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Gunnar Björk

Publications and source records attributed to Gunnar Björk.

31 records · Page 2Linked to original sources
arXiv2007

Bipartite entanglement measure based on covariances

We propose an entanglement measure for two qudits based on the covariances of a set of generators of the su(N) algebra. In particular, we represent this measure in terms of the mutually unbiased projectors for N prime. For pure states this measure quantify entanglement, we obtain an explicit expression which relates it to the concurrence hierarchy, specifically the I-concurrence and the 3-concurrence. For mixed states we propose a separability criterion.

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arXiv2006

Entanglement quantification through local observable correlations

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.

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arXiv2005

Local uncertainty relations serving as measures of entanglement in a bipartite two-level system

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.

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arXiv2005

Schwarz inequality and concurrence

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.

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arXiv2005

Complex multi-projective variety and entanglement

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.

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arXiv2004

Quantum polarization properties of two-mode energy eigenstates

We show that any pure, two-mode, $N$-photon state with $N$ odd or equal to two can be transformed into an orthogonal state using only linear optics. According to a recently suggested definition of polarization degree, this implies that all such states are fully polarized. This is also found to be true for any pure, two-mode, energy eigenstate belonging to a two-dimensional SU(2) orbit. Complete two- and three-photon bases whose basis states are related by only phase shifts or geometrical rotations are also derived.

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arXiv2004

Entanglement tensor for a general pure multipartite quantum state

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.

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arXiv2004

A size criterion for macroscopic superposition states

An operational measure to quantify the sizes of some ``macroscopic quantum superpositions'', realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric applications than its superposed constituent states. This enhanced sensitivity, or ``interference utility'', may then be used as a size criterion among superpositions.

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arXiv2004

Entanglement criterion for pure $M\otimes N$ 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.

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arXiv2003

An experimental demonstration of single photon nonlocality

In this letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett., vol. 66, 252 (1991)] and L. Hardy [Phys. Rev. Lett.,vol. 73, 2279 (1994)]. A double heterodyne 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 co-propagating 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.

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arXiv2003

A measurable entanglement criterion for two qubits

We propose a directly measurable criterion for the entanglement of two qubits. We compare the criterion with other criteria, and we find that for pure states, and some mixed states, it coincides with the state's concurrency. The measure can be obtained with a Bell state analyser and the ability to make general local unitary transformations. However, the procedure fails to measure the entanglement of a general mixed two-qubit state.

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arXiv2003

Mutual first order coherence of phase-locked lasers

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.

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