7,346 research outputs found
Recycling of quantum information: Multiple observations of quantum systems
Given a finite number of copies of an unknown qubit state that have already
been measured optimally, can one still extract any information about the
original unknown state? We give a positive answer to this question and quantify
the information obtainable by a given observer as a function of the number of
copies in the ensemble, and of the number of independent observers that, one
after the other, have independently measured the same ensemble of qubits before
him. The optimality of the protocol is proven and extensions to other states
and encodings are also studied. According to the general lore, the state after
a measurement has no information about the state before the measurement. Our
results manifestly show that this statement has to be taken with a grain of
salt, specially in situations where the quantum states encode confidential
information.Comment: 4 page
Secrecy content of two-qubit states
We analyze the set of two-qubit states from which a secret key can be
extracted by single-copy measurements plus classical processing of the
outcomes. We introduce a key distillation protocol and give the corresponding
necessary and sufficient condition for positive key extraction. Our results
imply that the critical error rate derived by Chau, Phys. Rev. A {\bf 66},
060302 (2002), for a secure key distribution using the six-state scheme is
tight. Remarkably, an optimal eavesdropping attack against this protocol does
not require any coherent quantum operation.Comment: 5 pages, RevTe
Multi-copy programmable discrimination of general qubit states
Quantum state discrimination is a fundamental primitive in quantum statistics
where one has to correctly identify the state of a system that is in one of two
possible known states. A programmable discrimination machine performs this task
when the pair of possible states is not a priori known, but instead the two
possible states are provided through two respective program ports. We study
optimal programmable discrimination machines for general qubit states when
several copies of states are available in the data or program ports. Two
scenarios are considered: one in which the purity of the possible states is a
priori known, and the fully universal one where the machine operates over
generic mixed states of unknown purity. We find analytical results for both,
the unambiguous and minimum error, discrimination strategies. This allows us to
calculate the asymptotic performance of programmable discrimination machines
when a large number of copies is provided, and to recover the standard state
discrimination and state comparison values as different limiting cases.Comment: Based on version published in Physical Review A, some errors in
appendix A corrected. 13 pages, 4 figure
Phase estimation for thermal Gaussian states
We give the optimal bounds on the phase-estimation precision for mixed
Gaussian states in the single-copy and many-copy regimes. Specifically, we
focus on displaced thermal and squeezed thermal states. We find that while for
displaced thermal states an increase in temperature reduces the estimation
fidelity, for squeezed thermal states a larger temperature can enhance the
estimation fidelity. The many-copy optimal bounds are compared with the minimum
variance achieved by three important single-shot measurement strategies. We
show that the single-copy canonical phase measurement does not always attain
the optimal bounds in the many-copy scenario. Adaptive homodyning schemes do
attain the bounds for displaced thermal states, but for squeezed states they
yield fidelities that are insensitive to temperature variations and are,
therefore, sub-optimal. Finally, we find that heterodyne measurements perform
very poorly for pure states but can attain the optimal bounds for sufficiently
mixed states. We apply our results to investigate the influence of losses in an
optical metrology experiment. In the presence of losses squeezed states cease
to provide Heisenberg limited precision and their performance is close to that
of coherent states with the same mean photon number.Comment: typos correcte
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
Universal field equations for metric-affine theories of gravity
We show that almost all metric--affine theories of gravity yield Einstein
equations with a non--null cosmological constant . Under certain
circumstances and for any dimension, it is also possible to incorporate a Weyl
vector field and therefore the presence of an anisotropy. The viability
of these field equations is discussed in view of recent astrophysical
observations.Comment: 13 pages. This is a copy of the published paper. We are posting it
here because of the increasing interest in f(R) theories of gravit
How to hide a secret direction
We present a procedure to share a secret spatial direction in the absence of
a common reference frame using a multipartite quantum state. The procedure
guarantees that the parties can determine the direction if they perform joint
measurements on the state, but fail to do so if they restrict themselves to
local operations and classical communication (LOCC). We calculate the fidelity
for joint measurements, give bounds on the fidelity achievable by LOCC, and
prove that there is a non-vanishing gap between the two of them, even in the
limit of infinitely many copies. The robustness of the procedure under particle
loss is also studied. As a by-product we find bounds on the probability of
discriminating by LOCC between the invariant subspaces of total angular
momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur
The quantum Chernoff bound as a measure of distinguishability between density matrices: application to qubit and Gaussian states
Hypothesis testing is a fundamental issue in statistical inference and has
been a crucial element in the development of information sciences. The Chernoff
bound gives the minimal Bayesian error probability when discriminating two
hypotheses given a large number of observations. Recently the combined work of
Audenaert et al. [Phys. Rev. Lett. 98, 160501] and Nussbaum and Szkola
[quant-ph/0607216] has proved the quantum analog of this bound, which applies
when the hypotheses correspond to two quantum states. Based on the quantum
Chernoff bound, we define a physically meaningful distinguishability measure
and its corresponding metric in the space of states; the latter is shown to
coincide with the Wigner-Yanase metric. Along the same lines, we define a
second, more easily implementable, distinguishability measure based on the
error probability of discrimination when the same local measurement is
performed on every copy. We study some general properties of these measures,
including the probability distribution of density matrices, defined via the
volume element induced by the metric, and illustrate their use in the
paradigmatic cases of qubits and Gaussian infinite-dimensional states.Comment: 16 page
Programmable discrimination with an error margin
The problem of optimally discriminating between two completely unknown qubit states is generalized by allowing an error margin. It is visualized as a device-the programmable discriminator-with one data and two program ports, each fed with a number of identically prepared qubits-the data and the programs. The device aims at correctly identifying the data state with one of the two program states. This scheme has the unambiguous and the minimum-error schemes as extremal cases, when the error margin is set to zero or it is sufficiently large, respectively. Analytical results are given in the two situations where the margin is imposed on the average error probability-weak condition-or it is imposed separately on the two probabilities of assigning the state of the data to the wrong program-strong condition. It is a general feature of our scheme that the success probability rises sharply as soon as a small error margin is allowed, thus providing a significant gain over the unambiguous scheme while still having high confidence results
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