582 research outputs found
A separability criterion for density operators
We give a necessary and sufficient condition for a mixed quantum mechanical
state to be separable. The criterion is formulated as a boundedness condition
in terms of the greatest cross norm on the tensor product of trace class
operators.Comment: REVTeX, 5 page
Some Properties of the Computable Cross Norm Criterion for Separability
The computable cross norm (CCN) criterion is a new powerful analytical and
computable separability criterion for bipartite quantum states, that is also
known to systematically detect bound entanglement. In certain aspects this
criterion complements the well-known Peres positive partial transpose (PPT)
criterion. In the present paper we study important analytical properties of the
CCN criterion. We show that in contrast to the PPT criterion it is not
sufficient in dimension 2 x 2. In higher dimensions we prove theorems
connecting the fidelity of a quantum state with the CCN criterion. We also
analyze the behaviour of the CCN criterion under local operations and identify
the operations that leave it invariant. It turns out that the CCN criterion is
in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte
Method of convex rigid frames and applications in studies of multipartite quNit pure-states
In this Letter we suggest a method of convex rigid frames in the studies of
the multipartite quNit pure-states. We illustrate what are the convex rigid
frames and what is the method of convex rigid frames. As the applications we
use this method to solve some basic problems and give some new results (three
theorems): The problem of the partial separability of the multipartite quNit
pure-states and its geometric explanation; The problem of the classification of
the multipartite quNit pure-states, and give a perfect explanation of the local
unitary transformations; Thirdly, we discuss the invariants of classes and give
a possible physical explanation.Comment: 6 pages, no figur
Classicality in discrete Wigner functions
Gibbons et al. [Phys. Rev. A 70, 062101(2004)] have recently defined a class
of discrete Wigner functions W to represent quantum states in a Hilbert space
with finite dimension. We show that the only pure states having non-negative W
for all such functions are stabilizer states, as conjectured by one of us
[Phys. Rev. A 71, 042302 (2005)]. We also show that the unitaries preserving
non-negativity of W for all definitions of W form a subgroup of the Clifford
group. This means pure states with non-negative W and their associated unitary
dynamics are classical in the sense of admitting an efficient classical
simulation scheme using the stabilizer formalism.Comment: 10 pages, 1 figur
Geometrical approach to mutually unbiased bases
We propose a unifying phase-space approach to the construction of mutually
unbiased bases for a two-qubit system. It is based on an explicit
classification of the geometrical structures compatible with the notion of
unbiasedness. These consist of bundles of discrete curves intersecting only at
the origin and satisfying certain additional properties. We also consider the
feasible transformations between different kinds of curves and show that they
correspond to local rotations around the Bloch-sphere principal axes. We
suggest how to generalize the method to systems in dimensions that are powers
of a prime.Comment: 10 pages. Some typos in the journal version have been correcte
Probabilistic Quantum Memories
Typical address-oriented computer memories cannot recognize incomplete or
noisy information. Associative (content-addressable) memories solve this
problem but suffer from severe capacity shortages. I propose a model of a
quantum memory that solves both problems. The storage capacity is exponential
in the number of qbits and thus optimal. The retrieval mechanism for incomplete
or noisy inputs is probabilistic, with postselection of the measurement result.
The output is determined by a probability distribution on the memory which is
peaked around the stored patterns closest in Hamming distance to the input.Comment: Revised version to appear in Phys. Rev. Let
Nonadditive measure and quantum entanglement in a class of mixed states of N^n-system
Through the generalization of Khinchin's classical axiomatic foundation, a
basis is developed for nonadditive information theory. The classical
nonadditive conditional entropy indexed by the positive parameter q is
introduced and then translated into quantum information. This quantity is
nonnegative for classically correlated states but can take negative values for
entangled mixed states. This property is used to study quantum entanglement in
the parametrized Werner-Popescu-like state of an N^n-system, that is, an
n-partite N-level system. It is shown how the strongest limitation on validity
of local realism (i.e., separability of the state) can be obtained in a novel
manner
Separability and Fourier representations of density matrices
Using the finite Fourier transform, we introduce a generalization of
Pauli-spin matrices for -dimensional spaces, and the resulting set of
unitary matrices is a basis for matrices. If and H^{[ N]}=\bigotimes H^{% [ d_{k}]}, we give a
sufficient condition for separability of a density matrix relative to
the in terms of the norm of the spin coefficients of
Since the spin representation depends on the form of the tensor
product, the theory applies to both full and partial separability on a given
space % . It follows from this result that for a prescribed form of
separability, there is always a neighborhood of the normalized identity in
which every density matrix is separable. We also show that for every prime
and the generalized Werner density matrix is fully
separable if and only if
Robust control of decoherence in realistic one-qubit quantum gates
We present an open loop (bang-bang) scheme to control decoherence in a
generic one-qubit quantum gate and implement it in a realistic simulation. The
system is consistently described within the spin-boson model, with interactions
accounting for both adiabatic and thermal decoherence. The external control is
included from the beginning in the Hamiltonian as an independent interaction
term. After tracing out the environment modes, reduced equations are obtained
for the two-level system in which the effects of both decoherence and external
control appear explicitly. The controls are determined exactly from the
condition to eliminate decoherence, i.e. to restore unitarity. Numerical
simulations show excellent performance and robustness of the proposed control
scheme.Comment: 21 pages, 8 figures, VIth International Conference on Quantum
Communication, Measurement and Computing (Boston, 2002
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