General polygamy inequality of multi-party quantum entanglement

Using entanglement of assistance, we establish a general polygamy inequality of multi-party entanglement in arbitrary dimensional quantum systems. For multi-party closed quantum systems, we relate our result with the monogamy of entanglement to show that the entropy of entanglement is an universal entanglement measure that bounds both monogamy and polygamy of multi-party quantum entanglement.Comment: 4 pages, 1 figur

Deterministic Entanglement of Assistance and Monogamy Constraints

Certain quantum information tasks require entanglement of assistance, namely a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that 'concurrence of assistance' (CoA) identifies capabilities and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that CoA is an entanglement monotone for $(2\times2\times n)$-dimensional pure states. Moreover, if the CoA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be transformed to the latter via local operations and classical communication, and we calculate the maximum probability for this transformation when this condition is not met.Comment: 5 pages, no figure

Generalized W-Class State and its Monogamy Relation

We generalize the W class of states from $n$ qubits to $n$ qudits and prove that their entanglement is fully characterized by their partial entanglements even for the case of the mixture that consists of a W-class state and a product state $\ket{0}^{\otimes n}$.Comment: 12 pages, 1 figur

Nonergodicity of entanglement and its complementary behavior to magnetization in infinite spin chain

We consider the problem of the validity of a statistical mechanical description of two-site entanglement in an infinite spin chain described by the XY model Hamiltonian. We show that the two-site entanglement of the state, evolved from the initial equilibrium state, after a change of the magnetic field, does not approach its equilibrium value. This suggests that two-site entanglement, like (single-site) magnetization, is a nonergodic quantity in this model. Moreover we show that these two nonergodic quantities behave in a complementary way.Comment: 4 pages, 2 eps figures, RevTeX4; v2: Published versio

Approximate quantum data storage and teleportation

In this paper we present an optimal protocol by which an unknown state on a Hilbert space of dimension $N$ can be approximately stored in an $M$-dimensional quantum system or be approximately teleported via an $M$-dimensional quantum channel. The fidelity of our procedure is determined for pure states as well as for mixed states and states which are entangled with auxiliary quantum systems of varying Hilbert space dimension, and it is compared with theoretical results for the maximally achievable fidelity.Comment: More detailed discussion of teleportation of entangled and mixed states. Added reference to work by Banaszek. 8 pages, 1 figur

Maximizing nearest neighbour entanglement in finitely correlated qubit--chains

We consider translationally invariant states of an infinite one dimensional chain of qubits or spin-1/2 particles. We maximize the entanglement shared by nearest neighbours via a variational approach based on finitely correlated states. We find an upper bound of nearest neighbour concurrence equal to C=0.434095 which is 0.09% away from the bound C_W=0.434467 obtained by a completely different procedure. The obtained state maximizing nearest neighbour entanglement seems to approximate the maximally entangled mixed states (MEMS). Further we investigate in detail several other properties of the so obtained optimal state.Comment: 12 pages, 4 figures, 2nd version minor change

SBF Distances to Dwarf Elliptical Galaxies in the Sculptor Group

As part of an ongoing search for dwarf elliptical galaxies (dE) in the vicinity of the Local Group, we acquired deep B and R-band images for five dE candidates identified in the Sculptor (Scl) group region. We carried out a surface brightness fluctuation (SBF) analysis on the R-band images to measure the apparent fluctuation magnitude \bar{m}_R for each dE. Using predictions from stellar population synthesis models the galaxy distances were determined. All of these dE candidates turned out to be satellites of Scl group major members. A redshift measurement of the dE candidate ESO294-010 yielded an independent confirmation of its group membership: the [OIII] and H$_\alpha$ emission lines from a small HII region gave a heliocentric velocity of 117(\pm 5) km s-1, in close agreement with the velocity of its parent galaxy NGC 55 (v_\odot=125 km s-1). The precision of the SBF distances (5 to 10%) contributes to delineating the cigar-like distribution of the Scl group members, which extend over distances from 1.7 to 4.4 Mpc and are concentrated in three, possibly four subclumps. The Hubble diagram for nine Scl galaxies, including two of our dEs, exhibits a tight linear velocity--distance relation with a steep slope of 119 km s-1 Mpc-1. The results indicate that gravitational interaction among the Scl group members plays only a minor role in the dynamics of the group. However, the Hubble flow of the entire system appears strongly disturbed by the large masses of our Galaxy and M31 leading to the observed shearing motion. From the distances and velocities of 49 galaxies located in the Local Group and towards the Scl group, we illustrate the continuity of the galaxy distribution which strongly supports the view that the two groups form a single supergalactic structure.Comment: To appear in The Astronomical Journal, December 1998; 28 pages with 22 figure

Entanglement monogamy of multipartite higher-dimensional quantum systems using convex-roof extended negativity

We propose replacing concurrence by convex-roof extended negativity (CREN) for studying monogamy of entanglement (MoE). We show that all proven MoE relations using concurrence can be rephrased in terms of CREN. Furthermore we show that higher-dimensional (qudit) extensions of MoE in terms of CREN are not disproven by any of the counterexamples used to disprove qudit extensions of MoE in terms of concurrence. We further test the CREN version of MoE for qudits by considering fully or partially coherent mixtures of a qudit W-class state with the vacuum and show that the CREN version of MoE for qudits is satisfied in this case as well. The CREN version of MoE for qudits is thus a strong conjecture with no obvious counterexamples.Comment: 9 page