318 research outputs found
Entanglement assisted alignment of reference frames using a dense covariant coding
We present a procedure inspired by dense coding, which enables a highly
efficient transmission of information of a continuous nature. The procedure
requires the sender and the recipient to share a maximally entangled state. We
deal with the concrete problem of aligning reference frames or trihedra by
means of a quantum system. We find the optimal covariant measurement and
compute the corresponding average error, which has a remarkably simple close
form. The connection of this procedure with that of estimating unitary
transformations on qubits is briefly discussed.Comment: 4 pages, RevTeX, Version to appear in PR
Probabilistic metrology or how some measurement outcomes render ultra-precise estimates
We show on theoretical grounds that, even in the presence of noise,
probabilistic measurement strategies (which have a certain probability of
failure or abstention) can provide, upon a heralded successful outcome,
estimates with a precision that exceeds the deterministic bounds for the
average precision. This establishes a new ultimate bound on the phase
estimation precision of particular measurement outcomes (or sequence of
outcomes). For probe systems subject to local dephasing, we quantify such
precision limit as a function of the probability of failure that can be
tolerated. Our results show that the possibility of abstaining can set back the
detrimental effects of noise.Comment: Improved version of arXiv:1407.6910 with an extended introduction
where we clarify our approach to metrology, and probabilistic metrology in
particular. Changed titl
Communication of Spin Directions with Product States and Finite Measurements
Total spin eigenstates can be used to intrinsically encode a direction, which
can later be decoded by means of a quantum measurement. We study the optimal
strategy that can be adopted if, as is likely in practical applications, only
product states of -spins are available. We obtain the asymptotic behaviour
of the average fidelity which provides a proof that the optimal states must be
entangled. We also give a prescription for constructing finite measurements for
general encoding eigenstates.Comment: 4 pages, minor changes, version to appear in PR
Optimal full estimation of qubit mixed states
We obtain the optimal scheme for estimating unknown qubit mixed states when
an arbitrary number N of identically prepared copies is available. We discuss
the case of states in the whole Bloch sphere as well as the restricted
situation where these states are known to lie on the equatorial plane. For the
former case we obtain that the optimal measurement does not depend on the prior
probability distribution provided it is isotropic. Although the
equatorial-plane case does not have this property for arbitrary N, we give a
prior-independent scheme which becomes optimal in the asymptotic limit of large
N. We compute the maximum mean fidelity in this asymptotic regime for the two
cases. We show that within the pointwise estimation approach these limits can
be obtained in a rather easy and rapid way. This derivation is based on
heuristic arguments that are made rigorous by using van Trees inequalities. The
interrelation between the estimation of the purity and the direction of the
state is also discussed. In the general case we show that they correspond to
independent estimations whereas for the equatorial-plane states this is only
true asymptotically.Comment: 19 pages, no figure
Bell's theorem without inequalities and without unspeakable information
A proof of Bell's theorem without inequalities is presented in which distant
local setups do not need to be aligned, since the required perfect correlations
are achieved for any local rotation of the local setups.Comment: REVTeX4, 4 pages, 1 figure; for Asher Peres' Festschrift, to be
published in Found. Phy
Hadrons with Charm and Beauty
By combining potential models and QCD spectral sum rules (QSSR), we discuss
the spectroscopy of the mesons and of the , and
baryons ( or ), the decay constant and the
(semi)leptonic decay modes of the meson. For the masses, the best
predictions come from potential models and read: ~MeV,
~MeV, ~GeV,
~GeV, ~GeV
and ~GeV. The decay constant is well determined from QSSR and leads to:
s.The uses of the vertex sum rules for the semileptonic decays of the
show that the -dependence of the form factors is much stronger than
predicted by vector meson dominance. It also predicts the almost equal strength
of about 0.30 sec for the semileptonic rates into
and J/. Besides these phenomenological results, we
also show explicitly how the Wilson coefficients of the and gluon condensates already contain the full
heavy quark- () and mixed- ()
condensate contributions in the OPE.}Comment: 32 pages, LaTeX, no changes in the 1994 paper, latex errors corrected
in 201
Beating noise with abstention in state estimation
We address the problem of estimating pure qubit states with non-ideal (noisy)
measurements in the multiple-copy scenario, where the data consists of a number
N of identically prepared qubits. We show that the average fidelity of the
estimates can increase significantly if the estimation protocol allows for
inconclusive answers, or abstentions. We present the optimal such protocol and
compute its fidelity for a given probability of abstention. The improvement
over standard estimation, without abstention, can be viewed as an effective
noise reduction. These and other results are exemplified for small values of N.
For asymptotically large N, we derive analytical expressions of the fidelity
and the probability of abstention, and show that for a fixed fidelity gain the
latter decreases with N at an exponential rate given by a Kulback-Leibler
(relative) entropy. As a byproduct, we obtain an asymptotic expression in terms
of this very entropy of the probability that a system of N qubits, all prepared
in the same state, has a given total angular momentum. We also discuss an
extreme situation where noise increases with N and where estimation with
abstention provides a most significant improvement as compared to the standard
approach
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