Bell correlation inequalities for two sites and 2 + n or 3 + 3 two-way measurements ("dichotomic observables") are considered. In the 2 + n case, any facet of the classical experience polytope is defined by a CHSH inequality involving only two pairs of the observables. In the 3+3 case, contrary to earlier results, the action of the symmetry group reduces the set of all Bell inequalities to just 3 orbits, only one of them being "new" (not known from the 2 + 2 case). A detailed calculation for the singlet state of two qubits reveals the configurations of a maximal violation for this class of inequalities.

We report the development of a photon-number resolving detector based on a fiber-optical setup and a pair of standard avalanche photodiodes. The detector is capable of resolving individual photon numbers, and operates on the well-known principle by which a single mode input state is split into a large number (eight) of output modes. We reconstruct the photon statistics of weak coherent input light from experimental data, and show that there is a high probability of inferring the input photon number from a measurement of the number of detection events on a single run.Many quantum information strategies require the preparation of nonclassical states. For example, the method of linear optical quantum computing proposed by Knill, Laflamme, and Milburn [1] demands the preparation of single photon states as well as maximally entangled photon multiplets. A number of schemes have been proposed for the preparation of such states, including single photon emitters [2,3,4] and conditionally prepared photon pairs from parametric downconversion [5,6,7]. Conditional state preparation requires the ability to distinguish states of different photon number, which is not possible using conventional photodetectors. Photon number resolution is also desirable to enhance the security of quantum cryptographic schemes [8,9]. In this case it is important to measure the photon statistics of the source at the sending and receiving stations. For implementations that use weak coherent states this means distinguishing between the detection of, say, one or two photons.According to the quantum theory of photodetection, the signal obtained from an ideal noise-free detector has a discrete form corresponding to the absorption of an integer number of quanta from the incident radiation. In practice, however, the granularity of the output signal is concealed by the noise of the detection mechanism. When very low light levels are detected using devices with single-photon sensitivity such as photomultipliers or Geiger-mode operated avalanche photodiodes (APDs), the electronic signal can be reliably converted into a binary message telling us with high efficiency whether an absorption event has occurred or not. However, the intrinsic noise of the gain mechanism necessary to bring the initial energy of absorbed radiation to the macroscopic level completely masks the information on exactly how many photons have triggered that event.There are several methods for constructing photon number resolving detectors. Among those demonstrated to date are the segmented photomultiplier [10], the superconducting bolometer [11], and the superconducting transimpedance amplifier [12]. These detectors operate at cryogenic temperatures and have single photon quantum efficiencies ranging from about 20% for the superconducting devices to approximately 70% in the case of the segmented photomultiplier. On the other hand, conventional room temperature APDs have intrinsic quantum efficiencies up to 80%, though they respond only to the presence or absence of radiation. The ease of...

Detectors that can resolve photon number are needed in many quantum information technologies. In order to be useful in quantum information processing, such detectors should be simple, easy to use, and be scalable to resolve any number of photons, as the application may require great portability such as in quantum cryptography. Here we describe the construction of a timemultiplexed detector, which uses a pair of standard avalanche photodiodes operated in Geiger mode. The detection technique is analysed theoretically and tested experimentally using a pulsed source of weak coherent light.

Exact analytic solutions of the time dependent Schrödinger equation are produced that exhibit a variety of vortex structures. The qualitative analysis of the motion of vortex lines is presented and various types of vortex behavior are identified. Vortex creation and annihilation and vortex interactions are illustrated in the special cases of the free motion, the motion in the harmonic potential, and in the constant magnetic field. Similar analysis of the vortex motions is carried out also for a relativistic wave equation.

A simple experimental setup consisting of a spontaneous parametric down-conversion source and passive linear optics is proposed for conditional preparation of a maximally entangled polarization state of two photons. Successful preparation is unambiguously heralded by coincident detection of four auxiliary photons. The proposed scheme utilizes the down-conversion term corresponding to the generation of three pairs of photons. We analyze imperfect detection of the auxiliary photons and demonstrate that its deleterious effect on the fidelity of the prepared state can be suppressed at the cost of decreasing the efficiency of the scheme. [4,5]. Indeed, the majority of current experiments is based on the production of photon pairs in the process of spontaneous parametric down-conversion [2], which is inherently random. Consequently, it is possible to determine whether a pair has been generated only by postselection, when looking a posteriori at the number of detected photons. This property is not essential in some applications such as tests of Bell's inequalities, but it becomes critical especially in experiments involving multiple photon pairs [4,6]. The random character of down-conversion sources may not be shared in the future by the solid-state sources of single photons or photon pairs that are presently being developed [7], though they will probably require operation at liquid-helium temperatures.From a practical point of view, spontaneous parametric down-conversion in nonlinear crystals is a stable and robust process that requires modest experimental means to set up. An interesting problem is therefore whether the randomness of the parametric sources could be overcome by means of conditional detection. In such a scheme, detecting a number of auxiliary photons by trigger detectors would provide a priori information that an entangled photon pair has been generated, without destructive photodetection. Such a pair could be used in the event-ready manner, or possibly stored in a cavity [8] or an atomic system [9] for later use at any instant of time. The most natural approach to realize this idea would be to perform the procedure of entanglement swapping on two entangled pairs generated independently, one by each of the two crystals. The Bell measurement would then play a twofold role of collapsing the state of the remaining photons onto an entangled state as well as assuring their presence [10]. However, when the pairs are generated in parametric down-conversion, it is necessary to take into account other processes whose probability of occurrence is of the same order of magnitude, such as generation of a double pair in one crystal and none in the second crystal [4]. This turns out to be a fundamental obstacle in the conditional preparation of maximal entanglement from four down-converted photons: it has been shown [5] that a maximally entangled state cannot be generated with a nonzero probability in any setup comprising down-converters and linear optics, based on detection of two auxiliary photons. This rules out t...