TY  - JOUR
A1  - Müller, Markus P.
A1  - Gross, David
A1  - Eisert, Jens
T1  - Concentration of Measure for Quantum States with a Fixed Expectation Value
T2  - Communications in mathematical physics
N2  - Given some observable H on a finite-dimensional quantum system, we investigate the typical properties of random state vectors vertical bar psi >> that have a fixed expectation value < psi vertical bar H vertical bar psi > = E with respect to H. Under some conditions on the spectrum, we prove that this manifold of quantum states shows a concentration of measure phenomenon: any continuous function on this set is almost everywhere close to its mean. We also give a method to estimate the corresponding expectation values analytically, and we prove a formula for the typical reduced density matrix in the case that H is a sum of local observables. We discuss the implications of our results as new proof tools in quantum information theory and to study phenomena in quantum statistical mechanics. As a by-product, we derive a method to sample the resulting distribution numerically, which generalizes the well-known Gaussian method to draw random states from the sphere.
Y1  - 2011
UR  - https://publishup.uni-potsdam.de/frontdoor/index/index/docId/36879
SN  - 0010-3616
VL  - 303
IS  - 3
SP  - 785
EP  - 824
PB  - Springer
CY  - New York
ER  -