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A major open problem in communication complexity is whether or not quantum protocols can be exponentially more efficient than classical protocols on _total_ Boolean functions in the two-party interactive model. The answer appears to be…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
The goal of demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity…
Semi-quantum protocols that allow some of the users to remain classical are proposed for a large class of problems associated with secure communication and secure multiparty computation. Specifically, first time semi-quantum protocols are…
Communication complexity is an area of classical computer science which studies how much communication is necessary to solve various distributed computational problems. Quantum information processing can be used to reduce the amount of…
The main conceptual contribution of this paper is investigating quantum multiparty communication complexity in the setting where communication is \emph{oblivious}. This requirement, which to our knowledge is satisfied by all quantum…
We consider a quantum and classical version multi-party function computation problem with $n$ players, where players $2, \dots, n$ need to communicate appropriate information to player 1, so that a "generalized" inner product function with…
So-called separation automata are in the core of several recently invented quasi-polynomial time algorithms for parity games. An explicit $q$-state separation automaton implies an algorithm for parity games with running time polynomial in…
We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for…
Since the seminal work of Paturi and Simon \cite[FOCS'84 & JCSS'86]{PS86}, the unbounded-error classical communication complexity of a Boolean function has been studied based on the arrangement of points and hyperplanes. Recently,…
A set of $n$ pure quantum states is called antidististinguishable if there exists an $n$-outcome measurement that never outputs the outcome `$k$' on the $k$-th quantum state. We describe sets of quantum states for which any subset of three…
In two-party quantum communication complexity, Alice and Bob receive some classical inputs and wish to compute some function that depends on both these inputs, while minimizing the communication. This model has found numerous applications…
We prove that the existence of finite combinatorial objects such as affine planes, mutually orthogonal Latin squares, and resolvable balanced incomplete block designs can be reformulated as the existence of certain algorithmic reductions…
We present a Karchmer-Wigderson game to study the complexity of hazard-free formulas. This new game is both a generalization of the monotone Karchmer-Wigderson game and an analog of the classical Boolean Karchmer-Wigderson game. Therefore,…
We describe new lower bounds for randomized communication complexity and query complexity which we call the partition bounds. They are expressed as the optimum value of linear programs. For communication complexity we show that the…
We show a near optimal direct-sum theorem for the two-party randomized communication complexity. Let $f\subseteq X \times Y\times Z$ be a relation, $\varepsilon> 0$ and $k$ be an integer. We show,…
We show several results related to interactive proof modes of communication complexity. First we show lower bounds for the QMA-communication complexity of the functions Inner Product and Disjointness. We describe a general method to prove…
Earlier two of us (J.L. and L.P.) considered a matrix model for a two-level system interacting with a $n\times n$ reservoir and assuming that the interaction is modelled by a random matrix. We presented there a formula for the reduced…
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B…
We consider the problem of the classical simulation of quantum measurements in the scenario of communication complexity. Regev and Toner (2007) have presented a 2-bit protocol which simulates one particular correlation function arising from…