57,382 research outputs found
All multipartite Bell correlation inequalities for two dichotomic observables per site
We construct a set of 2^(2^n) independent Bell correlation inequalities for
n-partite systems with two dichotomic observables each, which is complete in
the sense that the inequalities are satisfied if and only if the correlations
considered allow a local classical model. All these inequalities can be
summarized in a single, albeit non-linear inequality. We show that quantum
correlations satisfy this condition provided the state has positive partial
transpose with respect to any grouping of the n systems into two subsystems. We
also provide an efficient algorithm for finding the maximal quantum mechanical
violation of each inequality, and show that the maximum is always attained for
the generalized GHZ state.Comment: 11 pages, REVTe
Aspects of generic entanglement
We study entanglement and other correlation properties of random states in
high-dimensional bipartite systems. These correlations are quantified by
parameters that are subject to the "concentration of measure" phenomenon,
meaning that on a large-probability set these parameters are close to their
expectation. For the entropy of entanglement, this has the counterintuitive
consequence that there exist large subspaces in which all pure states are close
to maximally entangled. This, in turn, implies the existence of mixed states
with entanglement of formation near that of a maximally entangled state, but
with negligible quantum mutual information and, therefore, negligible
distillable entanglement, secret key, and common randomness. It also implies a
very strong locking effect for the entanglement of formation: its value can
jump from maximal to near zero by tracing over a number of qubits negligible
compared to the size of total system. Furthermore, such properties are generic.
Similar phenomena are observed for random multiparty states, leading us to
speculate on the possibility that the theory of entanglement is much simplified
when restricted to asymptotically generic states. Further consequences of our
results include a complete derandomization of the protocol for universal
superdense coding of quantum states.Comment: 22 pages, 1 figure, 1 tabl
Time scale for adiabaticity breakdown in driven many-body systems and orthogonality catastrophe
The adiabatic theorem is a fundamental result established in the early days
of quantum mechanics, which states that a system can be kept arbitrarily close
to the instantaneous ground state of its Hamiltonian if the latter varies in
time slowly enough. The theorem has an impressive record of applications
ranging from foundations of quantum field theory to computational recipes in
molecular dynamics. In light of this success it is remarkable that a
practicable quantitative understanding of what "slowly enough" means is limited
to a modest set of systems mostly having a small Hilbert space. Here we show
how this gap can be bridged for a broad natural class of physical systems,
namely many-body systems where a small move in the parameter space induces an
orthogonality catastrophe. In this class, the conditions for adiabaticity are
derived from the scaling properties of the parameter dependent ground state
without a reference to the excitation spectrum. This finding constitutes a
major simplification of a complex problem, which otherwise requires solving
non-autonomous time evolution in a large Hilbert space. We illustrate our
general results by analyzing conditions for the transport quantization in a
topological Thouless pump
H\"older-type inequalities and their applications to concentration and correlation bounds
Let be -valued random variables having a dependency
graph . We show that where is the -fold chromatic number
of . This inequality may be seen as a dependency-graph analogue of a
generalised H\"older inequality, due to Helmut Finner. Additionally, we provide
applications of H\"older-type inequalities to concentration and correlation
bounds for sums of weakly dependent random variables.Comment: 15 page
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