543 research outputs found
Irreversibility in asymptotic manipulations of entanglement
We show that the process of entanglement distillation is irreversible by
showing that the entanglement cost of a bound entangled state is finite. Such
irreversibility remains even if extra pure entanglement is loaned to assist the
distillation process.Comment: RevTex, 3 pages, no figures Result on indistillability of PPT states
under pure entanglement catalytic LOCC adde
On local invariants of pure three-qubit states
We study invariants of three-qubit states under local unitary
transformations, i.e. functions on the space of entanglement types, which is
known to have dimension 6. We show that there is no set of six independent
polynomial invariants of degree less than or equal to 6, and find such a set
with maximum degree 8. We describe an intrinsic definition of a canonical state
on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio
Output state in multiple entanglement swapping
The technique of quantum repeaters is a promising candidate for sending
quantum states over long distances through a lossy channel. The usual
discussions of this technique deals with only a finite dimensional Hilbert
space. However the qubits with which one implements this procedure will "ride"
on continuous degrees of freedom of the carrier particles. Here we analyze the
action of quantum repeaters using a model based on pulsed parametric down
conversion entanglement swapping. Our model contains some basic traits of a
real experiment. We show that the state created, after the use of any number of
parametric down converters in a series of entanglement swappings, is always an
entangled (actually distillable) state, although of a different form than the
one that is usually assumed. Furthermore, the output state always violates a
Bell inequality.Comment: 11 pages, 6 figures, RevTeX
Entanglement cost of mixed states
We compute the entanglement cost of several families of bipartite mixed
states, including arbitrary mixtures of two Bell states. This is achieved by
developing a technique that allows us to ascertain the additivity of the
entanglement of formation for any state supported on specific subspaces. As a
side result, the proof of the irreversibility in asymptotic local manipulations
of entanglement is extended to two-qubit systems.Comment: 4 pages, no figures, (v4) new results, including a new method to
determine E_c for more general mixed states, presentation changed
significantl
Pauli Exchange Errors in Quantum Computation
In many physically realistic models of quantum computation, Pauli exchange
interactions cause a subset of two-qubit errors to occur as a first order
effect of couplings within the computer, even in the absence of interactions
with the computer's environment. We give an explicit 9-qubit code that corrects
both Pauli exchange errors and all one-qubit errors.Comment: Final version accepted for publication in Phys. Rev. Let
Random walks and random fixed-point free involutions
A bijection is given between fixed point free involutions of
with maximum decreasing subsequence size and two classes of vicious
(non-intersecting) random walker configurations confined to the half line
lattice points . In one class of walker configurations the maximum
displacement of the right most walker is . Because the scaled distribution
of the maximum decreasing subsequence size is known to be in the soft edge GOE
(random real symmetric matrices) universality class, the same holds true for
the scaled distribution of the maximum displacement of the right most walker.Comment: 10 page
Lower bound for the quantum capacity of a discrete memoryless quantum channel
We generalize the random coding argument of stabilizer codes and derive a
lower bound on the quantum capacity of an arbitrary discrete memoryless quantum
channel. For the depolarizing channel, our lower bound coincides with that
obtained by Bennett et al. We also slightly improve the quantum
Gilbert-Varshamov bound for general stabilizer codes, and establish an analogue
of the quantum Gilbert-Varshamov bound for linear stabilizer codes. Our proof
is restricted to the binary quantum channels, but its extension of to l-adic
channels is straightforward.Comment: 16 pages, REVTeX4. To appear in J. Math. Phys. A critical error in
fidelity calculation was corrected by using Hamada's result
(quant-ph/0112103). In the third version, we simplified formula and
derivation of the lower bound by proving p(Gamma)+q(Gamma)=1. In the second
version, we added an analogue of the quantum Gilbert-Varshamov bound for
linear stabilizer code
Distributed Entanglement
Consider three qubits A, B, and C which may be entangled with each other. We
show that there is a trade-off between A's entanglement with B and its
entanglement with C. This relation is expressed in terms of a measure of
entanglement called the "tangle," which is related to the entanglement of
formation. Specifically, we show that the tangle between A and B, plus the
tangle between A and C, cannot be greater than the tangle between A and the
pair BC. This inequality is as strong as it could be, in the sense that for any
values of the tangles satisfying the corresponding equality, one can find a
quantum state consistent with those values. Further exploration of this result
leads to a definition of the "three-way tangle" of the system, which is
invariant under permutations of the qubits.Comment: 13 pages LaTeX; references added, derivation of Eq. (11) simplifie
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