Related papers: A Quantum Pigeonhole Principle and Two Semidefinit…
This essay advocates the view that any problem that has a meaningful empirical content, can be formulated in constructive, more definitely, finite terms. We consider combinatorial models of dynamical systems and approaches to statistical…
This thesis explores foundational aspects of quantum information theory and quantum cryptography. First, we investigate quantum correlations in interactive settings, including the CHSH and graph isomorphism games. We aim to distinguish…
The private simultaneous messages model is a non-interactive version of the multiparty secure computation, which has been intensively studied to examine the communication cost of the secure computation. We consider its quantum counterpart,…
We study the weakest model of quantum nondeterminism in which a classical proof has to be checked with probability one by a quantum protocol. We show the first separation between classical nondeterministic communication complexity and this…
This paper focuses on bounding the total communication complexity of collapsing protocols for multiparty pointer jumping problem ($MPJ_k^n$). Brody and Chakrabati in \cite{bc08} proved that in such setting one of the players must…
Quantum communication complexity studies the efficiency of information communication (that is, the minimum amount of communication required to achieve a certain task) using quantum states. One representative example is quantum…
Quantum systems are known to offer advantages over their classical counterpart in communication complexity protocols, where the aim is to minimize the amount of information exchange between distant parties to compute global functions of…
This work focuses on understanding the quantum message complexity of two central problems in distributed computing, namely, leader election and agreement in synchronous message-passing communication networks. We show that quantum…
We give elementary proof that theory $T^1_2(R)$ augmented by the weak pigeonhole principle for all $\Delta^b_1(R)$-definable relations does not prove the bijective pigeonhole principle for $R$. This can be derived from known more general…
Suppose Alice and Bob share a maximally entangled state of any finite dimension and each perform two-outcome measurements on the respective part of the state. It is known, due to the recent result of Regev and Toner, that if a classical…
We demonstrate a two-player communication problem that can be solved in the one-way quantum model by a 0-error protocol of cost O (log n) but requires exponentially more communication in the classical interactive (bounded error) model.
John Bell taught us that quantum mechanics can not be reproduced by non-contextual and local Hidden variable theory. The impossibility of replacing quantum mechanics by non-contextual Hidden Variable Theory can be turned to a impossible…
Proofs of the security of quantum key distribution are propositions about models written in the mathematical language of quantum mechanics, and the issue is the linking of such models to actual devices in an experiment on security. To…
We present a novel complex number formulation along with tight convex relaxations for the aircraft conflict resolution problem. Our approach combines both speed and heading control and provides global optimality guarantees despite…
Bell's Theorem shows that quantum mechanical correlations can violate the constraints that the causal structure of certain experiments impose on any classical explanation. It is thus natural to ask to which degree the causal assumptions --…
This paper introduces a novel lower bound on communication complexity using quantum relative entropy and mutual information, refining previous classical entropy-based results. By leveraging Uhlmann's lemma and quantum Pinsker inequalities,…
Quantum fidelity is one of the most important measures of similarity between mixed quantum states. However, the usual formulation is cumbersome and hard to understand when encountering the first time. This work shows in a novel, elegant…
In this paper we introduce a novel notion of probabilistic bisimulation for quantum processes and prove that it is congruent with respect to various process algebra combinators including parallel composition even when both classical and…
We describe the design of a quantifier elimination framework for the complex numbers in the language of ordered rings supplemented with symbols for the imaginary unit, real parts, imaginary parts, and conjugates. Technically, we use a…
Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called "Bell inequality violations." We give two new two-player games with Bell inequality violations that…