arXiv subjects

Boaz Tamir

Publications and source records attributed to Boaz Tamir.

11 recordsLinked to original sources

arXiv2021

Quantum logical entropy: fundamentals and general properties

Logical entropy gives a measure, in the sense of measure theory, of the distinctions of a given partition of a set, an idea that can be naturally generalized to classical probability distributions. Here, we analyze how fundamental concepts of this entropy and other related definitions can be applied to the study of quantum systems, leading to the introduction of the quantum logical entropy. Moreover, we prove several properties of this entropy for generic density matrices that may be relevant to various areas of quantum mechanics and quantum information. Furthermore, we extend the notion of quantum logical entropy to post-selected systems.

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arXiv2017

Tsallis entropy is natural in the formulation of quantum noise

In this paper we introduce an easy to compute upper bound on the Tsallis entropy of a density matrix describing a system coupled to a noise source. This suggests that the Tsallis entropy is most natural in the context of quantum information theory. Similarly we redefine entropy exchange and use the same bound.

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arXiv2016

Notes on Adiabatic Quantum Computers

We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong relations between the three. We conclude with a brief presentation of the D-Wave computer and some future challenges.

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arXiv2015

A Holevo-type bound for a Hilbert Schmidt distance measure

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob using a quantum channel, while Bob is performing some projective measurement. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.

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arXiv2015

Quantum Gaussian Channels with Weak Measurements

In this paper we perform a novel analysis of quantum Gaussian channels in the context of weak measurements. Suppose Alice sends classical information to Bob using a quantum channel. Suppose Bob is allowed to use only weak measurements, what would be the channel capacity? We formulate weak measurement theory in these terms and discuss the above question.

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arXiv2015

Quantum Noise Filtering via Cross-Correlations

Motivated by successful classical models for noise reduction, we suggest a quantum technique for filtering noise out of quantum states. The purpose of this paper is twofold: presenting a simple construction of quantum cross-correlations between two wave-functions, and presenting a scheme for a quantum noise filtering. We follow a well-known scheme in classical communication theory that attenuates random noise, and show that one can build a quantum analog by using non-trace-preserving operators. By this we introduce a classically motivated signal processing scheme to quantum information theory, which can help reducing quantum noise, and particularly, phase flip noise.

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arXiv2015

On the Power of Weak Measurements in Separating Quantum States

We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when and how a set of consecutive weak measurements converges to a strong measurement. Second, we show that for a small set of consecutive weak measurements, long before their convergence, one can separate close states without causing their collapse. We thus demonstrate a tradeoff between the success probability and the bias of the original vector towards collapse. Next we use post-selection within the Two-State-Vector Formalism and present the non-linear expansion of the expectation value of the measurement device's pointer to distinguish between two predetermined close vectors.

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arXiv2014

Logical Entropy for Quantum States

The novel concept of quantum logical entropy is presented and analyzed. We prove several basic properties of this entropy with regard to density matrices. We hereby motivate a different approach for the assignment of quantum entropy to density matrices.

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arXiv2014

Quantum Annealing - Foundations and Frontiers

We briefly review various computational methods for the solution of optimization problems. First, several classical methods such as Metropolis algorithm and simulated annealing are discussed. We continue with a description of quantum methods, namely adiabatic quantum computation and quantum annealing. Next, the new D-Wave computer and the recent progress in the field claimed by the D-Wave group are discussed. We present a set of criteria which could help in testing the quantum features of these computers. We conclude with a list of considerations with regard to future research.

cond-mat.stat-mech↗

arXiv2006

A quantum secret ballot

The paper concerns the protection of the secrecy of ballots, so that the identity of the voters cannot be matched with their vote. To achieve this we use an entangled quantum state to represent the ballots. Each ballot includes the identity of the voter, explicitly marked on the "envelope" containing it. Measuring the content of the envelope yields a random number which reveals no information about the vote. However, the outcome of the elections can be unambiguously decided after adding the random numbers from all envelopes. We consider a few versions of the protocol and their complexity of implementation.

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arXiv2006

Grover's Quantum Search Algorithm and Diophantine Approximation

In a fundamental paper [Phys. Rev. Lett. 78, 325 (1997)] Grover showed how a quantum computer can find a single marked object in a database of size N by using only O(N^{1/2}) queries of the oracle that identifies the object. His result was generalized to the case of finding one object in a subset of marked elements. We consider the following computational problem: A subset of marked elements is given whose number of elements is either M or K, M<K, our task is to determine which is the case. We show how to solve this problem with a high probability of success using only iterations of Grover's basic step (and no other algorithm). Let m be the required number of iterations; we prove that under certain restrictions on the sizes of M and K the estimation m < (2N^{1/2})/(K^{1/2}-M^{1/2}) obtains. This bound sharpens previous results and is known to be optimal up to a constant factor. Our method involves simultaneous Diophantine approximations, so that Grover's algorithm is conceptualized as an orbit of an ergodic automorphism of the torus. We comment on situations where the algorithm may be slow, and note the similarity between these cases and the problem of small divisors in classical mechanics.

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