56 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
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
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
Entropy and Exact Matrix Product Representation of the Laughlin Wave Function
An analytical expression for the von Neumann entropy of the Laughlin wave
function is obtained for any possible bipartition between the particles
described by this wave function, for filling fraction nu=1. Also, for filling
fraction nu=1/m, where m is an odd integer, an upper bound on this entropy is
exhibited. These results yield a bound on the smallest possible size of the
matrices for an exact representation of the Laughlin ansatz in terms of a
matrix product state. An analytical matrix product state representation of this
state is proposed in terms of representations of the Clifford algebra. For
nu=1, this representation is shown to be asymptotically optimal in the limit of
a large number of particles
Entanglement entropy in fermionic Laughlin states
We present analytic and numerical calculations on the bipartite entanglement
entropy in fractional quantum Hall states of the fermionic Laughlin sequence.
The partitioning of the system is done both by dividing Landau level orbitals
and by grouping the fermions themselves. For the case of orbital partitioning,
our results can be related to spatial partitioning, enabling us to extract a
topological quantity (the `total quantum dimension') characterizing the
Laughlin states. For particle partitioning we prove a very close upper bound
for the entanglement entropy of a subset of the particles with the rest, and
provide an interpretation in terms of exclusion statistics.Comment: 4+ pages, 3 figures. Minor changes in v
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