QIC Abstracts


Vol.2 No.5 August 15, 2002 (print: September 15, 2002)
Geometry and product states (pp333-347)
        R.B. Lockhart, M.J. Steiner, and K. Gerlach  
As separable states are a convex combination of product states, the geometry of the manifold of product states, $\Sigma$, is studied. Prior results by Sanpera, Vidal and Tarrach are extended. Furthermore, it is proven that states in the set tangent to $\Sigma$ at the maximally mixed state are separable; the set normal contains, among others, all extended GHZ states. A canonical decomposition is given. A surprising result is that for the case of two particles, the closest product state to the maximally entangled state is the maximally mixed state. An algorithm is provided to find the closest product state.

Purification of two-qubit mixed states (pp348-354)
        E. Jan\'e
We find the necessary and sufficient condition under which two two-qubit mixed states can be purified into a pure maximally entangled state by local operations and classical communication. The optimal protocol for such transformation is obtained. This result leads to a necessary and sufficient condition for the exact purification of $n$ copies of a two-qubit state.

The quantum monty hall problem (pp355-366)
        G.M. D'Ariano, R.D. Gill, M. Keyl, B. Kummerer, H. Maassen, and R.F. Werner
We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal strategy is to use a completely entangled quantum notepad, on which to encode his prior information.

Teleportation and dense coding via a multiparticle quantum channel of the GHZ-class  (pp367-378)
        V.N. Gorbachev, A.I. Zhiliba A.I. Trubilko, and A.A. Rodichkina
A set of protocols for teleportation and dense coding schemes based on a multiparticle quantum channel, represented by the $N$-particle entangled states of the GHZ class, is introduced. Using a found representation for the GHZ states, it was shown that for dense coding schemes enhancement of the classical capacity of the channel due from entanglement is $N/N-1$. Within the context of our schemes it becomes clear that there is no one-to one correspondence between teleportation and dense coding schemes in comparison when the EPR channel is exploited. A set of schemes, for which two additional operations as entanglement and disentanglement are permitted, is considered.

On quantum one-way permutations (pp379-398)
        E. Kashefi, H. Nishimura and V. Vedral
We discuss the question of the existence of quantum one-way permutations. First, we consider the question: if a state is difficult to prepare, is the reflection operator about that state difficult to construct? By revisiting Grover's algorithm, we present the relationship between this question and the existence of quantum one-way permutations. Next, we prove the equivalence between inverting a permutation and that of constructing polynomial size quantum networks for reflection operators about a class of quantum states. We will consider both the worst case and the average case complexity scenarios for this problem. Moreover, we compare our method to Grover's algorithm and discuss possible applications of our results.

Speed-up and entanglement in quantum Searching (pp399-409)
        S.L. Braunstein and A.K. Pati
We investigate the issue of speed-up and the necessity of entanglement in Grover's quantum search algorithm. We find that in a pure state implementation of Grover's algorithm entanglement is present even though the initial and target states are product states. In pseudo-pure state implementations, the separability of the states involved defines an entanglement boundary in terms of a bound on the purity parameter. Using this bound we investigate the necessity of entanglement in quantum searching for these pseudo-pure state implementations. If every active molecule involved in the ensemble is `charged for' then in existing machines speed-up without entanglement is not possible.

Book Review:
On "A New Kind of Science" by Stephen Wolfram  (pp410-423)
        S. Aaronson
Erratum (p424)

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