Vol.3 No.2
March 1,
2003
Researches: Asymptotic entanglement
capacity of the Ising and anisotropic Heisenberg interactions
(pp97105) A.M. Childs, D.W. Leung, F. Verstrarte, and G. Vidal
We calculate the asymptotic entanglement capacity of the
Ising interaction \sigma_z\otimes\sigma_z, the anisotropic Heisenberg
interaction \sigma_x\otimes\sigma_x + \sigma_y\otimes\sigma_y, and more
generally, any twoqubit Hamiltonian with canonical form K = \mu_x
\sigma_x\otimes \sigma_x + \mu_y \sigma_y \otimes \sigma_y. We
also describe an entanglement assisted classical communication protocol
using the Hamiltonian K with rate equal to the asymptotic entanglement
capacity.
Entanglement and
nonlocality for a mixture of a paircoherent state (pp106115) S. Mancini and P. Tombesi
We consider a bipartite continuous variables quantum
mixture coming from phase randomization of a paircoherent state. We
study the nonclassical properties of such a mixture. In particular, we
quantify its degree of entanglement, then we show possible violations of
Bell's inequalities. We also consider the use of this mixture in quantum
teleportation. Finally, we compare this mixture with that obtained from
a paircoherent state by single photon loss.
Generation and degree of
entanglement in a relativistic formulation (pp115120) J. Pachos and E. Solano
The generation of entangled states and their degree of
entanglement are studied in a relativistic formulation for the case of
two interacting spin1/2 charged particles. In the realm of quantum
electrodynamics, we revisit the interaction that produces entanglement
between the spin components of covariant Dirac spinors describing the
two particles. In this way, we derive the relativistic version of the
spinspin interaction, widely used in the nonrelativistic regime.
Following this consistent approach, the relativistic invariance of the
generated entanglement is discussed.
An analysis of reading
out the state of a charge quantum bit (pp121138) HS. Goan
We provide a unified picture for the master equation
approach and the quantum trajectory approach to a measurement problem of
a twostate quantum system (a qubit), an electron coherently tunneling
between two coupled quantum dots (CQD's) measured by a low transparency
point contact (PC) detector. We show that the master equation of
``partially'' reduced density matrix can be derived from the quantum
trajectory equation (stochastic master equation) by simply taking a
``partial'' average over the all possible outcomes of the measurement.
If a full ensemble average is taken, the traditional (unconditional)
master equation of reduced density matrix is then obtained. This unified
picture, in terms of averaging over (tracing out) different amount of
detection records (detector states), for these seemingly different
approaches reported in the literature is particularly easy to understand
using our formalism. To further demonstrate this connection, we analyze
an important ensemble quantity for an initial qubit state readout
experiment, P(N,t), the probability distribution of finding N electron
that have tunneled through the PC barrier(s) in time t. The simulation
results of P(N,t) using 10000 quantum trajectories and corresponding
measurement records are, as expected, in very good agreement with those
obtained from the Fourier analysis of the ``partially'' reduced density
matrix. However, the quantum trajectory approach provides more
information and more physical insights into the ensemble and time
averaged quantity P(N,t). Each quantum trajectory resembles a single
history of the qubit state in a single run of the continuous measurement
experiment. We finally discuss, in this approach, the possibility of
reading out the state of the qubit system in a singleshot experiment.
Optimal realizations of
controlled unitary gates (pp139155) G. Song and A. Klappenecker
The controllednot gate and the single qubit gates are
considered elementary gates in quantum computing. It is natural to ask
how many such elementary gates are needed to implement more elaborate
gates or circuits. Recall that a controlledU gate can be realized with
two controllednot gates and four single qubit gates. We prove that this
implementation is optimal if and only if the matrix U satisfies the
conditions trU\neq 0, tr(UX)\neq 0, and detU\neq 1. We also derive
optimal implementations in the remaining nongeneric cases.
Bell inequality for
quNits with binary measurements (pp157164) H. BechmannPasquinucci and N. Gisin
We present a generalized Bell inequality for two
entangled quNits. On one quNit the choice is between two standard von
Neumann measurements, whereas for the other quNit there are N^2
different binary measurements. These binary measurements are related to
the intermediate states known from eavesdropping in quantum
cryptography. The maximum violation by \sqrt{N} is reached for the
maximally entangled state. Moreover, for N=2 it coincides with the
familiar CHSHinequality.
Quantum lower bound for
recursive Fourier sampling (pp165174) S. Aaronson
We revisit the oftneglected `recursive Fourier sampling'
(RFS) problem, introduced by Bernstein and Vazirani to prove an oracle
separation between BPP and BQP. We show that the known quantum algorithm
for RFS is essentially optimal, despite its seemingly wasteful need to
uncompute information. This implies that, to place \mathsf{BQP} outside
of PH[\log] relative to an oracle, one would need to go outside the RFS
framework. Our proof argues that, given any variant of RFS, either the
adversary method of Ambainis yields a good quantum lower bound, or else
there is an efficient classical algorithm. This technique may be of
independent interest.
Circuit for Shor's
algorithm using 2n+3 qubits (pp175185) S. Beauregard
We try to minimize the number of qubits needed to factor
an integer of n bits using Shor's algorithm on a quantum computer. We
introduce a circuit which uses 2n+3 qubits and O(n^3 lg(n)) elementary
quantum gates in a depth of O(n^3) to implement the factorization
algorithm. The circuit is computable in polynomial time on a classical
computer and is completely general as it does not rely on any property
of the number to be factored.
Maximal pnorms of
entanglement breaking channels (pp186190)
C. King
It shown that when one
of the components of a product channel is entanglement breaking, the
output state with maximal pnorm is always a product state. This result
complements Shor's theorem that both minimal entropy and Holevo capacity
are additive for entanglement breaking channels. It is also shown how
Shor's results can be recovered from the pnorm results by considering
their behavior for p close to one.
Book
Review:
On “Statistical
Structure of Quantum Theory” by A.S. Holevo (pp191192)
C. Fuchs
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