Exploring boundaries of quantum convex structures: Special role of unitary processes

Puchała, Zbigniew; Jenčová, Anna; Sedlák, Michal; Ziman, Märio

doi:10.1103/physreva.92.012304

Cited by 4 publications

(3 citation statements)

References 17 publications

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“…) and a unitary channel. First we note, that if a quantum channel Φ is an interior point of the set of channels then, the best distinguishable one Ψ is some unitary channel [37]. Below we show, that in the case of d → ∞ almost all quantum channels are perfectly distinguishable from any unitary channel.…”

Section: Distance To the Nearest Unitary Channelmentioning

confidence: 70%

Almost all quantum channels are equidistant

Nechita

Puchała

Pawela

et al. 2018

Journal of Mathematical Physics

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In this work we analyze properties of generic quantum channels in the case of large system size. We use random matrix theory and free probability to show that the distance between two independent random channels converges to a constant value as the dimension of the system grows larger. As a measure of the distance we use the diamond norm. In the case of a flat Hilbert-Schmidt distribution on quantum channels, we obtain that the distance converges to 1 2 + 2 π , giving also an estimate for the maximum success probability for distinguishing the channels. We also consider the problem of distinguishing two random unitary rotations. * In Memory of Judyta Henek-Pawela: 1986-2016 † lpawela@iitis.pl arXiv:1612.00401v3 [quant-ph]

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Section: Distance To the Nearest Unitary Channelmentioning

confidence: 70%

Almost all quantum channels are equidistant

Nechita

Puchała

Pawela

et al. 2018

Journal of Mathematical Physics

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“…Today, the description of quantum phenomena through negative quasiprobabilities continues to have a broad impact on modern research and is the basis for a profound understanding of quantum physics. While remarkable progress has been made recently in the quasiprobability-based description of quantum coherence (see, e.g., [87][88][89][90]), the actual construction of an optimal decomposition in terms of quasiprobability distributions over classical states remained an open problem.…”

Section: Introductionmentioning

confidence: 99%

Quasiprobability representation of quantum coherence

Sperling

2018

Phys. Rev. A

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We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state. Conversely, quantum phenomena are certified in terms of signed distributions, i.e., quasiprobabilities, and a residual component unaccessible via classical states. Our unifying method combines well-established concepts, such as phase-space distributions in quantum optics, with resources of quantumness relevant for quantum technologies. We apply our approach to analyze various forms of quantum coherence in different physical systems. Moreover, our framework renders it possible to uncover complex quantum correlations between systems, for example, via quasiprobability representations of multipartite entanglement.

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“…In many cases, the convex structure determines the performance of the corresponding measurements, for example optimal measurements with respect to convex figures of merit are given by extremal process POVMs. On the other hand, the set of process POVMs can also be the subject of statistical inference and the convex structure plays a decisive role in discrimination tasks, see [14,19].…”

Section: Introduction and Basic Definitionsmentioning

confidence: 99%

On the convex structure of process positive operator valued measures

Jenčová

2015

Journal of Mathematical Physics

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Measurements on quantum channels are described by so-called process operator valued measures, or process POVMs. We study implementing schemes of extremal process POVMs. As it turns out, the corresponding measurement must satisfy certain extremality property, which is stronger that the usual extremality given by the convex structure. This property motivates the introduction and investigation of the A-convex structure of POVMs, which generalizes both the usual convex and C*-convex structure. We show that extremal points and faces of the set of process POVMs are closely related to A-extremal points and A-faces of POVMs, for a certain subalgebra A. We give a characterization of A-extremal and A-pure POVMs in the Appendix. Corollary 3. M ∈ M(H, n) is A-extremal if and only if whenever MProof of Lemma 2. Here we use similar techniques as in [7]. We first prove the assertion for M = X 1 N 1 X 1 + X 2 N 2 X 2 , with X 1 , X 2 ≥ 0. If both X 1 and X 2 are invertible, N 1 , N 2 ∈ F by the definition of an A-face. So suppose that, say, X 1 is not invertible. For any λ ∈ (0, 1), M = X 1 N 1 X 1 + (λX 2 )N 2 (λX 2 ) + ( 1 − λ 2 X 2 )N 2 ( 1 − λ 2 X 2 ).

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Exploring boundaries of quantum convex structures: Special role of unitary processes

Cited by 4 publications

References 17 publications

Almost all quantum channels are equidistant

Almost all quantum channels are equidistant

Quasiprobability representation of quantum coherence

On the convex structure of process positive operator valued measures

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