Universal measurement apparatus controlled by quantum software

We propose a quantum device that can approximate any projective measurement on a qubit. The desired measurement basis is selected by the quantum state of a "program register". The device is optimized with respect to maximal average fidelity (assuming uniform distribution of measurement bases). An interesting result is that if one uses two qubits in the same state as a program the average fidelity is higher than if he/she takes the second program qubit in the orthogonal state (with respect to the first one). The average information obtainable by the proposed measurements is also calculated and it is shown that it can get different values even if the average fidelity stays constant. Possible experimental realization of the simplest proposed device is presented.Comment: 4 pages, 2 figures, reference adde

Discrimination of the Bell states of qudits by means of linear optics

The question of the discrimination of the Bell states of two qudits (i.e., d-dimensional quantum systems) by means of passive linear optical elements and conditional measurements is discussed. A qudit is supposed to be represented by d optical modes containing exactly one photon altogether. From recent results of Calsamiglia it follows that there is no way how to distinguish the Bell states of two qudits for d>2 - not even with the probability of success lower than one - without any auxiliary photons in ancillary modes. Following the results of Carollo and Palma it is proved that it is impossible to distinguish even only one such a Bell state with certainty (i.e., with the probability of success equal to one), irrespective of how many auxiliary photons are involved. However, it is shown that auxiliary photons can help to discriminate the Bell states of qudits with the high probability of success: A Bell-state analyzer based on the idea of linear optics quantum computation that can achieve the probability of success arbitrarily close to one is described. It requires many auxiliary photons that must be first "combined" into entangled states.Comment: 4 pages, 5 figure

Analogy between optimal spin estimation and interferometry

Scheme for optimal spin state estimation is considered in analogy with phase detection in interferometry. Recently reported coherent measurements yielding the average fidelity (N+1)/(N+2) for N particle system corresponds to the standard limit of phase resolution 1/\sqrt{N}. It provides the bound for incoherent measurements when each particle is detected separately and information is used optimally. For specific states, improvement up to the value 1/N is possible in quantum theory. The best results are obtained combining sequentially coherent measurements on fractional groups of particles.Comment: 5 page

How quantum correlations enhance prediction of complementary measurements

If there are correlations between two qubits then the results of the measurement on one of them can help to predict measurement results on the other one. It is an interesting question what can be predicted about the results of two complementary projective measurements on the first qubit. To quantify these predictions the complementary \emph{knowledge excesses} are used. A non-trivial constraint restricting them is derived. For any mixed state and for arbitrary measurements the knowledge excesses are bounded by a factor depending only on the maximal violation of Bell's inequalities. This result is experimentally verified on two-photon Werner states prepared by means of spontaneous parametric down-conversion.Comment: 4 pages, 4 figure

Visibility bound caused by a distinguishable noise particle

We investigate how distinguishability of a "noise" particle degrades interference of the "signal" particle. The signal, represented by an equatorial state of a photonic qubit, is mixed with noise, represented by another photonic qubit, via linear coupling on the beam splitter. We report on the degradation of the "signal" photon interference depending on the degree of indistinguishability between "signal" and "noise" photon. When the photons are principally completely distinguishable but technically indistinguishable the visibility drops to the value 1/sqrt(2). As the photons become more indistinguishable the maximal visibility increases and reaches the unit value for completely indistinguishable photons. We have examined this effect experimentally using setup with fiber optics two-photon Mach-Zehnder interferometer.Comment: 5 pages, 3 figures, Accepted to Phys. Rev.

Probabilistic quantum multimeters

We propose quantum devices that can realize probabilistically different projective measurements on a qubit. The desired measurement basis is selected by the quantum state of a program register. First we analyze the phase-covariant multimeters for a large class of program states, then the universal multimeters for a special choice of program. In both cases we start with deterministic but erroneous devices and then proceed to devices that never make a mistake but from time to time they give an inconclusive result. These multimeters are optimized (for a given type of a program) with respect to the minimum probability of inconclusive result. This concept is further generalized to the multimeters that minimize the error rate for a given probability of an inconclusive result (or vice versa). Finally, we propose a generalization for qudits.Comment: 12 pages, 3 figure

Several experimental realizations of symmetric phase-covariant quantum cloner of single-photon qubits

We compare several optical implementations of phase-covariant cloning machines. The experiments are based on copying of the polarization state of a single photon in bulk optics by special unbalanced beam splitter or by balanced beam splitter accompanied by a state filtering. Also the all-fiber based setup is discussed, where the information is encoded into spatial modes, i.e., the photon can propagate through two optical fibers. Each of the four implementations possesses some advantages and disadvantages that are discussed.Comment: 8 pages, 11 figure