80 research outputs found
Quantum Relative States
We study quantum state estimation problems where the reference system with
respect to which the state is measured should itself be treated quantum
mechanically. In this situation, the difference between the system and the
reference tends to fade. We investigate how the overlap between two pure
quantum states can be optimally estimated, in several scenarios, and we
re-visit homodyne detection.Comment: 10 page
Cloning and Cryptography with Quantum Continuous Variables
The cloning of quantum variables with continuous spectra is investigated. We
define a Gaussian 1-to-2 cloning machine, which copies equally well two
conjugate variables such as position and momentum or the two quadrature
components of a light mode. The resulting cloning fidelity for coherent states,
namely , is shown to be optimal. An asymmetric version of this Gaussian
cloner is then used to assess the security of a continuous-variable quantum key
distribution scheme that allows two remote parties to share a Gaussian key. The
information versus disturbance tradeoff underlying this continuous quantum
cryptographic scheme is then analyzed for the optimal individual attack.
Methods to convert the resulting Gaussian keys into secret key bits are also
studied. The extension of the Gaussian cloner to optimal -to- continuous
cloners is then discussed, and it is shown how to implement these cloners for
light modes, using a phase-insensitive optical amplifier and beam splitters.
Finally, a phase-conjugated inputs -to- continuous cloner is
defined, yielding clones and anticlones from replicas of a
coherent state and replicas of its phase-conjugate (with ).
This novel kind of cloners is shown to outperform the standard -to-
cloners in some situations.Comment: 8 pages, 3 figures, submitted to the special issue of the European
Physical Journal D on "Quantum interference and cryptographic keys: novel
physics and advancing technologies", proceedings of the conference QUICK
2001, Corsica, April 7-13 2001. Minor correction, references adde
Symmetry reduction induced by anyon condensation: a tensor network approach
Topological ordered phases are related to changes in the properties of their
quasi-particle excitations (anyons). We study these relations in the framework
of projected entanglement pair states (\textsf{PEPS}) and show how condensing
and confining anyons reduces a local gauge symmetry to a global on-site
symmetry. We also study the action of this global symmetry over the
quasiparticle excitations. As a byproduct, we observe that this symmetry
reduction effect can be applied to one-dimensional systems as well, and brings
about appealing physical interpretations on the classification of phases with
symmetries using matrix product states (\textsf{MPS}). The case of
on-site symmetry is studied in detail.Comment: 21+5 pages, 15+3 figures. Introduction and conclusions enlarged,
references and figure added, minor typos corrected, appendix about dyons
adde
Relative states, quantum axes and quantum references
We address the problem of measuring the relative angle between two "quantum
axes" made out of N1 and N2 spins. Closed forms of our fidelity-like figure of
merit are obtained for an arbitrary number of parallel spins. The asymptotic
regimes of large N1 and/or N2 are discussed in detail. The extension of the
concept "quantum axis" to more general situations is addressed. We give optimal
strategies when the first quantum axis is made out of parallel spins whereas
the second is a general state made out of two spins.Comment: 6 pages, no figure
Quantum relative states
Abstract.: We study quantum state estimation problems where the reference system with respect to which the state is measured should itself be treated quantum mechanically. In this situation, the difference between the system and the reference tends to fade. We investigate how the overlap between two pure quantum states can be optimally estimated, in several scenarios, and we re-visit homodyne detection. uantum informatio
Decoding non-Abelian topological quantum memories
The possibility of quantum computation using non-Abelian anyons has been
considered for over a decade. However the question of how to obtain and process
information about what errors have occurred in order to negate their effects
has not yet been considered. This is in stark contrast with quantum computation
proposals for Abelian anyons, for which decoding algorithms have been
tailor-made for many topological error-correcting codes and error models. Here
we address this issue by considering the properties of non-Abelian error
correction in general. We also choose a specific anyon model and error model to
probe the problem in more detail. The anyon model is the charge submodel of
. This shares many properties with important models such as the
Fibonacci anyons, making our method applicable in general. The error model is a
straightforward generalization of those used in the case of Abelian anyons for
initial benchmarking of error correction methods. It is found that error
correction is possible under a threshold value of for the total
probability of an error on each physical spin. This is remarkably comparable
with the thresholds for Abelian models
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