Transfer of quantum states using finite resources

We discuss the problem of transfering a qubit from Alice to Bob using a noisy quantum channel and only finite resources. As the basic protocol for the transfer we apply quantum teleportation. It turns out that for a certain quality of the channel direct teleportation combined with qubit purification is superior to entanglement purification of the channel. If, however, the quality of the channel is rather low one should simply apply an estimation-preparation scheme.Comment: 9 pages RevTeX including 5 figures, replaced with revised version, to appear in Phys. Rev.

Enhanced Quantum Estimation via Purification

We analyze the estimation of a finite ensemble of quantum bits which have been sent through a depolarizing channel. Instead of using the depolarized qubits directly, we first apply a purification step and show that this improves the fidelity of subsequent quantum estimation. Even though we lose some qubits of our finite ensemble the information is concentrated in the remaining purified ones.Comment: 6 pages, including 3 figure

Collective versus local measurements on two parallel or antiparallel spins

We give a complete analysis of covariant measurements on two spins. We consider the cases of two parallel and two antiparallel spins, and we consider both collective measurements on the two spins, and measurements which require only Local Quantum Operations and Classical Communication (LOCC). In all cases we obtain the optimal measurements for arbitrary fidelities. In particular we show that if the aim is determine as well as possible the direction in which the spins are pointing, it is best to carry out measurements on antiparallel spins (as already shown by Gisin and Popescu), second best to carry out measurements on parallel spins and worst to be restricted to LOCC measurements. If the the aim is to determine as well as possible a direction orthogonal to that in which the spins are pointing, it is best to carry out measurements on parallel spins, whereas measurements on antiparallel spins and LOCC measurements are both less good but equivalent.Comment: 4 pages; minor revision

Optimal estimation of quantum dynamics

We construct the optimal strategy for the estimation of an unknown unitary transformation $U\in SU(d)$. This includes, in addition to a convenient measurement on a probe system, finding which is the best initial state on which $U$ is to act. When $U\in SU(2)$, such an optimal strategy can be applied to estimate simultaneously both the direction and the strength of a magnetic field, and shows how to use a spin 1/2 particle to transmit information about a whole coordinate system instead of only a direction in space.Comment: 4 pages, REVTE

Minimal measurements of the gate fidelity of a qudit map

We obtain a simple formula for the average gate fidelity of a linear map acting on qudits. It is given in terms of minimal sets of pure state preparations alone, which may be interesting from the experimental point of view. These preparations can be seen as the outcomes of certain minimal positive operator valued measures. The connection of our results with these generalized measurements is briefly discussed

Universality of optimal measurements

We present optimal and minimal measurements on identical copies of an unknown state of a qubit when the quality of measuring strategies is quantified with the gain of information (Kullback of probability distributions). We also show that the maximal gain of information occurs, among isotropic priors, when the state is known to be pure. Universality of optimal measurements follows from our results: using the fidelity or the gain of information, two different figures of merits, leads to exactly the same conclusions. We finally investigate the optimal capacity of $N$ copies of an unknown state as a quantum channel of information.Comment: Revtex, 5 pages, no figure

Selection rules for J^PC Exotic Hybrid Meson Decay in Large-N_c

The coupling of a neutral hybrid {1,3,5...}^-+ exotic particle (or current) to two neutral (hybrid) meson particles with the same J^PC and J=0 is proved to be sub-leading to the usual large-N_c QCD counting. The coupling of the same exotic particle to certain two - (hybrid) meson currents with the same J^PC and J=0 is also sub-leading. The decay of a {1,3,5...}^-+ hybrid to eta pi^0, eta' pi^0, eta' eta, eta(1295) pi^0, pi(1300)^0 pi0, eta(1440) pi^0, a_0(980)^0 sigma or f_0(980) sigma is sub-leading, assuming that these final state particles are (hybrid) mesons in the limit of large N_c.Comment: 16 pages, LaTeX. Main paper shortened/rewritten and appendices expanded. Implications for phenomenology of exotic hybrid mesons clarifie

(Field) Symmetrization Selection Rules

QCD and QED exhibit an infinite set of three-point Green's functions that contain only OZI rule violating contributions, and (for QCD) are subleading in the large N_c expansion. The Green's functions describe the ``decay'' of a J^{PC}={1,3,5 ...}^{-+} exotic hybrid meson current to two J=0 (hybrid) meson currents with identical P and C. We prove that the QCD amplitude for a neutral hybrid {1,3,5 ...}^{-+} exotic current to create eta pi0 only comes from OZI rule violating contributions under certain conditions, and is subleading in N_c.Comment: 20 pages, LaTeX. Two postscript figures. Final published versio

Block Spin Density Matrix of the Inhomogeneous AKLT Model

We study the inhomogeneous generalization of a 1-dimensional AKLT spin chain model. Spins at each lattice site could be different. Under certain conditions, the ground state of this AKLT model is unique and is described by the Valence-Bond-Solid (VBS) state. We calculate the density matrix of a contiguous block of bulk spins in this ground state. The density matrix is independent of spins outside the block. It is diagonalized and shown to be a projector onto a subspace. We prove that for large block the density matrix behaves as the identity in the subspace. The von Neumann entropy coincides with Renyi entropy and is equal to the saturated value.Comment: 20 page

Collective vs local measurements in qubit mixed state estimation

We discuss the problem of estimating a general (mixed) qubit state. We give the optimal guess that can be inferred from any given set of measurements. For collective measurements and for a large number $N$ of copies, we show that the error in the estimation goes as 1/N. For local measurements we focus on the simpler case of states lying on the equatorial plane of the Bloch sphere. We show that standard tomographic techniques lead to an error proportional to $1/N^{1/4}$, while with our optimal data processing it is proportional to $1/N^{3/4}$.Comment: 4 pages, 1 figure, minor style changes, refs. adde