Minimum-Entropy Couplings and Their Applications

Cicalese, Ferdinando; Gargano, Luisa; Vaccaro, Ugo

doi:10.1109/tit.2019.2894519

Cited by 19 publications

(30 citation statements)

References 56 publications

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“…Then, for any Q X that is not a point mass, 4 i.e., the contraction coefficient for the χ 2 -divergence is the minimal contraction coefficient among all f -divergences with f satisfying the above conditions. Remark 1: A weaker version of (15) was presented in [18,Proposition II.6.15] in the general alphabet setting, and the result in (15) was obtained in [54,Theorem 3.3] for finite alphabets.…”

Section: A Preliminaries and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

Sason

2019

Entropy

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This paper is focused on derivations of data-processing and majorization inequalities for f -divergences, and their applications in information theory and statistics. For the accessibility of the material, the main results are first introduced without proofs, followed by exemplifications of the theorems with further related analytical results, interpretations, and information-theoretic applications. One application refers to the performance analysis of list decoding with either fixed or variable list sizes; some earlier bounds on the list decoding error probability are reproduced in a unified way, and new bounds are obtained and exemplified numerically. Another application is related to a study of the quality of approximating a probability mass function, induced by the leaves of a Tunstall tree, by an equiprobable distribution. The compression rates of finite-length Tunstall codes are further analyzed for asserting their closeness to the Shannon entropy of a memoryless and stationary discrete source. Almost all the analysis is relegated to the appendices, which form the major part of this manuscript.

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Section: A Preliminaries and Related Workmentioning

confidence: 99%

“…Proof: See Appendix F. 15 Tsallis entropy was introduced in [68] as a generalization of the Shannon entropy (similarly to the Rényi entropy [56]), and it was applied to statistical physics in [68].…”

Section: Remarkmentioning

confidence: 99%

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

Sason

2019

Entropy

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“…where the vector ⃗ is called the aggregation of ⃗ s. [17] Relation (18) represents the quantum prediction of relation (16) but without quantum memory. The violation of the relation ⃗ s (+) ≺ ⃗ implies a violation of relation (17), which then implies the quantum steering in a bipartite state. [15] The correlation matrix of a bipartite state AB is defined as We consider a typical mixed and entangled state [19]…”

Section: Uncertainty Relation With Infinite Number Of Observablesmentioning

confidence: 99%

“…For example, the Bell non-locality, quantum steering, [16] and non-separability may be somehow distinguished by stronger correlations reached by optimal joint measurements in bipartite system. In statistical inference, a typical problem is to identify the extremal joint distribution that maximizes the correlation for given marginals, [17] which is closely related to infer a maximal correlation for given joint measurements.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Measurement Strategy to Beat the Quantum Uncertainty in Correlated System

2020

Adv Quantum Tech

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Uncertainty principle is an inherent nature of quantum system that undermines the precise measurement of incompatible observables and hence the applications of quantum theory. Entanglement, another unique feature of quantum physics, may help to reduce the quantum uncertainty. In this paper, a practical method is proposed to reduce the one party measurement uncertainty by determining the measurement on the other party of an entangled bipartite system. In light of this method, a family of conditional majorization uncertainty relations in the presence of quantum memory is constructed, which is applicable to arbitrary number of observables. The new family of uncertainty relations implies sophisticated structures of quantum uncertainty and non‐locality, that are usually studied by using scalar measures. Applications to reduce the local uncertainty and to witness quantum non‐locality are also presented.

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“…Shannon entropy [27] and minimum entropy [28] are effective tools to depict the statistical characteristics of random numbers. Shannon entropy can quantitatively evaluate the effective information in a random sequence, and the independence and uncertainty of each bit.…”

Section: A Select the Least Significant Bitsmentioning

confidence: 99%

Fast True Random Number Generator Based on Chaotic Oscillation in Self-Feedback Weakly Coupled Superlattices

et al. 2020

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Random numbers play a vital role in communications and cryptography. However, most existing true random number generators have difficulty in satisfying the requirements of high-speed communications due to their complexity and bulkiness, or low speed limitations due to equipment bandwidth. Then, the all-electron true random number generator was presented based on GaAs/Al 0.45 Ga 0.55 As superlattices conducted under direct current bias at room temperature, which not only possesses the characteristics of miniaturization but also generates random numbers at rates up to the Gbit/s. However, the bit rate of random number generators based on superlattices is still much slower compared to chaotic laser random number generators. In order to generate higher-rate random numbers, we modified a DC-excited superlattice and then redirected the signal generated by the superlattice back into itself, thus introducing a self-feedback, and achieved a self-feedback superlattice true random number generator. This improvement makes the superlattice have a more detailed signal shape, a more effective signal amplitude, and with lower power consumption. Therefore, these advances made the self-feedback superlattice more suitable for generating random numbers. Moreover, we propose a new post-processing method, called the adjacent bits reversal exclusive-or. This method can reduce the sequence bias and correlation without discarding any random bit. The random number obtained by the self-feedback superlattice at a sampling rate of 10 GS/s passed the triple standard deviation test and the random number standard test (NIST SP 800-22), indicating that it possessed good statistical properties as a miniaturized random number generator.

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Minimum-Entropy Couplings and Their Applications

Cited by 19 publications

References 56 publications

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

On Data-Processing and Majorization Inequalities for f-Divergences with Applications

An Optimal Measurement Strategy to Beat the Quantum Uncertainty in Correlated System

Fast True Random Number Generator Based on Chaotic Oscillation in Self-Feedback Weakly Coupled Superlattices

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