54 research outputs found
Novel schemes for measurement-based quantum computation
We establish a framework which allows one to construct novel schemes for
measurement-based quantum computation. The technique further develops tools
from many-body physics - based on finitely correlated or projected entangled
pair states - to go beyond the cluster-state based one-way computer. We
identify resource states that are radically different from the cluster state,
in that they exhibit non-vanishing correlation functions, can partly be
prepared using gates with non-maximal entangling power, or have very different
local entanglement properties. In the computational models, the randomness is
compensated in a different manner. It is shown that there exist resource states
which are locally arbitrarily close to a pure state. Finally, we comment on the
possibility of tailoring computational models to specific physical systems as,
e.g. cold atoms in optical lattices.Comment: 5 pages RevTeX, 1 figure, many diagrams. Title changed, presentation
improved, material adde
Supersonic quantum communication
When locally exciting a quantum lattice model, the excitation will propagate
through the lattice. The effect is responsible for a wealth of non-equilibrium
phenomena, and has been exploited to transmit quantum information through spin
chains. It is a commonly expressed belief that for local Hamiltonians, any such
propagation happens at a finite "speed of sound". Indeed, the Lieb-Robinson
theorem states that in spin models, all effects caused by a perturbation are
limited to a causal cone defined by a constant speed, up to exponentially small
corrections. In this work we show that for translationally invariant bosonic
models with nearest-neighbor interactions, this belief is incorrect: We prove
that one can encounter excitations which accelerate under the natural dynamics
of the lattice and allow for reliable transmission of information faster than
any finite speed of sound. The effect is only limited by the model's range of
validity (eventually by relativity). It also implies that in non-equilibrium
dynamics of strongly correlated bosonic models far-away regions may become
quickly entangled, suggesting that their simulation may be much harder than
that of spin chains even in the low energy sector.Comment: 4+3 pages, 1 figure, some material added, typographic error fixe
NP-Hardness and Undecidability
Tensor network states constitute an important variational set of quantum
states for numerical studies of strongly correlated systems in condensed-
matter physics, as well as in mathematical physics. This is specifically true
for finitely correlated states or matrix-product operators, designed to
capture mixed states of one-dimensional quantum systems. It is a well-known
open problem to find an efficient algorithm that decides whether a given
matrix-product operator actually represents a physical state that in
particular has no negative eigenvalues. We address and answer this question by
showing that the problem is provably undecidable in the thermodynamic limit
and that the bounded version of the problem is NP-hard (nondeterministic-
polynomial-time hard) in the system size. Furthermore, we discuss numerous
connections between tensor network methods and (seemingly) different concepts
treated before in the literature, such as hidden Markov models and tensor
trains
Optimal entanglement witnesses for continuous-variable systems
This paper is concerned with all tests for continuous-variable entanglement
that arise from linear combinations of second moments or variances of canonical
coordinates, as they are commonly used in experiments to detect entanglement.
All such tests for bi-partite and multi-partite entanglement correspond to
hyperplanes in the set of second moments. It is shown that all optimal tests,
those that are most robust against imperfections with respect to some figure of
merit for a given state, can be constructed from solutions to semi-definite
optimization problems. Moreover, we show that for each such test, referred to
as entanglement witness based on second moments, there is a one-to-one
correspondence between the witness and a stronger product criterion, which
amounts to a non-linear witness, based on the same measurements. This
generalizes the known product criteria. The presented tests are all applicable
also to non-Gaussian states. To provide a service to the community, we present
the documentation of two numerical routines, FULLYWIT and MULTIWIT, which have
been made publicly available.Comment: 14 pages LaTeX, 1 figure, presentation improved, references update
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