Random positive operator valued measures

Heinosaari, Teiko; Jivulescu, Maria Anastasia; Nechita, Ion

doi:10.1063/1.5131028

Cited by 19 publications

(12 citation statements)

References 66 publications

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“…To demonstrate this, we choose a rather extreme example of a random 4-qubit target state with the following measurement scheme: perform as many measurements and repetitions as prescribed by DFE for achieving a risk of 0.05 at a confidence level of 95%, but instead of performing Pauli measurements, we choose random POVMs, generated as per Ref. [32]. In this case, we obtain a risk of ≈ 0.023 from the minimax method, which is larger than the risk for Pauli measurements using the minimax method (see Tab.…”

Section: A Direct Fidelity Estimationmentioning

confidence: 99%

Theory of versatile fidelity estimation with confidence

Seshadri¹,

Ringbauer²,

Monz³

et al. 2021

Preprint

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Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the experimentalist to choose a convenient measurement setting. Our primary focus lies on a method that constructs an estimator with nearly minimax optimal confidence interval for any specified measurement setting. We demonstrate, through a combination of theoretical and numerical results, various desirable properties for the method: robustness against experimental imperfections, competitive sample complexity, and accurate estimates in practice. We compare this method with Maximum Likelihood Estimation and the associated Profile Likelihood method, a Semi-Definite Programming based approach, as well as a popular direct fidelity estimation technique.

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Section: A Direct Fidelity Estimationmentioning

confidence: 99%

Theory of versatile fidelity estimation with confidence

Seshadri¹,

Ringbauer²,

Monz³

et al. 2021

Preprint

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“…We sample N = 10 6 pairs of random POVMs in a manner explained at the beginning of this section. For further details on sampling, we refer the reader to [27,28].…”

Section: Lemmamentioning

confidence: 99%

Discrimination of POVMs with rank-one effects

Krawiec

Pawela

Puchała

2020

Quantum Inf Process

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The main goal of this work is to provide an insight into the problem of discrimination of positive operator-valued measures with rank-one effects. It is our intention to study multiple-shot discrimination of such measurements, that is the case when we are able to use to unknown measurement a given number of times. Furthermore, we are interested in comparing two possible discrimination schemes: the parallel and adaptive ones. To this end, we construct a pair of symmetric informationally complete positive operator-valued measures which can be perfectly discriminated in a two-shot adaptive scheme but cannot be distinguished in the parallel scheme. On top of this, we provide an explicit algorithm which allows us to find this adaptive scheme.

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“…This is Hermitian whenever both A and B are Hermitian. The Jordan product can be used to study the compatibility of measurements (see [23,24]). In particular, for POVMs {M 1 , .…”

Section: Jordan Products Of Matricesmentioning

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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Random positive operator valued measures

Cited by 19 publications

References 66 publications

Theory of versatile fidelity estimation with confidence

Theory of versatile fidelity estimation with confidence

Discrimination of POVMs with rank-one effects

Jordan products of quantum channels and their compatibility

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