16,098 research outputs found
A study of separability criteria for mixed three-qubit states
We study the noisy GHZ-W mixture. We demonstrate some necessary but not
sufficient criteria for different classes of separability of these states. It
turns out that the partial transposition criterion of Peres and the criteria of
G\"uhne and Seevinck dealing with matrix elements are the strongest ones for
different separability classes of this 2 parameter state. As a new result we
determine a set of entangled states of positive partial transpose.Comment: 18 pages, 10 figures, PRA styl
Structural approximations to positive maps and entanglement breaking channels
Structural approximations to positive, but not completely positive maps are
approximate physical realizations of these non-physical maps. They find
applications in the design of direct entanglement detection methods. We show
that many of these approximations, in the relevant case of optimal positive
maps, define an entanglement breaking channel and, consequently, can be
implemented via a measurement and state-preparation protocol. We also show how
our findings can be useful for the design of better and simpler direct
entanglement detection methods.Comment: 18 pages, 3 figure
Error-Correction in Flash Memories via Codes in the Ulam Metric
We consider rank modulation codes for flash memories that allow for handling
arbitrary charge-drop errors. Unlike classical rank modulation codes used for
correcting errors that manifest themselves as swaps of two adjacently ranked
elements, the proposed \emph{translocation rank codes} account for more general
forms of errors that arise in storage systems. Translocations represent a
natural extension of the notion of adjacent transpositions and as such may be
analyzed using related concepts in combinatorics and rank modulation coding.
Our results include derivation of the asymptotic capacity of translocation rank
codes, construction techniques for asymptotically good codes, as well as simple
decoding methods for one class of constructed codes. As part of our exposition,
we also highlight the close connections between the new code family and
permutations with short common subsequences, deletion and insertion
error-correcting codes for permutations, and permutation codes in the Hamming
distance
Quantum conditional operator and a criterion for separability
We analyze the properties of the conditional amplitude operator, the quantum
analog of the conditional probability which has been introduced in
[quant-ph/9512022]. The spectrum of the conditional operator characterizing a
quantum bipartite system is invariant under local unitary transformations and
reflects its inseparability. More specifically, it is shown that the
conditional amplitude operator of a separable state cannot have an eigenvalue
exceeding 1, which results in a necessary condition for separability. This
leads us to consider a related separability criterion based on the positive map
, where is an Hermitian operator. Any
separable state is mapped by the tensor product of this map and the identity
into a non-negative operator, which provides a simple necessary condition for
separability. In the special case where one subsystem is a quantum bit,
reduces to time-reversal, so that this separability condition is
equivalent to partial transposition. It is therefore also sufficient for
and systems. Finally, a simple connection between this
map and complex conjugation in the "magic" basis is displayed.Comment: 19 pages, RevTe
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