161 research outputs found
On Quantum Algorithms
Quantum computers use the quantum interference of different computational
paths to enhance correct outcomes and suppress erroneous outcomes of
computations. In effect, they follow the same logical paradigm as
(multi-particle) interferometers. We show how most known quantum algorithms,
including quantum algorithms for factorising and counting, may be cast in this
manner. Quantum searching is described as inducing a desired relative phase
between two eigenvectors to yield constructive interference on the sought
elements and destructive interference on the remaining terms.Comment: 15 pages, 8 figure
Stabilisation of Quantum Computations by Symmetrisation
We propose a method for the stabilisation of quantum computations (including
quantum state storage). The method is based on the operation of projection into
, the symmetric subspace of the full state space of redundant
copies of the computer. We describe an efficient algorithm and quantum network
effecting --projection and discuss the stabilising effect of the
proposed method in the context of unitary errors generated by hardware
imprecision, and nonunitary errors arising from external environmental
interaction. Finally, limitations of the method are discussed.Comment: 20 pages LaTeX, 2 postscript figure
Optimal Time-Reversal of Multi-phase Equatorial States
Even though the time-reversal is unphysical (it corresponds to the complex
conjugation of the density matrix), for some restricted set of states it can be
achieved unitarily, typically when there is a common de-phasing in a n-level
system. However, in the presence of multiple phases (i. e. a different
de-phasing for each element of an orthogonal basis occurs) the time reversal is
no longer physically possible. In this paper we derive the channel which
optimally approaches in fidelity the time-reversal of multi-phase equatorial
states in arbitrary (finite) dimension. We show that, in contrast to the
customary case of the Universal-NOT on qubits (or the universal conjugation in
arbitrary dimension), the optimal phase covariant time-reversal for equatorial
states is a nonclassical channel, which cannot be achieved via a
measurement/preparation procedure. Unitary realizations of the optimal
time-reversal channel are given with minimal ancillary dimension, exploiting
the simplex structure of the optimal maps.Comment: 7 pages, minor change
Quantum entanglement and classical communication through a depolarising channel
We analyse the role of entanglement for transmission of classical information
through a memoryless depolarising channel. Using the isotropic character of
this channel we prove analytically that the mutual information cannot be
increased by encoding classical bits into entangled states of two qubits.Comment: 6 pages, 2 figures; contribution to special issue of JMO on the
physics of quantum information; 2nd version: slight modifications and
improved presentatio
Experimental Purification of Single Qubits
We report the experimental realization of the purification protocol for
single qubits sent through a depolarization channel. The qubits are associated
with polarization encoded photon particles and the protocol is achieved by
means of passive linear optical elements. The present approach may represent a
convenient alternative to the distillation and error correction protocols of
quantum information.Comment: 10 pages, 2 figure
Entanglement production by quantum error correction in the presence of correlated environment
We analyze the effect of a quantum error correcting code on the entanglement
of encoded logical qubits in the presence of a dephasing interaction with a
correlated environment. Such correlated reservoir introduces entanglement
between physical qubits. We show that for short times the quantum error
correction interprets such entanglement as errors and suppresses it. However
for longer time, although quantum error correction is no longer able to correct
errors, it enhances the rate of entanglement production due to the interaction
with the environment.Comment: 7 pages, 3 figures, published versio
Dense coding with multipartite quantum states
We consider generalisations of the dense coding protocol with an arbitrary
number of senders and either one or two receivers, sharing a multiparty quantum
state, and using a noiseless channel. For the case of a single receiver, the
capacity of such information transfer is found exactly. It is shown that the
capacity is not enhanced by allowing the senders to perform joint operations.
We provide a nontrivial upper bound on the capacity in the case of two
receivers. We also give a classification of the set of all multiparty states in
terms of their usefulness for dense coding. We provide examples for each of
these classes, and discuss some of their properties.Comment: 14 pages, 1 figure, RevTeX
Qubit channels with small correlations
We introduce a class of quantum channels with correlations acting on pairs of
qubits, where the correlation takes the form of a shift operator onto a
maximally entangled state. We optimise the output purity and show that below a
certain threshold the optimum is achieved by partially entangled states whose
degree of entanglement increases monotonically with the correlation parameter.
Above this threshold, the optimum is achieved by the maximally entangled state
characterizing the shift. Although, a full analysis can only be done for the
2-norm, both numerical and heuristic arguments indicate that this behavior and
the optimal inputs are independent of p>1 when the optimal output purity is
measured using the p-norm.Comment: 11 pages, 4 figures, 2 table
Stochastic dynamics beyond the weak coupling limit: thermalization
We discuss the structure and asymptotic long-time properties of coupled
equations for the moments of a Brownian particle's momentum derived
microscopically beyond the lowest approximation in the weak coupling parameter.
Generalized fluctuation-dissipation relations are derived and shown to ensure
convergence to thermal equilibrium at any order of perturbation theory.Comment: 6+ page
Optimal universal quantum cloning and state estimation
We derive a tight upper bound for the fidelity of a universal N to M qubit
cloner, valid for any M \geq N, where the output of the cloner is required to
be supported on the symmetric subspace. Our proof is based on the concatenation
of two cloners and the connection between quantum cloning and quantum state
estimation. We generalise the operation of a quantum cloner to mixed and/or
entangled input qubits described by a density matrix supported on the symmetric
subspace of the constituent qubits. We also extend the validity of optimal
state estimation methods to inputs of this kind.Comment: 4 pages (RevTeX
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