QIC Abstracts

 Vol.4 No.1 January 30, 2004
Research and Review Articles:
Multiplicativity of accessible fidelity and quantumness for sets of quantum states (p001-011)
        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 quant-ph/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 entanglement-breaking quantum channels.

Compatibility between local and multipartite states (pp012-026)
        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 n-qubit diagonal computations (pp027-047)
        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 $0,1 \cdots ,2^n-1$, given $n$ qubits. Such operators do not affect outcomes of the projective measurement $\{ \ket{j}\bra{j} \; ; \; 0 \leq j \leq 2^n-1\}$ but rather create arbitrary relative phases among the computational basis states $\{ \ket{j} \; ; \; 0 \leq j \leq 2^n-1\}.

Ground state entanglement in quantum spin chains (pp048-092)
        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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