788 research outputs found
Retrodiction of Generalised Measurement Outcomes
If a generalised measurement is performed on a quantum system and we do not
know the outcome, are we able to retrodict it with a second measurement? We
obtain a necessary and sufficient condition for perfect retrodiction of the
outcome of a known generalised measurement, given the final state, for an
arbitrary initial state. From this, we deduce that, when the input and output
Hilbert spaces have equal (finite) dimension, it is impossible to perfectly
retrodict the outcome of any fine-grained measurement (where each POVM element
corresponds to a single Kraus operator) for all initial states unless the
measurement is unitarily equivalent to a projective measurement. It also
enables us to show that every POVM can be realised in such a way that perfect
outcome retrodiction is possible for an arbitrary initial state when the number
of outcomes does not exceed the output Hilbert space dimension. We then
consider the situation where the initial state is not arbitrary, though it may
be entangled, and describe the conditions under which unambiguous outcome
retrodiction is possible for a fine-grained generalised measurement. We find
that this is possible for some state if the Kraus operators are linearly
independent. This condition is also necessary when the Kraus operators are
non-singular. From this, we deduce that every trace-preserving quantum
operation is associated with a generalised measurement whose outcome is
unambiguously retrodictable for some initial state, and also that a set of
unitary operators can be unambiguously discriminated iff they are linearly
independent. We then examine the issue of unambiguous outcome retrodiction
without entanglement. This has important connections with the theory of locally
linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review
Extraction of the D13(1520) photon-decay couplings from pion- and eta-photoproduction data
We compare results for the D13(1520) photon-decay amplitudes determined in
analyses of eta- and pion-photoproduction data. The ratio of helicity
amplitudes (A_3/2 / A_1/2), determined from eta-photoproduction data, is quite
different from that determined in previous analyses of pion-photoproduction
data. We consider how strongly the existing pion-photoproduction data constrain
both this ratio and the individual photon-decay amplitudes.Comment: 7 pages, 2 figure
The minimum-error discrimination via Helstrom family of ensembles and Convex Optimization
Using the convex optimization method and Helstrom family of ensembles
introduced in Ref. [1], we have discussed optimal ambiguous discrimination in
qubit systems. We have analyzed the problem of the optimal discrimination of N
known quantum states and have obtained maximum success probability and optimal
measurement for N known quantum states with equiprobable prior probabilities
and equidistant from center of the Bloch ball, not all of which are on the one
half of the Bloch ball and all of the conjugate states are pure. An exact
solution has also been given for arbitrary three known quantum states. The
given examples which use our method include: 1. Diagonal N mixed states; 2. N
equiprobable states and equidistant from center of the Bloch ball which their
corresponding Bloch vectors are inclined at the equal angle from z axis; 3.
Three mirror-symmetric states; 4. States that have been prepared with equal
prior probabilities on vertices of a Platonic solid.
Keywords: minimum-error discrimination, success probability, measurement,
POVM elements, Helstrom family of ensembles, convex optimization, conjugate
states PACS Nos: 03.67.Hk, 03.65.TaComment: 15 page
Entanglement and purity of two-mode Gaussian states in noisy channels
We study the evolution of purity, entanglement and total correlations of
general two--mode Gaussian states of continuous variable systems in arbitrary
uncorrelated Gaussian environments. The time evolution of purity, Von Neumann
entropy, logarithmic negativity and mutual information is analyzed for a wide
range of initial conditions. In general, we find that a local squeezing of the
bath leads to a faster degradation of purity and entanglement, while it can
help to preserve the mutual information between the modes.Comment: 10 pages, 8 figure
Resonance fluorescence of a trapped three-level atom
We investigate theoretically the spectrum of resonance fluorescence of a
harmonically trapped atom, whose internal transitions are --shaped and
driven at two-photon resonance by a pair of lasers, which cool the
center--of--mass motion. For this configuration, photons are scattered only due
to the mechanical effects of the quantum interaction between light and atom. We
study the spectrum of emission in the final stage of laser--cooling, when the
atomic center-of-mass dynamics is quantum mechanical and the size of the wave
packet is much smaller than the laser wavelength (Lamb--Dicke limit). We use
the spectral decomposition of the Liouville operator of the master equation for
the atomic density matrix and apply second order perturbation theory. We find
that the spectrum of resonance fluorescence is composed by two narrow sidebands
-- the Stokes and anti-Stokes components of the scattered light -- while all
other signals are in general orders of magnitude smaller. For very low
temperatures, however, the Mollow--type inelastic component of the spectrum
becomes visible. This exhibits novel features which allow further insight into
the quantum dynamics of the system. We provide a physical model that interprets
our results and discuss how one can recover temperature and cooling rate of the
atom from the spectrum. The behaviour of the considered system is compared with
the resonance fluorescence of a trapped atom whose internal transition consists
of two-levels.Comment: 11 pages, 4 Figure
Finding optimal strategies for minimum-error quantum-state discrimination
We propose a numerical algorithm for finding optimal measurements for
quantum-state discrimination. The theory of the semidefinite programming
provides a simple check of the optimality of the numerically obtained results.Comment: 4 pages, 2 figure
Determination of the high-twist contribution to the structure function
We extract the high-twist contribution to the neutrino-nucleon structure
function from the analysis of the data collected by
the IHEP-JINR Neutrino Detector in the runs with the focused neutrino beams at
the IHEP 70 GeV proton synchrotron. The analysis is performed within the
infrared renormalon (IRR) model of high twists in order to extract the
normalization parameter of the model. From the NLO QCD fit to our data we
obtained the value of the IRR model normalization parameter
. We
also obtained from a similar fit to the CCFR data. The average of both results is
.Comment: preprint IHEP-01-18, 7 pages, LATEX, 1 figure (EPS
Tomographic Quantum Cryptography
We present a protocol for quantum cryptography in which the data obtained for
mismatched bases are used in full for the purpose of quantum state tomography.
Eavesdropping on the quantum channel is seriously impeded by requiring that the
outcome of the tomography is consistent with unbiased noise in the channel. We
study the incoherent eavesdropping attacks that are still permissible and
establish under which conditions a secure cryptographic key can be generated.
The whole analysis is carried out for channels that transmit quantum systems of
any finite dimension.Comment: REVTeX4, 9 pages, 3 figures, 1 tabl
Optimal discrimination of mixed quantum states involving inconclusive results
We propose a generalized discrimination scheme for mixed quantum states. In
the present scenario we allow for certain fixed fraction of inconclusive
results and we maximize the success rate of the quantum-state discrimination.
This protocol interpolates between the Ivanovic-Dieks-Peres scheme and the
Helstrom one. We formulate the extremal equations for the optimal positive
operator valued measure describing the discrimination device and establish a
criterion for its optimality. We also devise a numerical method for efficient
solving of these extremal equations.Comment: 5 pages, 1 figur
Coherent dynamics of Bose-Einstein condensates in high-finesse optical cavities
We study the mutual interaction of a Bose-Einstein condensed gas with a
single mode of a high-finesse optical cavity. We show how the cavity
transmission reflects condensate properties and calculate the self-consistent
intra-cavity light field and condensate evolution. Solving the coupled
condensate-cavity equations we find that while falling through the cavity, the
condensate is adiabatically transfered into the ground state of the periodic
optical potential. This allows time dependent non-destructive measurements on
Bose-Einstein condensates with intriguing prospects for subsequent controlled
manipulation.Comment: 5 pages, 5 figures; revised version: added reference
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