Abstract:
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.

Abstract:
We propose an entanglement tensor to 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. We also discuss the degree of entanglement of the multi-qubit $\ket{W_{M}}$-states.

Abstract:
We comment on the recent suggestion to use a family of local uncertainty relations as a standard way of quantifying entanglement in two-qubit systems. Some statements made on the applicability of the proposed "measures" are overly optimistic. We exemplify how these specific "measures" fall short, and present a minor modification of the general theory which uses the same experimentally gathered information, but in a slightly different, better way.

Abstract:
We propose a entanglement measure for pure $M \otimes N$ bipartite quantum states. We obtain the measure by generalizing the equivalent measure for a $2 \otimes 2$ system, via a $2 \otimes 3$ 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 $2 \otimes 3$ 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.

Abstract:
We present a significantly improved scheme of entanglement detection inspired by local uncertainty relations for a system consisting of two qubits. Developing the underlying idea of local uncertainty relations, namely correlations, we demonstrate that it's possible to define a measure which is invariant under local unitary transformations and which is based only on local measurements. It is quite simple to implement experimentally and it allows entanglement quantification in a certain range for mixed states and exactly for pure states, without first obtaining full knowledge (e.g. through tomography) of the state.

Abstract:
We study entanglement dynamics between four qubits interacting through two isolated Jaynes-Cummings hamiltonians, via the entanglement measure based on the wedge product. We compare the results with similar results obtained using bipartite concurrence resulting in what is referred to as "entanglement sudden death". We find a natural entanglement invariant under evolution demonstrating that entanglement sudden death is caused by ignoring (tracing over) some of the system's degrees of freedom that become entangled through the interaction.

Abstract:
We establish a relation between the Schwarz inequality and the generalized concurrence of an arbitrary, pure, bipartite or tripartite state. This relation places concurrence in a geometrical and functional-analytical setting.

Abstract:
We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.

Abstract:
In this paper, we will show that a vanishing generalized concurrence of a separable state can be seen as an algebraic variety called the Segre variety. This variety define a quadric space which gives a geometric picture of separable states. For pure, bi- and three-partite states the variety equals the generalized concurrence. Moreover, we generalize the Segre variety to a general multipartite state by relating to a quadric space defined by two-by-two subdeterminants.

Abstract:
We present two experiments that achieve phase super-resolution at telecommunication wavelengths. One of the experiments is realized in the space domain and the other in the time domain. Both experiments show high visibilities and are performed with standard lasers and single-photon detectors. The first experiment uses six-photon coincidences, whereas the latter needs no coincidence measurements, is easy to perform, and achieves, in principle, arbitrarily high phase super-resolution. Here, we demonstrate a 30-fold increase of the resolution. We stress that neither entanglement nor joint detection is needed in these experiments, demonstrating that neither is necessary to achieve phase super-resolution.