Contradictory entropic joint uncertainty relations for complementary observables in two-level systems

Alfredo, Luis

doi:10.48550/arxiv.1306.5211

Cited by 3 publications

(3 citation statements)

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“…Entropic bounds in terms of generalized entropies entropic bounds were utilized in studying many topics such as the case of conjugate observables [48,49], quantifying number-phase uncertainties [50,51], incompatibilities of anti-commuting observables [52] and reformulations in quasi-Hermitian models [53]. In the context of simultaneous measurements of complementary observables, uncertainty relations in terms of both the Tsallis and Rényi entropies are examined in [54]. The method of Maassen and Uffink uses the Riesz theorem.…”

Section: Uncertainty Relations Of the Maassen-uffink Typementioning

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: Uncertainty Relations Of the Maassen-uffink Typementioning

confidence: 99%

Notes on general SIC-POVMs

Rastegin

2014

Phys. Scr.

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“…The added noise is minimum in the sense that the Euclidean distance between p Z and the marginal probability pZ (defined in Eq. ( 7) below) is minimum [26]. It is worth noting that there is a deep connection of this measurement with the problem of state discrimination between two nonorthogonal states, such as |a ± (see e.g.…”

Section: Statistics and Simultaneous Measurementsmentioning

confidence: 96%

Entropic measures of joint uncertainty: Effects of lack of majorization

Luis

Bosyk

Portesi

2016

Physica A: Statistical Mechanics and its Applications

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We compute Rényi entropies for the statistics of a noisy simultaneous observation of two complementary observables in two-dimensional quantum systems. The relative amount of uncertainty between two states depends on the uncertainty measure used. These results are not reproduced by a more standard duality relation. We show that these behaviors are consistent with the lack of majorization relation between the corresponding statistics.

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“…As shown in appendix A of Ref. [43], the optimum choice holds for 2ϑ − θ = π/2. To gain insight, and without loss of generality, we can consider such a case.…”

Section: Joint Observation and Inversionmentioning

confidence: 99%