13 research outputs found
Optimal local discrimination of two multipartite pure states
In a recent paper, Walgate et. al. demonstrated that any two orthogonal
multipartite pure states can be optimally distinguished using only local
operations. We utilise their result to show that this is true for any two
multiparty pure states, in the sense of inconclusive discrimination. There are
also certain regimes of conclusive discrimination for which the same also
applies, although we can only conjecture that the result is true for all
conclusive regimes. We also discuss a class of states that can be distinguished
locally according to any discrimination measure, as they can be locally
recreated in the hands of one party. A consequence of this is that any two
maximally entangled states can always be optimally discriminated locally,
according to any figure of merit.Comment: Published version, results unchanged, although errors in the last
proof have been correcte
Constructing Entanglement Witness Via Real Skew-Symmetric Operators
In this work, new types of EWs are introduced. They are constructed by using
real skew-symmetric operators defined on a single party subsystem of a
bipartite dxd system and a maximal entangled state in that system. A canonical
form for these witnesses is proposed which is called canonical EW in
corresponding to canonical real skew-symmetric operator. Also for each possible
partition of the canonical real skew-symmetric operator corresponding EW is
obtained. The method used for dxd case is extended to d1xd2 systems. It is
shown that there exist Cd2xd1 distinct possibilities to construct EWs for a
given d1xd2 Hilbert space. The optimality and nd-optimality problem is studied
for each type of EWs. In each step, a large class of quantum PPT states is
introduced. It is shown that among them there exist entangled PPT states which
are detected by the constructed witnesses. Also the idea of canonical EWs is
extended to obtain other EWs with greater PPT entanglement detection power.Comment: 40 page
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
A Geometric Picture of Entanglement and Bell Inequalities
We work in the real Hilbert space H_s of hermitian Hilbert-Schmid operators
and show that the entanglement witness which shows the maximal violation of a
generalized Bell inequality (GBI) is a tangent functional to the convex set S
subset H_s of separable states. This violation equals the euclidean distance in
H_s of the entangled state to S and thus entanglement, GBI and tangent
functional are only different aspects of the same geometric picture. This is
explicitly illustrated in the example of two spins, where also a comparison
with familiar Bell inequalities is presented.Comment: 17 pages, 5 figures, 4 references adde
Many body physics from a quantum information perspective
The quantum information approach to many body physics has been very
successful in giving new insight and novel numerical methods. In these lecture
notes we take a vertical view of the subject, starting from general concepts
and at each step delving into applications or consequences of a particular
topic. We first review some general quantum information concepts like
entanglement and entanglement measures, which leads us to entanglement area
laws. We then continue with one of the most famous examples of area-law abiding
states: matrix product states, and tensor product states in general. Of these,
we choose one example (classical superposition states) to introduce recent
developments on a novel quantum many body approach: quantum kinetic Ising
models. We conclude with a brief outlook of the field.Comment: Lectures from the Les Houches School on "Modern theories of
correlated electron systems". Improved version new references adde
Generalizations of entanglement based on coherent states and convex sets
Unentangled pure states on a bipartite system are exactly the coherent states
with respect to the group of local transformations. What aspects of the study
of entanglement are applicable to generalized coherent states? Conversely, what
can be learned about entanglement from the well-studied theory of coherent
states? With these questions in mind, we characterize unentangled pure states
as extremal states when considered as linear functionals on the local Lie
algebra. As a result, a relativized notion of purity emerges, showing that
there is a close relationship between purity, coherence and (non-)entanglement.
To a large extent, these concepts can be defined and studied in the even more
general setting of convex cones of states. Based on the idea that entanglement
is relative, we suggest considering these notions in the context of partially
ordered families of Lie algebras or convex cones, such as those that arise
naturally for multipartite systems. The study of entanglement includes notions
of local operations and, for information-theoretic purposes, entanglement
measures and ways of scaling systems to enable asymptotic developments. We
propose ways in which these may be generalized to the Lie-algebraic setting,
and to a lesser extent to the convex-cones setting. One of our original
motivations for this program is to understand the role of entanglement-like
concepts in condensed matter. We discuss how our work provides tools for
analyzing the correlations involved in quantum phase transitions and other
aspects of condensed-matter systems.Comment: 37 page
Entanglement, Bell Inequalities and Decoherence in Particle Physics
We demonstrate the relevance of entanglement, Bell inequalities and
decoherence in particle physics. In particular, we study in detail the features
of the ``strange'' system as an example of entangled
meson--antimeson systems. The analogies and differences to entangled spin--1/2
or photon systems are worked, the effects of a unitary time evolution of the
meson system is demonstrated explicitly. After an introduction we present
several types of Bell inequalities and show a remarkable connection to CP
violation. We investigate the stability of entangled quantum systems pursuing
the question how possible decoherence might arise due to the interaction of the
system with its ``environment''. The decoherence is strikingly connected to the
entanglement loss of common entanglement measures. Finally, some outlook of the
field is presented.Comment: Lectures given at Quantum Coherence in Matter: from Quarks to Solids,
42. Internationale Universit\"atswochen f\"ur Theoretische Physik,
Schladming, Austria, Feb. 28 -- March 6, 2004, submitted to Lecture Notes in
Physics, Springer Verlag, 45 page
Disorder-assisted error correction in Majorana chains
It was recently realized that quenched disorder may enhance the reliability
of topological qubits by reducing the mobility of anyons at zero temperature.
Here we compute storage times with and without disorder for quantum chains with
unpaired Majorana fermions - the simplest toy model of a quantum memory.
Disorder takes the form of a random site-dependent chemical potential. The
corresponding one-particle problem is a one-dimensional Anderson model with
disorder in the hopping amplitudes. We focus on the zero-temperature storage of
a qubit encoded in the ground state of the Majorana chain. Storage and
retrieval are modeled by a unitary evolution under the memory Hamiltonian with
an unknown weak perturbation followed by an error-correction step. Assuming
dynamical localization of the one-particle problem, we show that the storage
time grows exponentially with the system size. We give supporting evidence for
the required localization property by estimating Lyapunov exponents of the
one-particle eigenfunctions. We also simulate the storage process for chains
with a few hundred sites. Our numerical results indicate that in the absence of
disorder, the storage time grows only as a logarithm of the system size. We
provide numerical evidence for the beneficial effect of disorder on storage
times and show that suitably chosen pseudorandom potentials can outperform
random ones.Comment: 50 pages, 7 figure
Finite-time destruction of entanglement and non-locality by environmental influences
Entanglement and non-locality are non-classical global characteristics of
quantum states important to the foundations of quantum mechanics. Recent
investigations have shown that environmental noise, even when it is entirely
local in influence, can destroy both of these properties in finite time despite
giving rise to full quantum state decoherence only in the infinite time limit.
These investigations, which have been carried out in a range of theoretical and
experimental situations, are reviewed here.Comment: 27 pages, 6 figures, review article to appear in Foundations of
Physic