In this Letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett. 66, 252 (1991)] and L. Hardy [Phys. Rev. Lett. 73, 2279 (1994)]. A double homodyne measurement is used to measure correlations in the Fock space spanned by zero and one photons. Local oscillators used in the correlation measurement are distributed to two observers by copropagating it in an orthogonal polarization mode. This method eliminates the need for interferometrical stability in the setup, consequently making it a robust and scalable method.

We propose an entanglement measure for pure M ⊗N bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a 2 ⊗ 2 system, via a 2 ⊗ 3 system, to the general bipartite case. The measure emphasizes the role Bell states have, both for forming the measure, and for experimentally measuring the entanglement. The form of the measure is similar to generalized concurrence. In the case of 2 ⊗ 3 systems, we prove that our measure, that is directly measurable, equals the concurrence. It is also shown that in order to measure the entanglement, it is sufficient to measure the projections of the state onto a maximum of M(M - 1)N(N - 1)/2 Bell states.

3.

Heydari, Hoshang

KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.

We propose an explicit formula for a measure of entanglement of pure multipartite quantum states. We discuss the mathematical structure of the measure and give a brief explanation of its physical motivation. We apply the measure on some pure, tripartite, qubit states and demonstrate that, in general, the entanglement can depend on what actions are performed on the various subsystems, and specifically if the parties in possession of the subsystems cooperate or not. We also give some simple but illustrative examples of the entanglement of four-qubit and m-qubit states.

We propose an entanglement measure for pure M circle times N bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a 2 circle times 2 system, via a 2 circle times 3 system, to the general bipartite case. The measure emphasizes the role Bell states have, both for forming the measure and for experimentally measuring the entanglement. The form of the measure is similar to the generalized concurrence. In the case of 2 circle times 3 systems, we prove that our measure, which is directly measurable, equals the concurrence. It is also shown that, in order to measure the entanglement, it is sufficient to measure the projections of the state onto a maximum of M(M-1)N(N-1)/2 Bell states.

We propose an entanglement tensor to quantitatively compute the entanglement of a general pure multipartite quantum state. We compare the ensuing tensor with the concurrence for bipartite state and apply the tensor measure to some interesting examples of entangled three-qubit and four-qubit states. It is shown that in defining the degree of entanglement of a multi-partite state, one needs to make assumptions about the willingness of the parties to cooperate. For such states our tensor becomes a measure of generalized entanglement of assistance. We also discuss the degree of entanglement and the concurrence of assistance of two generic multi-qubit states.

7.

Heydari, Hoshang

et al.

KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.

Björk, Gunnar

KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.

We argue that (first-order) coherence is a relative, and not an absolute, property. It is shown how feedforward or feedback can be employed to make two (or more) lasers relatively coherent. We also show that after the relative coherence is established, the two lasers will,stay relatively coherent for some time even if the feedforward or feedback loop has been turned off, enabling, e.g., demonstration of unconditional quantum teleportation using lasers.