arXiv subjects

Maor Ganz

Publications and source records attributed to Maor Ganz.

4 recordsLinked to original sources

arXiv2017

Dining Philosophers, Leader Election and Ring Size problems, in the quantum setting

We provide the first quantum (exact) protocol for the Dining Philosophers problem (DP), a central problem in distributed algorithms. It is well known that the problem cannot be solved exactly in the classical setting. We then use our DP protocol to provide a new quantum protocol for the tightly related problem of exact leader election (LE) on a ring, improving significantly in both time and memory complexity over the known LE protocol by Tani et. al. To do this, we show that in some sense the exact DP and exact LE problems are equivalent; interestingly, in the classical non-exact setting they are not. Hopefully, the results will lead to exact quantum protocols for other important distributed algorithmic questions; in particular, we discuss interesting connections to the ring size problem, as well as to a physically motivated question of breaking symmetry in 1D translationally invariant systems.

quant-ph↗

arXiv2017

Quantum coin hedging, and a counter measure

A quantum board game is a multi-round protocol between a single quantum player against the quantum board. Molina and Watrous discovered quantum hedging. They gave an example for perfect quantum hedging: a board game with winning probability < 1, such that the player can win with certainty at least 1-out-of-2 quantum board games played in parallel. Here we show that perfect quantum hedging occurs in a cryptographic protocol - quantum coin flipping. For this reason, when cryptographic protocols are composed, hedging may introduce serious challenges into their analysis. We also show that hedging cannot occur when playing two-outcome board games in sequence. This is done by showing a formula for the value of sequential two-outcome board games, which depends only on the optimal value of a single board game; this formula applies in a more general setting, in which hedging is only a special case.

quant-ph↗

arXiv2016

Quantum Leader Election

Leader election between n parties is known to be impossible classically. This work gives a simple algorithm that does it, based on the weak coin flipping protocol with arbitrarily small bias derived by Mochon in 2007, and recently published and simplified in Aharonov et al in 2016. A protocol with linear number of coin flipping rounds is quite simple to achieve; We further provide an improvement to logarithmic number of coin flipping rounds. This is a much improved journal version of a preprint posted in 2009: many typos are corrected, proofs are more rigorous and accurate, and the analysis of complexity is significantly tightened which gives a stronger result in terms of efficiency; The first protocol with linear number of rounds, was achieved independently also by Aharon and Silman in 2010.

quant-ph↗

arXiv2014

A simpler proof of existence of quantum weak coin flipping with arbitrarily small bias

Mochon's proof [Moc07] of existence of quantum weak coin flipping with arbitrarily small bias is a fundamental result in quantum cryptography, but at the same time one of the least understood. Though used several times as a black box in important follow-up results [Gan09, CK09, AS10, CK11, KZ13] the result has not been peer-reviewed, its novel techniques (and in particular Kitaev's point game formalism) have not been applied anywhere else, and an explicit protocol is missing. We believe that truly understanding the existence proof and the novel techniques it relies on would constitute a major step in quantum information theory, leading to deeper understanding of entanglement and of quantum protocols in general. In this work, we make a first step in this direction. We simplify parts of Mochon's construction considerably, making about 20 pages of analysis in the original proof superfluous, clarifying some other parts of the proof on the way, and presenting the proof in a way which is conceptually easier to grasp. We believe the resulting proof of existence is easier to understand, more readable, and certainly verifiable. Moreover, we analyze the resources needed to achieve a bias $ε$ and show that the number of qubits is $O(\log 1/ε)$, while the number of rounds is $(1/ε)^{O(1/ε)}$. A true understanding of the proof, including Kitaev's point game techniques and their applicability, as well as completing the task of constructing an explicit (and also simpler and more efficient) protocol, are left to future work.

quant-ph↗