19 research outputs found
Combinatorial Topology Of Multipartite Entangled States
With any state of a multipartite quantum system its separability polytope is
associated. This is an algebro-topological object (non-trivial only for mixed
states) which captures the localisation of entanglement of the state.
Particular examples of separability polytopes for 3-partite systems are
explicitly provided. It turns out that this characterisation of entanglement is
associated with simulation of arbitrary unitary operations by 1- and 2-qubit
gates. A topological description of how entanglement changes in course of such
simulation is provided.Comment: 14 pages, LaTeX2e. Slightly revised version of the poster resented on
the International Conference on Quantum Information, Oviedo, Spain, 13-18
July, 2002. To appear in the special issue of Journal of Modern Optic
Husimi coordinates of multipartite separable states
A parametrization of multipartite separable states in a finite-dimensional
Hilbert space is suggested. It is proved to be a diffeomorphism between the set
of zero-trace operators and the interior of the set of separable density
operators. The result is applicable to any tensor product decomposition of the
state space. An analytical criterion for separability of density operators is
established in terms of the boundedness of a sequence of operators.Comment: 19 pages, 1 figure, LaTe
How `hot' are mixed quantum states?
Given a mixed quantum state of a qudit, we consider any observable
as a kind of `thermometer' in the following sense. Given a source which emits
pure states with these or those distributions, we select such distributions
that the appropriate average value of the observable is equal to the
average Tr of in the stare . Among those distributions we find
the most typical one, namely, having the highest differential entropy. We call
this distribution conditional Gibbs ensemble as it turns out to be a Gibbs
distribution characterized by a temperature-like parameter . The
expressions establishing the liaisons between the density operator and
its temperature parameter are provided. Within this approach, the
uniform mixed state has the highest `temperature', which tends to zero as the
state in question approaches to a pure state.Comment: Contribution to Quantum 2006: III workshop ad memoriam of Carlo
Novero: Advances in Foundations of Quantum Mechanics and Quantum Information
with atoms and photons. 2-5 May 2006 - Turin, Ital
Spacetime topology from the tomographic histories approach I: Non-relativistic Case
The tomographic histories approach is presented. As an inverse problem, we
recover in an operational way the effective topology of the extended
configuration space of a system. This means that from a series of experiments
we get a set of points corresponding to events. The difference between
effective and actual topology is drawn. We deduce the topology of the extended
configuration space of a non-relativistic system, using certain concepts from
the consistent histories approach to Quantum Mechanics, such as the notion of a
record. A few remarks about the case of a relativistic system, preparing the
ground for a forthcoming paper sequel to this, are made in the end.Comment: 19 pages, slight chang in title and corrected typos in second
version. To appear to a special proceedings issue (Glafka 2004) of the
International Journal of Theoretical Physic
Backpropagation training in adaptive quantum networks
We introduce a robust, error-tolerant adaptive training algorithm for
generalized learning paradigms in high-dimensional superposed quantum networks,
or \emph{adaptive quantum networks}. The formalized procedure applies standard
backpropagation training across a coherent ensemble of discrete topological
configurations of individual neural networks, each of which is formally merged
into appropriate linear superposition within a predefined, decoherence-free
subspace. Quantum parallelism facilitates simultaneous training and revision of
the system within this coherent state space, resulting in accelerated
convergence to a stable network attractor under consequent iteration of the
implemented backpropagation algorithm. Parallel evolution of linear superposed
networks incorporating backpropagation training provides quantitative,
numerical indications for optimization of both single-neuron activation
functions and optimal reconfiguration of whole-network quantum structure.Comment: Talk presented at "Quantum Structures - 2008", Gdansk, Polan
Spacetime topology from the tomographic histories approach: Part II
As an inverse problem, we recover the topology of the effective spacetime
that a system lies in, in an operational way. This means that from a series of
experiments we get a set of points corresponding to events. This continues the
previous work done by the authors. Here we use the existence of upper bound in
the speed of transfer of matter and information to induce a partial order on
the set of events. While the actual partial order is not known in our
operational set up, the grouping of events to (unordered) subsets corresponding
to possible histories, is given. From this we recover the partial order up to
certain ambiguities that are then classified. Finally two different ways to
recover the topology are sketched and their interpretation is discussed.Comment: 21 pages, slight change in title and certain minor corrections in
this second version. To apear in IJT