279 research outputs found
Quantum information becomes classical when distributed to many users
Any physical transformation that equally distributes quantum information over
a large number M of users can be approximated by a classical broadcasting of
measurement outcomes. The accuracy of the approximation is at least of the
order 1/M. In particular, quantum cloning of pure and mixed states can be
approximated via quantum state estimation. As an example, for optimal qubit
cloning with 10 output copies, a single user has error probability p > 0.45 in
distinguishing classical from quantum output--a value close to the error
probability of the random guess.Comment: 4 pages, no figures, published versio
Experimental Purification of Single Qubits
We report the experimental realization of the purification protocol for
single qubits sent through a depolarization channel. The qubits are associated
with polarization encoded photon particles and the protocol is achieved by
means of passive linear optical elements. The present approach may represent a
convenient alternative to the distillation and error correction protocols of
quantum information.Comment: 10 pages, 2 figure
Universal and phase covariant superbroadcasting for mixed qubit states
We describe a general framework to study covariant symmetric broadcasting
maps for mixed qubit states. We explicitly derive the optimal N to M
superbroadcasting maps, achieving optimal purification of the single-site
output copy, in both the universal and the phase covariant cases. We also study
the bipartite entanglement properties of the superbroadcast states.Comment: 19 pages, 8 figures, strictly related to quant-ph/0506251 and
quant-ph/051015
Quantum state estimation and large deviations
In this paper we propose a method to estimate the density matrix \rho of a
d-level quantum system by measurements on the N-fold system. The scheme is
based on covariant observables and representation theory of unitary groups and
it extends previous results concerning the estimation of the spectrum of \rho.
We show that it is consistent (i.e. the original input state \rho is recovered
with certainty if N \to \infty), analyze its large deviation behavior, and
calculate explicitly the corresponding rate function which describes the
exponential decrease of error probabilities in the limit N \to \infty. Finally
we discuss the question whether the proposed scheme provides the fastest
possible decay of error probabilities.Comment: LaTex2e, 40 pages, 2 figures. Substantial changes in Section 4: one
new subsection (4.1) and another (4.2 was 4.1 in the previous version)
completely rewritten. Minor changes in Sect. 2 and 3. Typos corrected.
References added. Accepted for publication in Rev. Math. Phy
The optimal cloning of quantum coherent states is non-Gaussian
We consider the optimal cloning of quantum coherent states with single-clone
and joint fidelity as figures of merit. Both optimal fidelities are attained
for phase space translation covariant cloners. Remarkably, the joint fidelity
is maximized by a Gaussian cloner, whereas the single-clone fidelity can be
enhanced by non-Gaussian operations: a symmetric non-Gaussian 1-to-2 cloner can
achieve a single-clone fidelity of approximately 0.6826, perceivably higher
than the optimal fidelity of 2/3 in a Gaussian setting. This optimal cloner can
be realized by means of an optical parametric amplifier supplemented with a
particular source of non-Gaussian bimodal states. Finally, we show that the
single-clone fidelity of the optimal 1-to-infinity cloner, corresponding to a
measure-and-prepare scheme, cannot exceed 1/2. This value is achieved by a
Gaussian scheme and cannot be surpassed even with supplemental bound entangled
states.Comment: 4 pages, 2 figures, revtex; changed title, extended list of authors,
included optical implementation of optimal clone
Clean Positive Operator Valued Measures
In quantum mechanics the statistics of the outcomes of a measuring apparatus
is described by a positive operator valued measure (POVM). A quantum channel
transforms POVM's into POVM's, generally irreversibly, thus loosing some of the
information retrieved from the measurement. This poses the problem of which
POVM's are "undisturbed", namely they are not irreversibly connected to another
POVM. We will call such POVM clean. In a sense, the clean POVM's would be
"perfect", since they would not have any additional "extrinsical" noise. Quite
unexpectedly, it turns out that such cleanness property is largely unrelated to
the convex structure of POVM's, and there are clean POVM's that are not
extremal and vice-versa. In this paper we solve the cleannes classification
problem for number n of outcomes n<=d (d dimension of the Hilbert space), and
we provide a a set of either necessary or sufficient conditions for n>d, along
with an iff condition for the case of informationally complete POVM's for
n=d^2.Comment: Minor changes. amsart 21 pages. Accepted for publication on J. Math.
Phy
Universal approximation of multi-copy states and universal quantum lossless data compression
We have proven that there exists a quantum state approximating any multi-copy
state universally when we measure the error by means of the normalized relative
entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE
Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been
open for more than ten years. For a deeper analysis, we have solved the
mini-max problem concerning `approximation error' up to the second order.
Furthermore, we have applied this result to quantum lossless data compression,
and have constructed a universal quantum lossless data compression
Symmetric qubits from cavity states
Two-mode cavities can be prepared in quantum states which represent symmetric
multi-qubit states. However, the qubits are impossible to address individually
and as such cannot be independently measured or otherwise manipulated. We
propose two related schemes to coherently transfer the qubits which the cavity
state represents onto individual atoms, so that the qubits can then be
processed individually. In particular, our scheme can be combined with the
quantum cloning scheme of Simon and coworkers [C. Simon et al, PRL 84, 2993
(2000)] to allow the optimal clones which their scheme produces to be spatially
separated and individually utilized.Comment: 8 pages, 4 figures, minor typographical errors correcte
The asymptotic entanglement cost of preparing a quantum state
We give a detailed proof of the conjecture that the asymptotic entanglement
cost of preparing a bipartite state \rho is equal to the regularized
entanglement of formation of \rho.Comment: 7 pages, no figure
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