493 research outputs found
Multiparticle entanglement and its experimental detection
We discuss several aspects of multiparticle mixed state entanglement and its
experimental detection. First we consider entanglement between two particles
which is robust against disposals of other particles. To completely detect
these kinds of entanglement, full knowledge of the multiparticle density matrix
(or of all reduced density matrixes) is required. Then we review the relation
of the separability properties of l-partite splittings of a state to its
multipartite entanglement properties. We show that it suffices to determine the
diagonal matrix elements of in a certain basis in order to detect
multiparticle entanglement properties of . We apply these observations to
analyze two recent experiments, where multiparticle entangled states of 3 (4)
particles were produced. Finally, we focus on bound entangled states
(non-separable, non-distillable states) and show that they can be activated by
joint actions of the parties. We also provide several examples which show the
activation of bound entanglement with bound entanglement.Comment: 9 pages, no figures; submitted to The Journal of Physics A:
Mathematical and General, special issue in Quantum Information and
Computatio
Activating bound entanglement in multi-particle systems
We analyze the existence of activable bound entangled states in
multi-particle systems. We first give a series of examples which illustrate
some different ways in which bound entangled states can be activated by letting
some of the parties to share maximally entangled states. Then, we derive
necessary conditions for a state to be distillable as well as to be activable.
These conditions turn out to be also sufficient for a certain family of
multi-qubit states. We use these results to explicitely to construct states
displaying novel properties related to bound entanglement and its activation.Comment: 8 pages, 3 figure
Remote operations and interactions for systems of arbitrary dimensional Hilbert space: a state-operator approach
We present a systematic simple method for constructing deterministic remote
operations on single and multiple systems of arbitrary discrete dimensionality.
These operations include remote rotations, remote interactions and
measurements. The resources needed for an operation on a two-level system are
one ebit and a bidirectional communication of two cbits, and for an n-level
system, a pair of entangled n-level particles and two classical ``nits''. In
the latter case, there are possible distinct operations per one n-level
entangled pair. Similar results apply for generating interaction between a pair
of remote systems and for remote measurements. We further consider remote
operations on spatially distributed systems, and show that the number of
possible distinct operations increases here exponentially, with the available
number of entangled pairs that are initial distributed between the systems. Our
results follow from the properties of a hybrid state-operator object
(``stator''), which describes quantum correlations between states and
operations.Comment: 18 pages, 3 figures, typo correction
Multipartite bound entangled states that violate Bell's inequality
We study the relation between distillability of multipartite states and
violation of Bell's inequality. We prove that there exist multipartite bound
entangled states (i.e. non-separable, non-distillable states) that violate a
multipartite Bell inequality. This implies that (i) violation of Bell's
inequality is not a sufficient condition for distillability and (ii) some bound
entangled states cannot be described by a local hidden variable model.Comment: 4 pages, no figure
Non-local Operations: Purification, storage, compression, tomography, and probabilistic implementation
We provide several applications of a previously introduced isomorphism
between physical operations acting on two systems and entangled states [1]. We
show: (i) how to implement (weakly) non-local two qubit unitary operations with
a small amount of entanglement; (ii) that a known, noisy, non-local unitary
operation as well as an unknown, noisy, local unitary operation can be
purified; (iii) how to perform the tomography of arbitrary, unknown, non-local
operations; (iv) that a set of local unitary operations as well as a set of
non-local unitary operations can be stored and compressed; (v) how to implement
probabilistically two-qubit gates for photons. We also show how to compress a
set of bipartite entangled states locally, as well as how to implement certain
non-local measurements using a small amount of entanglement. Finally, we
generalize some of our results to multiparty systems.Comment: 15 pages, no figure
Completeness of the classical 2D Ising model and universal quantum computation
We prove that the 2D Ising model is complete in the sense that the partition
function of any classical q-state spin model (on an arbitrary graph) can be
expressed as a special instance of the partition function of a 2D Ising model
with complex inhomogeneous couplings and external fields. In the case where the
original model is an Ising or Potts-type model, we find that the corresponding
2D square lattice requires only polynomially more spins w.r.t the original one,
and we give a constructive method to map such models to the 2D Ising model. For
more general models the overhead in system size may be exponential. The results
are established by connecting classical spin models with measurement-based
quantum computation and invoking the universality of the 2D cluster states.Comment: 4 pages, 1 figure. Minor change
Universal quantum computer from a quantum magnet
We show that a local Hamiltonian of spin-3/2 particles with only two-body
nearest-neighbor Affleck-Kennedy-Lieb-Tasaki and exchange-type interactions has
an unique ground state, which can be used to implement universal quantum
computation merely with single-spin measurements. We prove that the Hamiltonian
is gapped, independent of the system size. Our result provides a further step
towards utilizing systems with condensed matter-type interactions for
measurement-based quantum computation.Comment: 5 pages, 3 figure
Multiparticle entanglement purification for two-colorable graph states
We investigate multiparticle entanglement purification schemes which allow
one to purify all two colorable graph states, a class of states which includes
e.g. cluster states, GHZ states and codewords of various error correction
codes. The schemes include both recurrence protocols and hashing protocols. We
analyze these schemes under realistic conditions and observe for a generic
error model that the threshold value for imperfect local operations depends on
the structure of the corresponding interaction graph, but is otherwise
independent of the number of parties. The qualitative behavior can be
understood from an analytically solvable model which deals only with a
restricted class of errors. We compare direct multiparticle entanglement
purification protocols with schemes based on bipartite entanglement
purification and show that the direct multiparticle entanglement purification
is more efficient and the achievable fidelity of the purified states is larger.
We also show that the purification protocol allows one to produce private
entanglement, an important aspect when using the produced entangled states for
secure applications. Finally we discuss an experimental realization of a
multiparty purification protocol in optical lattices which is issued to improve
the fidelity of cluster states created in such systems.Comment: 22 pages, 8 figures; replaced with published versio
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