Results 1 
8 of
8
On causally asymmetric versions of Occam’s Razor and their relation to thermodynamics
, 2007
"... and their relation to thermodynamics ..."
(Show Context)
Superpolynomial speedups based on almost any quantum circuit
 In Proceedings of the 34th Annual ACM Symposium on Theory of Computing (STOC’02
, 2002
"... Abstract. The first separation between quantum polynomial time and classical boundederror polynomial time was due to Bernstein and Vazirani in 1993. They first showed a O(1) vs. Ω(n) quantumclassical oracle separation based on the quantum Hadamard transform, and then showed how to amplify this int ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
Abstract. The first separation between quantum polynomial time and classical boundederror polynomial time was due to Bernstein and Vazirani in 1993. They first showed a O(1) vs. Ω(n) quantumclassical oracle separation based on the quantum Hadamard transform, and then showed how to amplify this into a n O(1) time quantum algorithm and a n Ω(log n) classical query lower bound. We generalize both aspects of this speedup. We show that a wide class of unitary circuits (which we call dispersing circuits) can be used in place of Hadamards to obtain a O(1) vs. Ω(n) separation. The class of dispersing circuits includes all quantum Fourier transforms (including over nonabelian groups) as well as nearly all sufficiently long random circuits. Second, we give a general method for amplifying quantumclassical separations that allows us to achieve a n O(1) vs. n Ω(log n) separation from any dispersing circuit. 1
Universal Probability Distribution for the Wave Function of an Open Quantum System
"... An open quantum system (i.e., one that interacts with its environment) is almost always entangled with its environment; it is therefore usually not attributed a wave function but only a reduced density matrix ρ. Nevertheless, there is a precise way of attributing to it a wave function ψ1, called its ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
An open quantum system (i.e., one that interacts with its environment) is almost always entangled with its environment; it is therefore usually not attributed a wave function but only a reduced density matrix ρ. Nevertheless, there is a precise way of attributing to it a wave function ψ1, called its conditional wave function, which is a random wave function of the system whose probability distribution µ1 depends on the entangled wave function ψ ∈ H1 ⊗ H2 in the Hilbert space of system and environment together. We prove several universality (or typicality) results about µ1; they show that if the environment is sufficiently large then µ1 does not depend much on the details of ψ and is approximately given by one of the socalled GAP measures. Specifically, for most entangled states ψ with given reduced density matrix ρ1, µ1 is close to GAP (ρ1). We also show that, if the coupling between the system and the environment is weak, then for most entangled states ψ from a microcanonical subspace corresponding to energies in a narrow interval [E, E + δE] (and most bases of H2), µ1 is close to GAP (ρβ) with ρβ the canonical density matrix on H1 at inverse temperature β = β(E). This provides the mathematical justification of the claim that GAP (ρβ) is the thermal equilibrium distribution of ψ1.
Asymptotics of random density matrices Ion Nechita ∗
, 2007
"... We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random d ..."
Abstract
 Add to MetaCart
(Show Context)
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random density matrices, including convergence of the empirical spectral measure. We also study the largest eigenvalue (almost sure convergence and fluctuations). 1
Asymptotics of random density matrices Ion Nechita ∗
, 2007
"... We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random d ..."
Abstract
 Add to MetaCart
(Show Context)
We investigate random density matrices obtained by partial tracing larger random pure states. We show that there is a strong connection between these random density matrices and the Wishart ensemble of random matrix theory. We provide asymptotic results on the behavior of the eigenvalues of random density matrices, including convergence of the empirical spectral measure. We also study the largest eigenvalue (almost sure convergence and fluctuations). 1
ETH Zurich
"... The decoupling technique was originally developed for informationtheoretical purposes. It describes the conditions under which the correlations in a bipartite state disappear if one part undergoes an evolution separated from the other. In the past years there has been enormous progress in understan ..."
Abstract
 Add to MetaCart
The decoupling technique was originally developed for informationtheoretical purposes. It describes the conditions under which the correlations in a bipartite state disappear if one part undergoes an evolution separated from the other. In the past years there has been enormous progress in understanding the foundations of statistical mechanics from first principles of quantum mechanics. By use of the decoupling technique we are able to reproduce and generalize major results of this development and to approach open problems. As a first application of the decoupling technique we generalize the result of [Popescu et al., Nat. Phys. 2, 754758 (2006)] about the apparent validity of the postulate of equal a priori probabilities to states which may be correlated to a reference. We express it in a form which allows to apply recent results about random twoqubit interactions. We give a criterion for the apparent validity of the postulate which is tight up to differences between different entropy measures. Similarly, we generalize the result of [Linden et al., Phys. Rev. E 79, 061103 (2009)] about the independence of the temporal average of a quantum mechanical system of its initial