Universality and optimality of programmable quantum processors

We analyze and compare the optimality of approximate and probabilistic universal programmable quantum processors. We define several characteristics how to quantify the optimality and we study in detail performance of three types of programmable quantum processors based on (1) the C-NOT gate, (2) the SWAP operation, and (3) the model of the quantum information distributor - the QID processor. We show under which conditions the measurement assisted QID processor is optimal. We also investigate optimality of the so-called U-processors and we also compare the optimal approximative implementation of U(1) qubit rotations with the known probabilistic implementation as introduced by Vidal, Masanes and Cirac [ {\em Phys. Rev. Lett.} {\bf 88}, 047905 (2002)].Comment: 9 page

Single-shot discrimination of quantum unitary processes

We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a "fidelity-like" lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of apriori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimization of the same quantity called completely bounded process fidelity.Comment: 11 pages, 1 figur

Entanglement-induced state ordering under local operations

We analyze how entanglement between two components of a bipartite system behaves under the action of local channels of the form \cE\otimes\cI. We show that a set of maximally entangled states is by the action of \cE\otimes\cI transformed into the set of states that exhibit the same degree of entanglement. Moreover, this degree represents an upper bound on entanglement that is available at the output of the channel irrespective what is the input state of the composite system. We show that within this bound the the entanglement-induced state ordering is ``relative'' and can be changed by the action of local channels. That is, two states $\varrho_1^{(in)}$ and $\varrho_2^{(in)}$ such that the entanglement $E[\varrho_1^{(in)}]$ of the first state is larger than the entanglement $E[\varrho_2^{(in)}]$ of the second state are transformed into states $\varrho_1^{(out)}$ and $\varrho_2^{(out)}$ such that $E[\varrho_2^{(out)}] > E[\varrho_1^{(out)}]$.Comment: 5 pages, 1 figure, comments welcom