20,233 research outputs found
Deterministic submanifolds and analytic solution of the stochastic differential master equation describing a qubit
This paper studies the stochastic differential equation (SDE) associated to a
two-level quantum system (qubit) subject to Hamiltonian evolution as well as
unmonitored and monitored decoherence channels. The latter imply a stochastic
evolution of the quantum state (density operator), whose associated probability
distribution we characterize. We first show that for two sets of typical
experimental settings, corresponding either to weak quantum non demolition
measurements or to weak fluorescence measurements, the three Bloch coordinates
of the qubit remain confined to a deterministically evolving surface or curve
inside the Bloch sphere. We explicitly solve the deterministic evolution, and
we provide a closed-form expression for the probability distribution on this
surface or curve. Then we relate the existence in general of such
deterministically evolving submanifolds to an accessibility question of control
theory, which can be answered with an explicit algebraic criterion on the SDE.
This allows us to show that, for a qubit, the above two sets of weak
measurements are essentially the only ones featuring deterministic surfaces or
curves
Frequent observations accelerate decay: The anti-Zeno effect
The quantum Zeno effect (QZE) is the striking prediction that the decay of
any unstable quantum state can be inhibited by sufficiently frequent
observations (measurements). The consensus opinion has upheld the QZE as a
general feature of quantum mechanics, which should lead to the inhibition of
any decay. The claim of QZE generality hinges on the assumption that successive
observations can in principle be made at time intervals too short for the
system to change appreciably. However, this assumption and the generality of
the QZE have scarcely been investigated thus far. We have addressed these
issues by showing that (i) the QZE is principally unattainable in radiative or
radioactive decay, because the required measurement rates would cause the
system to disintegrate; (ii) decay acceleration by frequent measurements (the
anti-Zeno effect -- AZE) is much more ubiquitous than its inhibition. The AZE
is shown to be observable as the enhancement of tunneling rates (e.g., for
atoms trapped in ramped-up potentials or in current-swept Josephson junctions),
fluorescence rates (e.g., for Rydberg atoms perturbed by noisy optical fields)
and photon depolarization rates (in randomly modulated Pockels cells).Comment: 8 pages, 13 figures, 1 table; revised version. Submitted to Z.
Naturforsch.
Continuous Variable Quantum Cryptography using Two-Way Quantum Communication
Quantum cryptography has been recently extended to continuous variable
systems, e.g., the bosonic modes of the electromagnetic field. In particular,
several cryptographic protocols have been proposed and experimentally
implemented using bosonic modes with Gaussian statistics. Such protocols have
shown the possibility of reaching very high secret-key rates, even in the
presence of strong losses in the quantum communication channel. Despite this
robustness to loss, their security can be affected by more general attacks
where extra Gaussian noise is introduced by the eavesdropper. In this general
scenario we show a "hardware solution" for enhancing the security thresholds of
these protocols. This is possible by extending them to a two-way quantum
communication where subsequent uses of the quantum channel are suitably
combined. In the resulting two-way schemes, one of the honest parties assists
the secret encoding of the other with the chance of a non-trivial superadditive
enhancement of the security thresholds. Such results enable the extension of
quantum cryptography to more complex quantum communications.Comment: 12 pages, 7 figures, REVTe
Optimal detection of losses by thermal probes
We consider the discrimination of lossy bosonic channels and focus to the
case when one of the values for the loss parameter is zero, i.e., we address
the detection of a possible loss against the alternative hypothesis of an ideal
lossless channel. This discrimination is performed by inputting one-mode or
two-mode squeezed thermal states with fixed total energy. By optimizing over
this class of states, we find that the optimal inputs are pure, thus
corresponding to single- and two-mode squeezed vacuum states. In particular, we
show that for any value of the damping rate smaller than a critical value there
is a threshold on the energy that makes the two-mode squeezed vacuum state more
convenient than the corresponding single-mode state, whereas for damping larger
than this critical value two-mode squeezed vacua are always better. We then
consider the discrimination in realistic conditions, where it is unlikely to
have pure squeezing. Thus by fixing both input energy and squeezing, we show
that two-mode squeezed thermal states are always better than their single- mode
counterpart when all the thermal photons are directed into the dissipative
channel. Besides, this result also holds approximately for unbalanced
distribution of the thermal photons. Finally, we also investigate the role of
correlations in the improvement of detection. For fixed input squeezing
(single-mode or two-mode), we find that the reduction of the quantum Chernoff
bound is a monotone function of the two-mode entanglement as well as the
quantum mutual information and the quantum discord. We thus verify that
employing squeezing in the form of correlations (quantum or classical) is
always a resource for loss detection whenever squeezed thermal states are taken
as input.Comment: 13 pages, 8 figures. Revised versio
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