84 research outputs found
Cloning by positive maps in von Neumann algebras
We investigate cloning in the general operator algebra framework in arbitrary
dimension assuming only positivity instead of strong positivity of the cloning
operation, generalizing thus results obtained so far under that stronger assumption.
The weaker positivity assumption turns out quite natural when considering cloning in
the general C∗-algebra framework
Collective spin systems in dispersive optical cavity QED: Quantum phase transitions and entanglement
We propose a cavity QED setup which implements a dissipative
Lipkin-Meshkov-Glick model -- an interacting collective spin system. By varying
the external model parameters the system can be made to undergo both first-and
second-order quantum phase transitions, which are signified by dramatic changes
in cavity output field properties, such as the probe laser transmission
spectrum. The steady-state entanglement between pairs of atoms is shown to peak
at the critical points and can be experimentally determined by suitable
measurements on the cavity output field. The entanglement dynamics also
exhibits pronounced variations in the vicinities of the phase transitions.Comment: 19 pages, 18 figures, shortened versio
Einstein-Podolsky-Rosen paradox without entanglement
We claim that the nonlocality without entanglement revealed quite recently by
Bennett {\it et al.} [quant-ph/9804053] should be rather interpreted as {\it
Einstein-Podolsky-Rosen paradox without entanglement}. It would be true
nonlocality without entanglement if one knew that quantum mechnics provides the
best possible means for extracting information from physical system i.e. that
it is ``operationally complete''.Comment: RevTeX, 2 page
Dissipation-driven quantum phase transitions in collective spin systems
We consider two different collective spin systems subjected to strong
dissipation -- on the same scale as interaction strengths and external fields
-- and show that either continuous or discontinuous dissipative quantum phase
transitions can occur as the dissipation strength is varied. First, we consider
a well known model of cooperative resonance fluorescence that can exhibit a
second-order quantum phase transition, and analyze the entanglement properties
near the critical point. Next, we examine a dissipative version of the
Lipkin-Meshkov-Glick interacting collective spin model, where we find that
either first- or second-order quantum phase transitions can occur, depending
only on the ratio of the interaction and external field parameters. We give
detailed results and interpretation for the steady state entanglement in the
vicinity of the critical point, where it reaches a maximum. For the first-order
transition we find that the semiclassical steady states exhibit a region of
bistability.Comment: 12 pages, 16 figures, removed section on homodyne spectr
Fidelity for Multimode Thermal Squeezed States
In the theory of quantum transmission of information the concept of fidelity
plays a fundamental role. An important class of channels, which can be
experimentally realized in quantum optics, is that of Gaussian quantum
channels. In this work we present a general formula for fidelity in the case of
two arbitrary Gaussian states. From this formula one can get a previous result
(H. Scutaru, J. Phys. A: Mat. Gen {\bf 31}, 3659 (1998)), for the case of a
single mode; or, one can apply it to obtain a closed compact expression for
multimode thermal states.Comment: 5 pages, RevTex, submitted to Phys. Rev.
On 1-qubit channels
The entropy H_T(rho) of a state rho with respect to a channel T and the
Holevo capacity of the channel require the solution of difficult variational
problems. For a class of 1-qubit channels, which contains all the extremal
ones, the problem can be significantly simplified by associating an Hermitian
antilinear operator theta to every channel of the considered class. The
concurrence of the channel can be expressed by theta and turns out to be a flat
roof. This allows to write down an explicit expression for H_T. Its maximum
would give the Holevo (1-shot) capacity.Comment: 12 pages, several printing or latex errors correcte
Active stabilisation, quantum computation and quantum state synthesis
Active stabilisation of a quantum system is the active suppression of noise
(such as decoherence) in the system, without disrupting its unitary evolution.
Quantum error correction suggests the possibility of achieving this, but only
if the recovery network can suppress more noise than it introduces. A general
method of constructing such networks is proposed, which gives a substantial
improvement over previous fault tolerant designs. The construction permits
quantum error correction to be understood as essentially quantum state
synthesis. An approximate analysis implies that algorithms involving very many
computational steps on a quantum computer can thus be made possible.Comment: 8 pages LaTeX plus 4 figures. Submitted to Phys. Rev. Let
The geometry of entanglement: metrics, connections and the geometric phase
Using the natural connection equivalent to the SU(2) Yang-Mills instanton on
the quaternionic Hopf fibration of over the quaternionic projective space
with an fiber the geometry of
entanglement for two qubits is investigated. The relationship between base and
fiber i.e. the twisting of the bundle corresponds to the entanglement of the
qubits. The measure of entanglement can be related to the length of the
shortest geodesic with respect to the Mannoury-Fubini-Study metric on between an arbitrary entangled state, and the separable state nearest to
it. Using this result an interpretation of the standard Schmidt decomposition
in geometric terms is given. Schmidt states are the nearest and furthest
separable ones lying on, or the ones obtained by parallel transport along the
geodesic passing through the entangled state. Some examples showing the
correspondence between the anolonomy of the connection and entanglement via the
geometric phase is shown. Connections with important notions like the
Bures-metric, Uhlmann's connection, the hyperbolic structure for density
matrices and anholonomic quantum computation are also pointed out.Comment: 42 page
Numerical simulation of information recovery in quantum computers
Decoherence is the main problem to be solved before quantum computers can be
built. To control decoherence, it is possible to use error correction methods,
but these methods are themselves noisy quantum computation processes. In this
work we study the ability of Steane's and Shor's fault-tolerant recovering
methods, as well a modification of Steane's ancilla network, to correct errors
in qubits. We test a way to measure correctly ancilla's fidelity for these
methods, and state the possibility of carrying out an effective error
correction through a noisy quantum channel, even using noisy error correction
methods.Comment: 38 pages, Figures included. Accepted in Phys. Rev. A, 200
Violations of local realism with quNits up to N=16
Predictions for systems in entangled states cannot be described in local
realistic terms. However, after admixing some noise such a description is
possible. We show that for two quNits (quantum systems described by N
dimensional Hilbert spaces) in a maximally entangled state the minimal
admixture of noise increases monotonically with N. The results are a direct
extension of those of Kaszlikowski et. al., Phys. Rev. Lett. {\bf 85}, 4418
(2000), where results for were presented. The extension up to N=16 is
possible when one defines for each N a specially chosen set of observables. We
also present results concerning the critical detectors efficiency beyond which
a valid test of local realism for entangled quNits is possible.Comment: 5 pages, 3 ps picture
- …