30 research outputs found
Separability and distillability in composite quantum systems -a primer-
Quantum mechanics is already 100 years old, but remains alive and full of
challenging open problems. On one hand, the problems encountered at the
frontiers of modern theoretical physics like Quantum Gravity, String Theories,
etc. concern Quantum Theory, and are at the same time related to open problems
of modern mathematics. But even within non-relativistic quantum mechanics
itself there are fundamental unresolved problems that can be formulated in
elementary terms. These problems are also related to challenging open questions
of modern mathematics; linear algebra and functional analysis in particular.
Two of these problems will be discussed in this article: a) the separability
problem, i.e. the question when the state of a composite quantum system does
not contain any quantum correlations or entanglement and b) the distillability
problem, i.e. the question when the state of a composite quantum system can be
transformed to an entangled pure state using local operations (local refers
here to component subsystems of a given system).
Although many results concerning the above mentioned problems have been
obtained (in particular in the last few years in the framework of Quantum
Information Theory), both problems remain until now essentially open. We will
present a primer on the current state of knowledge concerning these problems,
and discuss the relation of these problems to one of the most challenging
questions of linear algebra: the classification and characterization of
positive operator maps.Comment: 11 pages latex, 1 eps figure. Final version, to appear in J. Mod.
Optics, minor typos corrected, references adde
Concurrence classes for general pure multipartite states
We propose concurrence classes for general pure multipartite states based on
an orthogonal complement of a positive operator valued measure on quantum
phase. In particular, we construct class, , and
class concurrences for general pure -partite states. We give explicit
expressions for and class concurrences for general pure
three-partite states and for , , and class
concurrences for general pure four-partite states.Comment: 14 page
Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
In this paper, we propose concurrence classes for an arbitrary multi-qubit
state based on orthogonal complement of a positive operator valued measure, or
POVM in short, on quantum phase. In particular, we construct concurrence for an
arbitrary two-qubit state and concurrence classes for the three- and four-qubit
states. And finally, we construct and class concurrences for
multi-qubit states. The unique structure of our POVM enables us to distinguish
different concurrence classes for multi-qubit states.Comment: 8 page
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