In a 1991 paper, Asher Peres and the author theoretically analyzed a set of unentangled bipartite quantum states that could apparently be distinguished better by a global measurement than by any sequence of local measurements on the individual subsystems. The present paper returns to the same example, and shows that the best result so far achieved can alternatively be attained by a measurement ...

Does the world really need another article about Pythagorean triples? Here is why we think so. The set of Pythagorean triples has a lot of interesting structure, which has intrigued both amateur and professional mathematicians. It is the topic of an extensive mathematical literature, almost all of which relies on an enumeration of primitive Pythagorean triples that has been known since ancient ...

In this paper we approach some questions about quantum contextuality with tools from formal logic. In particular, we consider an experiment associated with the PeresMermin square. The language of all possible sequences of outcomes of the experiment is classified in the Chomsky hierarchy and seen to be a regular language. Next, we make the rather evident observation that a finite set of hidden f...

Filters are widely used in the world of communication and computation. To design a finite impulse response (FIR) filter that satisfies all the required conditions is a challenge. Power consumption by the multiplier and adder blocks in the architecture is the prime cause for concern in FIR design. In this paper, design of an FIR filter entirely using Reversible logic is presented. Reversible log...

It was recently shown in Lubetzky and Peres (2016) Sardari (2019) that Ramanujan graphs, i.e., graphs with the optimal spectrum, exhibit cutoff of simple random walk an time have almost-diameter. We show this spectral condition can be replaced by a weaker condition, Sarnak–Xue density property, to deduce similar results. This allows us prove some natural families Schreier SL2Ft-action on projec...

Peres [1] claims that our protocol [2] does not present any novel feature, and it is very similar to the oldest protocol of Bennett and Brassard [3] (BB84). We completely disagree with this claim and with other points raised in the Comment. The essential novelty of our protocol is that the carrier of information is in a quantum state belonging to a definite set of orthonormal states. Any other ...

We study the Glauber dynamics Markov chain for k-colourings of trees with maximum degree ∆.For k ≥ 3, we show that the mixing time on every tree is at most n . This bound istight up to the constant factor in the exponent, as evidenced by the complete tree. Our proof uses aweighted canonical paths analysis and a variation of the block dynamics in which we exploit the differing<lb...