Admissible invariant estimators in a linear model

Stępniak, Czesław

doi:10.14736/kyb-2014-3-0310

Cited by 2 publications

(2 citation statements)

References 21 publications

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“…As the Rényi α-entropy does not increase with α, the bound (51) is valid for all Rényiʼs entropies of order α ∈ (0; 2], including the Shannon-entropy case (37). For ρ ψ ψ = , the entropic bound (47) is reduced to its pure-state form…”

Section: Tsallis' and Rényiʼs Formulations For A Single Sic-povmmentioning

confidence: 99%

Notes on general SIC-POVMs

Rastegin

2014

Phys. Scr.

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An unavoidable task in quantum information processing is how to obtain data about the state of an individual system by suitable measurements. Informationally complete measurements are relevant in quantum state tomography, quantum cryptography, quantum cloning, and other questions. Symmetric informationally complete measurements (SIC-POVMs) form an especially important class of such measurements. We formulate some novel properties and relations for general SIC-POVMs in a finite-dimensional Hilbert space. For a given density matrix and any general SIC-POVM, the so-called index of coincidence of generated probability distribution is exactly calculated. Using this result, we obtain state-dependent entropic bounds for a single general SIC-POVM. Lower entropic bounds are derived in terms of the Rényi α-entropies for α ∈ [2; ∞) and the Tsallis α-entropies for α ∈ (0; 2]. A lower bound on the min-entropy of a SIC-POVM is separately examined. For a pair of general SIC-POVMs, entropic uncertainty relations of the Maassen-Uffink type are considered.

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Section: Tsallis' and Rényiʼs Formulations For A Single Sic-povmmentioning

confidence: 99%

Notes on general SIC-POVMs

Rastegin

2014

Phys. Scr.

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“…In general, information-theoretic functions of the Rényi type do not succeed all the properties of the standard functions. In more detail, these questions are discussed in [60][61][62][63]. In particular, some popular measures to quantify mutual information are not completely legitimate in the context of quantum cryptography [64].…”

Section: Definitions and Notationmentioning

confidence: 99%

Rényi formulation of uncertainty relations for POVMs assigned to a quantum design

Rastegin¹

2020

J. Phys. A: Math. Theor.

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Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle. This approach seems to be very suitable in application to problems of quantum information theory. It is typical that questions of such a kind involve measurements having one or another specific structure. The latter often allows us to improve entropic bounds that follow from uncertainty relations of sufficiently general scope. Quantum designs have found use in many issues of quantum information theory, whence uncertainty relations for related measurements are of interest. In this paper, we obtain uncertainty relations in terms of min-entropies and Rényi entropies for POVMs assigned to a quantum design. Relations of the Landau-Pollak type are addressed as well. Using examples of quantum designs in two dimensions, the obtained lower bounds are then compared with the previous ones. An impact on entropic steering inequalities is briefly discussed.

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Admissible invariant estimators in a linear model

Cited by 2 publications

References 21 publications

Notes on general SIC-POVMs

Notes on general SIC-POVMs

Rényi formulation of uncertainty relations for POVMs assigned to a quantum design

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