103/physreva.100.032113

Cited by 6 publications

(7 citation statements)

References 48 publications

(78 reference statements)

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“…We have dealt with the necessary and sufficient conditions of incompatibility for a finite number of measurements with arbitrary finite outcomes. Our approach toward quantum incompatibility covers essentially the theoretic framework of [17] and connects with the results in [29] and [30] in the case of qubit measurements with two-outcomes. Based on the necessary and sufficient conditions of compatibility for qubit measurements, we have analytically worked out the incompatibility probability of a pair of unbiased qubit measurements.…”

Section: Discussionmentioning

confidence: 99%

“…Concerning quantum incompatibility, an important problem is the development of an effective method to judge whether a set of measurements is compatible (i.e., jointly measurable), which has received much attention [15][16][17]. The authors of [15] and [16] used the notion of free spectrahedra in the optimization theory to characterize the measurement compatibility (also known as the joint measurability).…”

Section: Introductionmentioning

confidence: 99%

“…Due to the abstract construction of free spectahedra, characterization of incompatibility along this approach is not very operational. The authors of a recent study [17] presented a more operational way toward the characterization of quantum incompatibility for the case where both measurements have the same number of measurement outcomes.…”

Section: Introductionmentioning

confidence: 99%

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Incompatibility probability of random quantum measurements

et al. 2019

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Incompatibility of quantum measurements is of fundamental importance in quantum mechanics. It is closely related to many nonclassical phenomena such as Bell nonlocality, quantum uncertainty relations, and quantum steering. We study the necessary and sufficient conditions of quantum compatibility for a given collection of n measurements in d-dimensional space. From the compatibility criterion for two-qubit measurements, we compute the incompatibility probability of a pair of independent random measurements. For a pair of unbiased random qubit measurements, we derive that the incompatibility probability is exactly 3 5 . Detailed results are also presented in figures for pairs of general qubit measurements.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Incompatibility probability of random quantum measurements

et al. 2019

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“…There is an analogous task for quantum measurements called the measurement compatibility problem (see [11,12] for POVMS and [13,14] for the special case of qubits). This task can be stated as follows.…”

Section: The Measurement Compatibility Problemmentioning

confidence: 99%

Jordan products of quantum channels and their compatibility

Girard,

Plávala,

Sikora

2020

Preprint

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Given two quantum channels, we examine the task of determining whether they are compatible-meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). We show several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-andprepare channels (i.e., entanglement-breaking channels) do not necessarily have a measureand-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolaring channels are compatible.

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“…There is an analogous task for quantum measurements called the measurement compatibility problem (see 12 , 13 for POVMs (positive operator-valued measures) and 14 , 15 for the special case of qubits). This task can be stated as follows.…”

Section: Introductionmentioning

confidence: 99%

Jordan products of quantum channels and their compatibility

2021

View full text Add to dashboard Cite

Given two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

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Necessary and sufficient condition for joint measurability

Cited by 6 publications

References 48 publications

Incompatibility probability of random quantum measurements

Incompatibility probability of random quantum measurements

Jordan products of quantum channels and their compatibility

Jordan products of quantum channels and their compatibility

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