Entanglement measure for general pure multipartite quantum states

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.Comment: 5 page

Generalized Chaplygin gas as geometrical dark energy

The generalized Chaplygin gas provides an interesting candidate for the present accelerated expansion of the universe. We explore a geometrical explanation for the generalized Chaplygin gas within the context of brane world theories where matter fields are confined to the brane by means of the action of a confining potential. We obtain the modified Friedmann equations, deceleration parameter and age of the universe in this scenario and show that they are consistent with the present observational data.Comment: 11 pages, 3 figures, to appear in PR

The invariant-comb approach and its relation to the balancedness of multipartite entangled states

The invariant-comb approach is a method to construct entanglement measures for multipartite systems of qubits. The essential step is the construction of an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. An appealing feature of this approach is that for qubits (or spins 1/2) the combs are automatically invariant under SL(2,\CC), which implies that the obtained invariants are entanglement monotones by construction. By asking which property of a state determines whether or not it is detected by a polynomial SL(2,\CC) invariant we find that it is the presence of a {\em balanced part} that persists under local unitary transformations. We present a detailed analysis for the maximally entangled states detected by such polynomial invariants, which leads to the concept of {\em irreducibly balanced} states. The latter indicates a tight connection with SLOCC classifications of qubit entanglement. \\ Combs may also help to define measures for multipartite entanglement of higher-dimensional subsystems. However, for higher spins there are many independent combs such that it is non-trivial to find an invariant one. By restricting the allowed local operations to rotations of the coordinate system (i.e. again to the SL(2,\CC)) we manage to define a unique extension of the concurrence to general half-integer spin with an analytic convex-roof expression for mixed states.Comment: 17 pages, revtex4. Substantially extended manuscript (e.g. proofs have been added); title and abstract modified

Concurrence classes for general pure multipartite states

We propose concurrence classes for general pure multipartite states based on an orthogonal complement of a positive operator valued measure on quantum phase. In particular, we construct $W^{m}$ class, $GHZ^{m}$, and $GHZ^{m-1}$ class concurrences for general pure $m$-partite states. We give explicit expressions for $W^{3}$ and $GHZ^{3}$ class concurrences for general pure three-partite states and for $W^{4}$, $GHZ^{4}$, and $GHZ^{3}$ class concurrences for general pure four-partite states.Comment: 14 page

Entanglement criterion for pure M⊗NM\otimes N bipartite quantum states

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.Comment: 6 page

Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure

In this paper, we propose concurrence classes for an arbitrary multi-qubit state based on orthogonal complement of a positive operator valued measure, or POVM in short, on quantum phase. In particular, we construct concurrence for an arbitrary two-qubit state and concurrence classes for the three- and four-qubit states. And finally, we construct $W^{m}$ and $GHZ^{m}$ class concurrences for multi-qubit states. The unique structure of our POVM enables us to distinguish different concurrence classes for multi-qubit states.Comment: 8 page

Defending Continuous Variable Teleportation: Why a laser is a clock, not a quantum channel

It has been argued [T. Rudolph and B.C. Sanders, Phys. Rev. Lett. {\bf 87}, 077903 (2001)] that continuous-variable quantum teleportation at optical frequencies has not been achieved because the source used (a laser) was not `truly coherent'. Van Enk, and Fuchs [Phys. Rev. Lett, {\bf 88}, 027902 (2002)], while arguing against Rudolph and Sanders, also accept that an `absolute phase' is achievable, even if it has not been achieved yet. I will argue to the contrary that `true coherence' or `absolute phase' is always illusory, as the concept of absolute time (at least for frequencies beyond direct human experience) is meaningless. All we can ever do is to use an agreed time standard. In this context, a laser beam is fundamentally as good a `clock' as any other. I explain in detail why this claim is true, and defend my argument against various objections. In the process I discuss super-selection rules, quantum channels, and the ultimate limits to the performance of a laser as a clock. For this last topic I use some earlier work by myself [Phys. Rev. A {\bf 60}, 4083 (1999)] and Berry and myself [Phys. Rev. A {\bf 65}, 043803 (2002)] to show that a Heisenberg-limited laser with a mean photon number $\mu$ can synchronize $M$ independent clocks each with a mean-square error of $\sqrt{M}/4\mu$ radians$^2$.Comment: 22 pages, to be published in a special issue of J. Opt. B. This is an extended version of quant-ph/0303116 (the SPIE conference paper

Glimmers of a pre-geometric perspective

Space-time measurements and gravitational experiments are made by using objects, matter fields or particles and their mutual relationships. As a consequence, any operationally meaningful assertion about space-time is in fact an assertion about the degrees of freedom of the matter (\emph{i.e} non gravitational) fields; those, say for definiteness, of the Standard Model of particle physics. As for any quantum theory, the dynamics of the matter fields can be described in terms of a unitary evolution of a state vector in a Hilbert space. By writing the Hilbert space as a generic tensor product of "subsystems" we analyse the evolution of a state vector on an information theoretical basis and attempt to recover the usual space-time relations from the information exchanges between these subsystems. We consider generic interacting second quantized models with a finite number of fermionic degrees of freedom and characterize on physical grounds the tensor product structure associated with the class of "localized systems" and therefore with "position". We find that in the case of free theories no space-time relation is operationally definable. On the contrary, by applying the same procedure to the simple interacting model of a one-dimensional Heisenberg spin chain we recover the tensor product structure usually associated with "position". Finally, we discuss the possible role of gravity in this framework.Comment: 30 page

Stability of circular orbits of spinning particles in Schwarzschild-like space-times

Circular orbits of spinning test particles and their stability in Schwarzschild-like backgrounds are investigated. For these space-times the equations of motion admit solutions representing circular orbits with particles spins being constant and normal to the plane of orbits. For the de Sitter background the orbits are always stable with particle velocity and momentum being co-linear along them. The world-line deviation equations for particles of the same spin-to-mass ratios are solved and the resulting deviation vectors are used to study the stability of orbits. It is shown that the orbits are stable against radial perturbations. The general criterion for stability against normal perturbations is obtained. Explicit calculations are performed in the case of the Schwarzschild space-time leading to the conclusion that the orbits are stable.Comment: eps figures, submitted to General Relativity and Gravitatio