Refinements of Pinsker's inequality

Fedotov, Alexander; Harremoës, Peter; Topsøe, Flemming

doi:10.1109/tit.2003.811927

Cited by 131 publications

(133 citation statements)

References 14 publications

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“…Using p Y (y) α ≤ p Y (y) for α > 1 and Jensen's inequality for the concave function (2.5), we have 14) and also y p Y (y) α q(e|y) α ≤ y p Y (y) q(e|y) α = P α e . By these two points, the inequality (6.5) immediately leads to (6.10).…”

Section: Notes On the Fano And Fannes Inequalitiesmentioning

confidence: 99%

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Rastegin

2013

Math Phys Anal Geom

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Pinsker's and Fannes' type bounds on the Tsallis relative entropy are derived. The monotonicity property of the quantum f -divergence is used for its estimating from below. For order α ∈ (0, 1), a family of lower bounds of Pinsker type is obtained. For α > 1 and the commutative case, upper continuity bounds on the relative entropy in terms of the minimal probability in its second argument are derived. Both the lower and upper bounds presented are reformulated for the case of Rényi's entropies. The Fano inequality is extended to Tsallis' entropies for all α > 0. The deduced bounds on the Tsallis conditional entropy are used for obtaining inequalities of Fannes' type.

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Section: Notes On the Fano And Fannes Inequalitiesmentioning

confidence: 99%

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Rastegin

2013

Math Phys Anal Geom

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“…As discussed in [5], a straightforward application of the Alicki-Fannes inequality [27] implies that if D δ/2, then I acc 4δ log d + 2h 2 (δ), where h 2 (δ) = −δ log δ − (1 − δ) log (1 − δ) is the binary entropy. On the other hand, the Pinsker inequality implies that (see e.g., [28], and references therein) D (2 ln 2)I acc .…”

Section: P(l|m)p(m)mentioning

confidence: 99%

Robust quantum data locking from phase modulation

2014

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Quantum data locking is a uniquely quantum phenomenon that allows a relatively short key of constant size to (un)lock an arbitrarily long message encoded in a quantum state, in such a way that an eavesdropper who measures the state but does not know the key has essentially no information about the message. The application of quantum data locking in cryptography would allow one to overcome the limitations of the one-time pad encryption, which requires the key to have the same length as the message. However, it is known that the strength of quantum data locking is also its Achilles heel, as the leakage of a few bits of the key or the message may in principle allow the eavesdropper to unlock a disproportionate amount of information. In this paper we show that there exist quantum data locking schemes that can be made robust against information leakage by increasing the length of the key by a proportionate amount. This implies that a constant size key can still lock an arbitrarily long message as long as a fraction of it remains secret to the eavesdropper. Moreover, we greatly simplify the structure of the protocol by proving that phase modulation suffices to generate strong locking schemes, paving the way to optical experimental realizations. Also, we show that successful data locking protocols can be constructed using random code words, which very well could be helpful in discovering random codes for data locking over noisy quantum channels.

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“…The Kullback-Leibler divergence is lower bounded by the variational distance V, which is known as the Pinsker inequality [6,7] …”

Section: On Lower Bound By Variational Distancementioning

confidence: 99%

A Note on Bound for Jensen-Shannon Divergence by Jeffreys

Yamano

2014

Proceedings of 1st International Electronic Conference on Entropy and Its Applications

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Abstract:We present a lower bound on the Jensen-Shannon divergence by the Jeffrers' divergence when ≥ is satisfied. In the original Lin's paper [IEEE Trans. Info. Theory, 37, 145 (1991)], where the divergence was introduced, the upper bound in terms of the Jeffreys was the quarter of it. In view of a recent shaper one reported by Crooks, we present a discussion on upper bounds by transcendental functions of Jeffreys by comparing those values for a binary distribution.

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Refinements of Pinsker's inequality

Cited by 131 publications

References 14 publications

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Bounds of the Pinsker and Fannes Types on the Tsallis Relative Entropy

Robust quantum data locking from phase modulation

A Note on Bound for Jensen-Shannon Divergence by Jeffreys

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