9 research outputs found
Iterative Optimization of Quantum Error Correcting Codes
We introduce a convergent iterative algorithm for finding the optimal coding
and decoding operations for an arbitrary noisy quantum channel. This algorithm
does not require any error syndrome to be corrected completely, and hence also
finds codes outside the usual Knill-Laflamme definition of error correcting
codes. The iteration is shown to improve the figure of merit "channel fidelity"
in every step.Comment: 5 pages, 2 figures, REVTeX 4; stability of algorithm include
Comment on "Optimum Quantum Error Recovery using Semidefinite Programming"
In a recent paper ([1]=quant-ph/0606035) it is shown how the optimal recovery
operation in an error correction scheme can be considered as a semidefinite
program. As a possible future improvement it is noted that still better error
correction might be obtained by optimizing the encoding as well. In this note
we present the result of such an improvement, specifically for the four-bit
correction of an amplitude damping channel considered in [1]. We get a strict
improvement for almost all values of the damping parameter. The method (and the
computer code) is taken from our earlier study of such correction schemes
(quant-ph/0307138).Comment: 2 pages, 1 figur
Estimating entanglement measures in experiments
We present a method to estimate entanglement measures in experiments. We show
how a lower bound on a generic entanglement measure can be derived from the
measured expectation values of any finite collection of entanglement witnesses.
Hence witness measurements are given a quantitative meaning without the need of
further experimental data. We apply our results to a recent multi-photon
experiment [M. Bourennane et al., Phys. Rev. Lett. 92, 087902 (2004)], giving
bounds on the entanglement of formation and the geometric measure of
entanglement in this experiment.Comment: 4 pages, 1 figure, v2: final versio
Lower bounds on entanglement measures from incomplete information
How can we quantify the entanglement in a quantum state, if only the
expectation value of a single observable is given? This question is of great
interest for the analysis of entanglement in experiments, since in many
multiparticle experiments the state is not completely known. We present several
results concerning this problem by considering the estimation of entanglement
measures via Legendre transforms. First, we present a simple algorithm for the
estimation of the concurrence and extensions thereof. Second, we derive an
analytical approach to estimate the geometric measure of entanglement, if the
diagonal elements of the quantum state in a certain basis are known. Finally,
we compare our bounds with exact values and other estimation methods for
entanglement measures.Comment: 9 pages, 4 figures, v2: final versio
Experimental entanglement verification and quantification via uncertainty relations
We report on experimental studies on entanglement quantification and
verification based on uncertainty relations for systems consisting of two
qubits. The new proposed measure is shown to be invariant under local unitary
transformations, by which entanglement quantification is implemented for
two-qubit pure states. The nonlocal uncertainty relations for two-qubit pure
states are also used for entanglement verification which serves as a basic
proposition and promise to be a good choice for verification of multipartite
entanglement.Comment: 5 pages, 3 figures and 2 table
Tema Con Variazioni: Quantum Channel Capacity
Channel capacity describes the size of the nearly ideal channels, which can
be obtained from many uses of a given channel, using an optimal error
correcting code. In this paper we collect and compare minor and major
variations in the mathematically precise statements of this idea which have
been put forward in the literature. We show that all the variations considered
lead to equivalent capacity definitions. In particular, it makes no difference
whether one requires mean or maximal errors to go to zero, and it makes no
difference whether errors are required to vanish for any sequence of block
sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl
When are correlations quantum? -- Verification and quantification of entanglement by simple measurements
The verification and quantification of experimentally created entanglement by simple measurements, especially between distant particles, is an important basic task in quantum processing. When composite systems are subjected to local measurements the measurement data will exhibit correlations, whether these systems are classical or quantum. Therefore, the observation of correlations in the classical measurement record does not automatically imply the presence of quantum correlations in the system under investigation. In this work we explore the question of when correlations, or other measurement data, are sufficient to guarantee the existence of a certain amount of quantum correlations in the system and when additional information, such as the degree of purity of the system, is needed to do so. Various measurement settings are discussed, both numerically and analytically. Exact results and lower bounds on the least entanglement consistent with the observations are presented. The approach is suitable both for the bi-partite and the multi-partite setting