Vol.4 No.1 January 30,
2004
Research and
Review Articles:
Multiplicativity of accessible
fidelity and quantumness for sets of quantum states
(p001011)
K.M.R. Audenaert, C.A. Fuchs, C. King
and A. Winter
Two measures of sensitivity to eavesdropping for alphabets of quantum
states were recently introduced by Fuchs and Sasaki in
quantph/0302092. These are the accessible fidelity and quantumness.
In this paper we prove an important property of both measures: They are
multiplicative under tensor products. The proof in the case of
accessible fidelity shows a connection between the measure and
characteristics of entanglementbreaking quantum channels.
Compatibility between local and
multipartite states (pp012026)
S. Bravyi
We consider a partial trace transformation which maps a multipartite
quantum state to collection of local density matrices. We call this
collection a mean field state. For the Hilbert spaces $(\CC^2)^{\otimes
n}$ and $\CC^2\otimes\CC^2\otimes\CC^4$ the necessary and sufficient
conditions under which a mean field state is compatible with at least
one multipartite pure state are found. Compatibility of mean field
states with more general classes of multipartite quantum states is
discussed.
Asymptotically optimal circuits for
arbitrary nqubit diagonal computations
(pp027047)
S.S. Bullock and I.L. Markov
A unitary operator $U=\sum_{j,k} u_{j,k} \ket{k} \bra{j}$ is called
\emph{diagonal} when $u_{j,k}=0$ unless $j=k$. The definition extends to
quantum computations, where $j$ and $k$ vary over the $2^n$ binary
expressions for integers $0,1 \cdots ,2^n1$, given $n$ qubits. Such
operators do not affect outcomes of the projective measurement $\{ \ket{j}\bra{j}
\; ; \; 0 \leq j \leq 2^n1\}$ but rather create arbitrary relative
phases among the computational basis states $\{ \ket{j} \; ; \; 0 \leq j
\leq 2^n1\}.
Ground state entanglement in quantum
spin chains (pp048092)
J.I. Latorre, E. Rico and G. Vidal
A microscopic calculation of ground state entanglement for the XY and
Heisenberg models shows the emergence of universal scaling behavior at
quantum phase transitions. Entanglement is thus controlled by
conformal symmetry. Away from the critical point, entanglement gets
saturated by a mass scale. Results borrowed from conformal field theory
imply irreversibility of entanglement loss along renormalization group
trajectories. Entanglement does not saturate in higher dimensions which
appears to limit the success of the density matrix renormalization group
technique. A possible connection between majorization and
renormalization group irreversibility emerges from our numerical
analysis.
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