Grover's search algorithm: An optical approach

The essential operations of a quantum computer can be accomplished using solely optical elements, with different polarization or spatial modes representing the individual qubits. We present a simple all-optical implementation of Grover's algorithm for efficient searching, in which a database of four elements is searched with a single query. By `compiling' the actual setup, we have reduced the required number of optical elements from 24 to only 12. We discuss the extension to larger databases, and the limitations of these techniques.Comment: 6 pages, 5 figures. To appear in a special issue of the Journal of Modern Optics -- "The Physics of Quantum Information

Optical simulation of quantum logic

A constructive method for simulating small-scale quantum circuits by use of linear optical devices is presented. It relies on the representation of several quantum bits by a single photon, and on the implementation of universal quantum gates using simple optical components (beam splitters, phase shifters, etc.). This suggests that the optical realization of small quantum networks with present-day quantum optics technology is a reasonable goal. This technique could be useful for demonstrating basic concepts of simple quantum algorithms or error-correction schemes. The optical analog of a nontrivial three-bit quantum circuit is presented as an illustration

Hyperentangled Bell-state analysis

It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using only linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of freedom, has been shown to assist the complete Bell analysis of the four Bell states (given a fixed state of the other degrees of freedom). Yet introducing other degrees of freedom also enlarges the total number of Bell-like states. We investigate the limits for unambiguously distinguishing these Bell-like states. In particular, when the additional degree of freedom is qubit-like, we find that the optimal one-shot discrimination schemes are to group the 16 states into 7 distinguishable classes, and that an unambiguous discrimination is possible with two identical copies.Comment: typos corrected, to appear in PRA, 5 pages, 2 figures, 2 table

How many photons are needed to distinguish two transparencies?

We give a bound on the minimum number of photons that must be absorbed by any quantum protocol to distinguish between two transparencies. We show how a quantum Zeno method in which the angle of rotation is varied at each iteration can attain this bound in certain situations.Comment: 5 pages, 4 figure

On EPR paradox, Bell's inequalities and experiments which prove nothing

This article shows that the there is no paradox. Violation of Bell's inequalities should not be identified with a proof of non locality in quantum mechanics. A number of past experiments is reviewed, and it is concluded that the experimental results should be re-evaluated. The results of the experiments with atomic cascade are shown not to contradict the local realism. The article points out flaws in the experiments with down-converted photons. The experiments with neutron interferometer on measuring the "contextuality" and Bell-like inequalities are analyzed, and it is shown that the experimental results can be explained without such notions. Alternative experiment is proposed to prove the validity of local realism.Comment: 27 pages, 8 figures. I edited a little the text and abstract I corrected equations (49) and (50

Distinguishability of hyperentangled Bell state by linear evolution and local projective measurement

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in $n$ two-state variables. We show that at most $2^{n+1}-1$ classes out of $4^n$ hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.Comment: 5 pages, 2 figure

Interaction-free measurement and forward scattering

Interaction-free measurement is shown to arise from the forward-scattered wave accompanying absorption: a "quantum silhouette" of the absorber. Accordingly, the process is not free of interaction. For a perfect absorber the forward-scattered wave is locked both in amplitude and in phase. For an imperfect one it has a nontrivial phase of dynamical origin (``colored silhouette"), measurable by interferometry. Other examples of quantum silhouettes, all controlled by unitarity, are briefly discussed.Comment: 4 pages in RevTex + 1 figure in eps; submitted to Phys. Rev. A since 09Jan98; now update

Hyperentanglement of two photons in three degrees of freedom

A 6-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2-crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a novel witness criterium specifically introduced for hyperentangled states. The experiment represents the first realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given Hilbert space.Comment: 4 pages, 2 figures, Revtex