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Entangled states represent correlations between two separate systems that are too precise to be represented by products of local quantum states. We show that this limit of precision for the local quantum states of a pair of N-level systems can be defined by an appropriate class of uncertainty relations. The violation of such local uncertainty relations may be used as an experimental test of entanglement generation.

We report the first experimental demonstration of an optical quantum controlled-NOT gate without any path interference, where the two interacting path interferometers of the original proposals have been replaced by three partially polarizing beam splitters with suitable polarization dependent transmittance and reflectance. The performance of the device is evaluated using a recently proposed method, by which the quantum process fidelity and the entanglement capability can be estimated from the 32 measurement results of two classical truth tables, significantly less than the 256 measurement results required for full quantum tomography.

The density operator of a quantum state can be represented as a complex joint probability of any two observables whose eigenstates have nonzero mutual overlap. Transformations to a new basis set are then expressed in terms of complex conditional probabilities that describe the fundamental relation between precise statements about the three different observables. Since such transformations merely change the representation of the quantum state, these conditional probabilities provide a state-independent definition of the reversible and therefore effectively deterministic relations between the outcomes of different quantum measurements, including measurements of the same property performed at different times. In this paper, it is shown how classical reality emerges as an approximation to the fundamental laws of quantum determinism expressed by complex conditional probabilities. The quantum mechanical origin of phase spaces and trajectories is identified and implications for the interpretation of quantum measurements are considered. It is argued that the transformation laws of quantum determinism provide a fundamental description of the measurement dependence of empirical reality.

We show that a beam splitter of reflectivity one-third can be used to realize a quantum phase gate operation if only the outputs conserving the number of photons on each side are postselected. DOI: 10.1103/PhysRevA.66.024308 PACS number͑s͒: 03.67.Lx, 42.50.Ϫp The main difficulty in realizing quantum computation and quantum-information processing for single photon qubits is the optical implementation of controlled interactions between individual qubits. A deterministic interaction between separate photons would require the ability to apply strong nonlinearities during well-defined time intervals ͓1͔. At present, there are still many technological difficulties preventing the realization of such reliable quantum gates for photonic qubits. Recently, however, it has been shown that optical nonlinearities are not necessary for photonic qubit operation if reliable single photon sources and single photon detectors are available ͓2͔. The desired interaction between photonic qubits can also be realized by postselection. In particular, quantum phase gates and quantum control-not gates have been proposed, using additional input ports for single photons and additional output ports for postselection ͓2,3͔. In particular, the postselection condition for a successful gate operation requires that the number of photons detected in the postselection ports is equal to the number previously added to the system. It is then possible to predict the success of the operation without further measurements on the output ports. In principle, quantum feedback and teleportation could then be used to realize a scalable optical quantum computer. However, the technological difficulties associated with the requirements of single photon sources and fast feedback are such that a realization of networks using these quantum gates is unlikely in the near future. In this Brief Report we show that a quantum phase gate operation can also be achieved using only beam splitters if postselection in the output port is permitted. Additional single photon inputs are not necessary, since the effective nonlinearity can be realized by the direct interaction of the photonic qubits at the beam splitter. While the operation of such a random gate cannot be confirmed without measuring the output, the fact that single photon sources are not necessary and that higher efficiency can be achieved with fewer optical elements should make this proposal an attractive alternative in the experimental realization of networks processing multiple photonic qubits.The starting point for all linear optics manipulations of single photon qubits is the unitary operation Û R of a beam splitter of reflectivity R on the two mode input. In the following, we consider only the four-dimensional Hilbert space associated with zero or one photon in each input mode. The unitary operation Û R is then characterized by Û R ͉0;0͘ϭ͉0;0͘, Û R ͉0;1͘ϭͱR͉0;1͘Ϫiͱ1ϪR͉1;0͘, ͑1͒ Û R ͉1;0͘ϭͱR͉1;0͘Ϫiͱ1ϪR͉0;1͘, Û R ͉1;1͘ϭ͑2RϪ1 ͉͒1;1͘Ϫiͱ2R͑ 1ϪR ͉͒͑2;0͘ϩ͉0;2͘).Note that the assignment of phases is somewhat arbitra...