746 research outputs found
Complete Weight Enumerators of Generalized Doubly-Even Self-Dual Codes
For any q which is a power of 2 we describe a finite subgroup of the group of
invertible complex q by q matrices under which the complete weight enumerators
of generalized doubly-even self-dual codes over the field with q elements are
invariant.
An explicit description of the invariant ring and some applications to
extremality of such codes are obtained in the case q=4
Space shuttle navigation analysis. Volume 2: Baseline system navigation
Studies related to the baseline navigation system for the orbiter are presented. The baseline navigation system studies include a covariance analysis of the Inertial Measurement Unit calibration and alignment procedures, postflight IMU error recovery for the approach and landing phases, on-orbit calibration of IMU instrument biases, and a covariance analysis of entry and prelaunch navigation system performance
Mixture of multiple copies of maximally entangled states is quasi-pure
Employing the general BXOR operation and local state discrimination, the
mixed state of the form
\rho^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|\phi_{mn}><\phi_{mn}|)^{\otim
es k} is proved to be quasi-pure, where is the canonical set
of mutually orthogonal maximally entangled states in . Therefore
irreversibility does not occur in the process of distillation for this family
of states. Also, the distillable entanglement is calculated explicitly.Comment: 6 pages, 1 figure. The paper is subtantially revised and the general
proof is give
A logarithmic-depth quantum carry-lookahead adder
We present an efficient addition circuit, borrowing techniques from the
classical carry-lookahead arithmetic circuit. Our quantum carry-lookahead
(QCLA) adder accepts two n-bit numbers and adds them in O(log n) depth using
O(n) ancillary qubits. We present both in-place and out-of-place versions, as
well as versions that add modulo 2^n and modulo 2^n - 1.
Previously, the linear-depth ripple-carry addition circuit has been the
method of choice. Our work reduces the cost of addition dramatically with only
a slight increase in the number of required qubits. The QCLA adder can be used
within current modular multiplication circuits to reduce substantially the
run-time of Shor's algorithm.Comment: 21 pages, 4 color figure
A Note on the Pfaffian Integration Theorem
Two alternative, fairly compact proofs are presented of the Pfaffian
integration theorem that is surfaced in the recent studies of spectral
properties of Ginibre's Orthogonal Ensemble. The first proof is based on a
concept of the Fredholm Pfaffian; the second proof is purely linear-algebraic.Comment: 8 pages; published versio
Rates of asymptotic entanglement transformations for bipartite mixed states: Maximally entangled states are not special
We investigate the asymptotic rates of entanglement transformations for
bipartite mixed states by local operations and classical communication (LOCC).
We analyse the relations between the rates for different transitions and obtain
simple lower and upper bound for these transitions. In a transition from one
mixed state to another and back, the amount of irreversibility can be different
for different target states. Thus in a natural way, we get the concept of
"amount" of irreversibility in asymptotic manipulations of entanglement. We
investigate the behaviour of these transformation rates for different target
states. We show that with respect to asymptotic transition rates under LOCC,
the maximally entangled states do not have a special status. In the process, we
obtain that the entanglement of formation is additive for all maximally
correlated states. This allows us to show irreversibility in asymptotic
entanglement manipulations for maximally correlated states in 2x2. We show that
the possible nonequality of distillable entanglement under LOCC and that under
operations preserving the positivity of partial transposition, is related to
the behaviour of the transitions (under LOCC) to separable target states.Comment: 9 pages, 3 eps figures, REVTeX4; v2: presentation improved, new
considerations added, title changed; v3: minor changes, published versio
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
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
Reversible transformations from pure to mixed states, and the unique measure of information
Transformations from pure to mixed states are usually associated with
information loss and irreversibility. Here, a protocol is demonstrated allowing
one to make these transformations reversible. The pure states are diluted with
a random noise source. Using this protocol one can study optimal
transformations between states, and from this derive the unique measure of
information. This is compared to irreversible transformations where one does
not have access to noise. The ideas presented here shed some light on attempts
to understand entanglement manipulations and the inevitable irreversibility
encountered there where one finds that mixed states can contain "bound
entanglement".Comment: 10 pages, no figures, revtex4, table added, to appear in Phys. Rev.
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
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