Vol.10
No.11&12 November 1, 2010
Research Articles:
Are
quantum correlations symmetric?
(pp09010910)
Karol
Horodecki, Michal Horodecki, and Pawel Horodecki
We provide operational definition of asymmetry of entanglement: An
entangled state contains asymmetric entanglement if its subsystems can
not be exchanged (swapped) by means of local operations and classical
communication. We show that in general states have asymmetric
entanglement. This allows to construct nonsymmetric measure of
entanglement, and a parameter that reports asymmetry of entanglement
contents of quantum state. We propose asymptotic measure of asymmetry of
entanglement, and show that states for which it is nonzero, contain
necessarily bound entanglement.
A lower
bound on the value of entangled binary games
(pp09110924)
Salman Beigi
A twoplayer oneround binary game consists of two cooperative players
who each replies by one bit to a message that he receives privately;
they win the game if both questions and answers satisfy some
predetermined property. A game is called entangled if the players are
allowed to share a priori entanglement. It is wellknown that the
maximum winning probability (value) of entangled XORgames (binary games
in which the predetermined property depends only on the XOR of the two
output bits) can be computed by a semidefinite program. In this paper we
extend this result in the following sense; if a binary game is uniform,
meaning that in an optimal strategy the marginal distributions of the
output of each player are uniform, then its entangled value can be
efficiently computed by a semidefinite program. We also introduce a
lower bound on the entangled value of a general twoplayer oneround
game; this bound depends on the size of the output set of each player
and can be computed by a semidefinite program. In particular, we show
that if the game is binary, $\omega_q$ is its entangled value, and $\omega_{sdp}$
is the optimum value of the corresponding semidefinite program, then
$0.68\,\omega_{sdp} < \omega_q \leq \omega_{sdp}$.
When is
there a multipartite maximum entangled state?
(pp09250935)
Runyao
Duan and Yaoyun Shi
For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes\cdots\otimes
d_n$, where $d_1\ge d_2\ge\cdots\ge d_n\ge2$, is there an entangled
state {\em maximum} in the sense that all other states in the system can
be obtained from the state through local quantum operations and
classical communications (LOCC)? When $d_1\ge\Pi_{i=2}^n d_i$, such
state exists. We show that this condition is also necessary. Our proof,
somewhat surprisingly, uses results from algebraic complexity theory.
Highfidelity universal quantum gates
(pp09360946)
Ran
Li and Frank Gaitan
Twisted rapid passage is a type of nonadiabatic rapid passage that
generates controllable quantum interference effects that were first
observed experimentally in $2003$. It is shown that twisted rapid
passage sweeps can be used to implement a universal set of quantum gates
$\calGU$ that operate with highfidelity. The gate set $\calGU$ consists
of the Hadamard and NOT gates, together with variants of the phase, $\pi
/8$, and controlledphase gates. For each gate $g$ in $\calGU$, sweep
parameter values are provided which simulations indicate will produce a
unitary operation that approximates $g$ with error probability$P_{e} <
10^{4}$. Note that \textit{all\/} gates in $\calGU$ are implemented
using a \textit{single family\/} of controlfield, and the error
probability for each gate falls below the roughandready estimate for
the accuracy threshold $P_{a}\sim 10^{4}$.
Quantum
entanglement of Dirac field in background of an asymptotically flat
static black hole
(pp09470955)
Jieci
Wang, Qiyuan Pan, Songbai Chen, and Jiliang Jing
The entanglement of the Dirac field in the asymptotically flat black
hole is investigated. Unlike the bosonic case in which the initial
entanglement vanishes in the limit of infinite Hawking temperature, in
this case the entanglement achieves a nonvanishing minimum values, which
shows that the entanglement is never completely destroyed when black
hole evaporates completely. Another interesting result is that the
mutual information in this limit equals to just half of its own initial
value, which may be an universal property for any fields.
New
classes of TQC associated with selfdual, quasi selfdual and
denser
tessellations
(pp09560970)
C.
D. Albuquerque, R. Palazzo Jr., and E. B. Silva
In this paper we present six classes of topological quantum codes (TQC)
on compact surfaces with genus $g\ge 2$. These codes are derived from
selfdual, quasi selfdual and denser tessellations associated with
embeddings of selfdual complete graphs and complete bipartite graphs on
the corresponding compact surfaces. The majority of the new classes has
the selfdual tessellations as their algebraic and geometric supporting
mathematical structures. Every code achieves minimum distance 3 and its
encoding rate is such that $\frac{k}{n} \rightarrow 1$ as $n \rightarrow
\infty$, except for the one case where $\frac{k}{n} \rightarrow
\frac{1}{3}$ as $n \rightarrow \infty$.
Nocloning
theorem for a single POVM
(pp09710980)
Alexey
E. Rastegin
Cloning of statistics of general quantum measurement is discussed. The
presented approach is connected with the known concept of observable
cloning, but differs in some essential respects. The reasons are
illustrated within some variety of the B92 protocol. As it is shown,
there exist pairs of states such that the perfect cloning of given POVM
is not possible. We discuss some properties of these intolerant sets. An
example allowing the perfect cloning is presented as well.
On
Steane's enlargement of CalderbankShorSteane codes
(pp09810993)
Hachiro
Fujita
In this paper we present the Hilbert space representation and the
decoding of the enlarged CalderbankShorSteane code constructed by
Steane. We also give a generalization of the code.
Geometric
measure of quantum discord under decoherence
(pp09941003)
XiaoMing
Lu, Zhengjun Xi, Zhe Sun, and Xiaoguang Wang
The dynamics of a geometric measure of the quantum discord (GMQD) under
decoherence is investigated. We show that the GMQD of a twoqubit state
can be alternatively obtained through the singular values of a
$3\times4$ matrix whose elements are the expectation values of Pauli
matrices of the two qubits. By using Heisenberg picture, the analytic
results of the GMQD is obtained for three typical kinds of the quantum
decoherence channels. We compare the dynamics of the GMQD with that of
the quantum discord and of entanglement. We show that a sudden change in
the decay rate of the GMQD does not always imply that of the quantum
discord, and vice versa. We also give a general analysis on the sudden
change in behavior and find that at least for the Bell diagonal states,
the sudden changes in decay rates of the GMQD and that of the quantum
discord occur simultaneously.
Limit
theorems for quantum walks with memory
(pp10041017)
Norio
Konno and Takuya Machida
Recently Mc Gettrick introduced and studied a discretetime 2state
quantum walk (QW) with a memory in one dimension. He gave an expression
for the amplitude of the QW by path counting method. Moreover he showed
that the return probability of the walk is more than 1/2 for any even
time. In this paper, we compute the stationary distribution by
considering the walk as a 4state QW without memory. Our result is
consistent with his claim. In addition, we obtain the weak limit theorem
of the rescaled QW. This behavior is strikingly different from the
corresponding classical random walk and the usual 2state QW without
memory as his numerical simulations suggested.
Relationship between the ntangle and the residual entanglement
of even n qubits
(pp10181028)
Xiangrong
Li and Dafa Li
We show that for even $n$ qubits,$\ n$tangle is the square of the SLOCC
polynomial invariant of degree 2. We find that the $n$tangle is not the
residual entanglement for any even $n\geq 4$\ qubits. We give a
necessary and sufficient condition for the vanishing of the concurrence
$C_{1(2...n)}$. The condition implies that the concurrence
$C_{1(2...n)}$ is always positive for any entangled states while the
$n$tangle vanishes for some entangled states. We argue that for even
$n$\ qubits, the concurrence $ C_{1(2...n)}$\ is equal to or greater
than the $n$tangle.\ Further, we reveal that the residual entanglement
is a partial measure for product states of any $n$ qubits while the
$n$tangle is multiplicative for some product states.
Symmetric
states: local unitary equivalence via stabilizers
(pp10291041)
Curt D.
Cenci, David W. Lyons, Laura M. Snyder, and Scott N. Walck
We classify local unitary equivalence classes of symmetric states via a
classification of their local unitary stabilizer subgroups. For states
whose local unitary stabilizer groups have a positive number of
continuous degrees of freedom, the classification is exhaustive. We show
that local unitary stabilizer groups with no continuous degrees of
freedom are isomorphic to finite subgroups of the rotation group
$SO(3)$, and give examples of states with discrete stabilizers.
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