Related papers: The Entangled Quantum Polynomial Hierarchy Collaps…
Large complexity classes, like the exponential time hierarchy, received little attention in terms of finding complete problems. In this work a generalization of propositional logic is investigated which fills this gap with the introduction…
We consider one-round games between a classical referee and two players. One of the main questions in this area is the parallel repetition question: Is there a way to decrease the maximum winning probability of a game without increasing the…
This paper initiates the study of quantum computing within the constraints of using a polylogarithmic ($O(\log^k n), k\geq 1$) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has…
The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones: this leads to a frame in which two kinds of correlations emerge: the classical…
Repeated quantum game theory addresses long term relations among players who choose quantum strategies. In the conventional quantum game theory, single round quantum games or at most finitely repeated games have been widely studied, however…
A heap is a structure with a ternary operation which is intuitively a group with forgotten unit element. Quantum heaps are associative algebras with a ternary cooperation which are to the Hopf algebras what heaps are to groups, and, in…
We consider the task of verifying the correctness of quantum computation for a restricted class of circuits which contain at most two basis changes. This contains circuits giving rise to the second level of the Fourier Hierarchy, the lowest…
A line of work initiated by Terhal and DiVincenzo and Bremner, Jozsa, and Shepherd, shows that quantum computers can efficiently sample from probability distributions that cannot be exactly sampled efficiently on a classical computer,…
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…
In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
Many problems in information theory can be reduced to optimizations over matrices, where the rank of the matrices is constrained. We establish a link between rank-constrained optimization and the theory of quantum entanglement. More…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems,…
Quantum key distribution (QKD) allows Alice and Bob to share a secret key over an insecure channel with proven information-theoretic security against an adversary whose strategy is bounded only by the laws of physics. Composability-based…
We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either 'win' or 'lose'. Molina and…
A precise physical description and understanding of the classical dual content of quantum theory is necessary in many disciplines today: from concepts and interpretation to quantum technologies and computation. In this paper we investigate…
It is well known that quantum, randomized and deterministic (sequential) query complexities are polynomially related for total boolean functions. We find that significantly larger separations between the parallel generalizations of these…
We show that combining two different hypothetical enhancements to quantum computation---namely, quantum advice and non-collapsing measurements---would let a quantum computer solve any decision problem whatsoever in polynomial time, even…
We prove a general lower bound of quantum decision tree complexity in terms of some entropy notion. We regard the computation as a communication process in which the oracle and the computer exchange several rounds of messages, each round…
This work addresses the complexities involved in designing distributed quantum algorithms, highlighting that quantum entanglement does not bypass the Fischer-Lynch-Paterson (FLP) impossibility theorem in asynchronous networks. Although…