379 research outputs found
Continuity bounds on the quantum relative entropy
The quantum relative entropy is frequently used as a distance, or
distinguishability measure between two quantum states. In this paper we study
the relation between this measure and a number of other measures used for that
purpose, including the trace norm distance. More precisely, we derive lower and
upper bounds on the relative entropy in terms of various distance measures for
the difference of the states based on unitarily invariant norms. The upper
bounds can be considered as statements of continuity of the relative entropy
distance in the sense of Fannes. We employ methods from optimisation theory to
obtain bounds that are as sharp as possible.Comment: 13 pages (ReVTeX), 3 figures, replaced with published versio
A quantum central limit theorem for non-equilibrium systems: Exact local relaxation of correlated states
We prove that quantum many-body systems on a one-dimensional lattice locally
relax to Gaussian states under non-equilibrium dynamics generated by a bosonic
quadratic Hamiltonian. This is true for a large class of initial states - pure
or mixed - which have to satisfy merely weak conditions concerning the decay of
correlations. The considered setting is a proven instance of a situation where
dynamically evolving closed quantum systems locally appear as if they had truly
relaxed, to maximum entropy states for fixed second moments. This furthers the
understanding of relaxation in suddenly quenched quantum many-body systems. The
proof features a non-commutative central limit theorem for non-i.i.d. random
variables, showing convergence to Gaussian characteristic functions, giving
rise to trace-norm closeness. We briefly relate our findings to ideas of
typicality and concentration of measure.Comment: 27 pages, final versio
Dynamics of entanglement of bosonic modes on symmetric graphs
We investigate the dynamics of an initially disentangled Gaussian state on a
general finite symmetric graph. As concrete examples we obtain properties of
this dynamics on mean field graphs of arbitrary sizes. In the same way that
chains can be used for transmitting entanglement by their natural dynamics,
these graphs can be used to store entanglement. We also consider two kinds of
regular polyhedron which show interesting features of entanglement sharing.Comment: 14 pages, 11 figures, Accepted for publication in Physics Letters
Measurement-based quantum computation beyond the one-way model
We introduce novel schemes for quantum computing based on local measurements
on entangled resource states. This work elaborates on the framework established
in [Phys. Rev. Lett. 98, 220503 (2007), quant-ph/0609149]. Our method makes use
of tools from many-body physics - matrix product states, finitely correlated
states or projected entangled pairs states - to show how measurements on
entangled states can be viewed as processing quantum information. This work
hence constitutes an instance where a quantum information problem - how to
realize quantum computation - was approached using tools from many-body theory
and not vice versa. We give a more detailed description of the setting, and
present a large number of new examples. We find novel computational schemes,
which differ from the original one-way computer for example in the way the
randomness of measurement outcomes is handled. Also, schemes are presented
where the logical qubits are no longer strictly localized on the resource
state. Notably, we find a great flexibility in the properties of the universal
resource states: They may for example exhibit non-vanishing long-range
correlation functions or be locally arbitrarily close to a pure state. We
discuss variants of Kitaev's toric code states as universal resources, and
contrast this with situations where they can be efficiently classically
simulated. This framework opens up a way of thinking of tailoring resource
states to specific physical systems, such as cold atoms in optical lattices or
linear optical systems.Comment: 21 pages, 7 figure
Multi-mode bosonic Gaussian channels
A complete analysis of multi-mode bosonic Gaussian channels is proposed. We
clarify the structure of unitary dilations of general Gaussian channels
involving any number of bosonic modes and present a normal form. The maximum
number of auxiliary modes that is needed is identified, including all rank
deficient cases, and the specific role of additive classical noise is
highlighted. By using this analysis, we derive a canonical matrix form of the
noisy evolution of n-mode bosonic Gaussian channels and of their weak
complementary counterparts, based on a recent generalization of the normal mode
decomposition for non-symmetric or locality constrained situations. It allows
us to simplify the weak-degradability classification. Moreover, we investigate
the structure of some singular multi-mode channels, like the additive classical
noise channel that can be used to decompose a noisy channel in terms of a less
noisy one in order to find new sets of maps with zero quantum capacity.
Finally, the two-mode case is analyzed in detail. By exploiting the composition
rules of two-mode maps and the fact that anti-degradable channels cannot be
used to transfer quantum information, we identify sets of two-mode bosonic
channels with zero capacity.Comment: 37 pages, 3 figures (minor editing), accepted for publication in New
Journal of Physic
Many-Body Localization Implies that Eigenvectors are Matrix-Product States
The phenomenon of many-body localization has received a lot of attention
recently, both for its implications in condensed-matter physics of allowing
systems to be an insulator even at nonzero temperature as well as in the
context of the foundations of quantum statistical mechanics, providing
examples of systems showing the absence of thermalization following out-of-
equilibrium dynamics. In this work, we establish a novel link between
dynamical properties—a vanishing group velocity and the absence of
transport—with entanglement properties of individual eigenvectors. For systems
with a generic spectrum, we prove that strong dynamical localization implies
that all of its many-body eigenvectors have clustering correlations. The same
is true for parts of the spectrum, thus allowing for the existence of a
mobility edge above which transport is possible. In one dimension these
results directly imply an entanglement area law; hence, the eigenvectors can
be efficiently approximated by matrix-product states
Dynamics and manipulation of entanglement in coupled harmonic systems with many degrees of freedom
Published versio
Diagnosing Topological Edge States via Entanglement Monogamy
Topological phases of matter possess intricate correlation patterns typically probed by entanglement entropies or entanglement spectra. In this Letter, we propose an alternative approach to assessing topologically induced edge states in free and interacting fermionic systems. We do so by focussing on the fermionic covariance matrix. This matrix is often tractable either analytically or numerically, and it precisely captures the relevant correlations of the system. By invoking the concept of monogamy of entanglement, we show that highly entangled states supported across a system bipartition are largely disentangled from the rest of the system, thus, usually appearing as gapless edge states. We then define an entanglement qualifier that identifies the presence of topological edge states based purely on correlations present in the ground states. We demonstrate the versatility of this qualifier by applying it to various free and interacting fermionic topological systems
Geometric measure of entanglement and applications to bipartite and multipartite quantum states
The degree to which a pure quantum state is entangled can be characterized by
the distance or angle to the nearest unentangled state. This geometric measure
of entanglement, already present in a number of settings (see Shimony 1995 and
Barnum and Linden 2001), is explored for bipartite and multipartite pure and
mixed states. The measure is determined analytically for arbitrary two-qubit
mixed states and for generalized Werner and isotropic states, and is also
applied to certain multipartite mixed states. In particular, a detailed
analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W
states. Along the way, we point out connections of the geometric measure of
entanglement with entanglement witnesses and with the Hartree approximation
method.Comment: 13 pages, 11 figures, this is a combination of three previous
manuscripts (quant-ph/0212030, quant-ph/0303079, and quant-ph/0303158) made
more extensive and coherent. To appear in PR
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