Parametrization of projector-based witnesses for bipartite systems

Entanglement witnesses are nonpositive Hermitian operators which can detect the presence of entanglement. In this paper, we provide a general parametrization for orthonormal basis of ${\mathbb C}^n$ and use it to construct projector-based witness operators for entanglement detection in the vicinity of pure bipartite states. Our method to parameterize entanglement witnesses is operationally simple and could be used for doing symbolic and numerical calculations. As an example we use the method for detecting entanglement between an atom and the single mode of quantized field, described by the Jaynes-Cummings model. We also compare the detection of witnesses with the negativity of the state, and show that in the vicinity of pure stats such constructed witnesses able to detect entanglement of the state.Comment: 12 pages, four figure

Test for entanglement using physically observable witness operators and positive maps

Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives a new family of positive but non-completely positive maps of arbitrary high dimensions which provide a much better test than the witness operators themselves. Moreover, we find there are two types of positive maps that can detect 2xN and 4xN bound entangled states. Since entanglement witnesses are physical observables and may be measured locally our construction could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl

Some Properties of the Computable Cross Norm Criterion for Separability

The computable cross norm (CCN) criterion is a new powerful analytical and computable separability criterion for bipartite quantum states, that is also known to systematically detect bound entanglement. In certain aspects this criterion complements the well-known Peres positive partial transpose (PPT) criterion. In the present paper we study important analytical properties of the CCN criterion. We show that in contrast to the PPT criterion it is not sufficient in dimension 2 x 2. In higher dimensions we prove theorems connecting the fidelity of a quantum state with the CCN criterion. We also analyze the behaviour of the CCN criterion under local operations and identify the operations that leave it invariant. It turns out that the CCN criterion is in general not invariant under local operations.Comment: 7 pages; accepted by Physical Review A; error in Appendix B correcte

One-and-a-half quantum de Finetti theorems

We prove a new kind of quantum de Finetti theorem for representations of the unitary group U(d). Consider a pure state that lies in the irreducible representation U_{mu+nu} for Young diagrams mu and nu. U_{mu+nu} is contained in the tensor product of U_mu and U_nu; let xi be the state obtained by tracing out U_nu. We show that xi is close to a convex combination of states Uv, where U is in U(d) and v is the highest weight vector in U_mu. When U_{mu+nu} is the symmetric representation, this yields the conventional quantum de Finetti theorem for symmetric states, and our method of proof gives near-optimal bounds for the approximation of xi by a convex combination of product states. For the class of symmetric Werner states, we give a second de Finetti-style theorem (our 'half' theorem); the de Finetti-approximation in this case takes a particularly simple form, involving only product states with a fixed spectrum. Our proof uses purely group theoretic methods, and makes a link with the shifted Schur functions. It also provides some useful examples, and gives some insight into the structure of the set of convex combinations of product states.Comment: 14 pages, 3 figures, v4: minor additions (including figures), published versio

Differential Geometry of Bipartite Quantum States

We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given Schmidt ranks or Schmidt coefficients are explicitly presented. The dimensions of the related manifolds are calculated.Comment: 10 page

Nonlinear Inequalities and Entropy-Concurrence Plane

Nonlinear inequalities based on the quadratic Renyi entropy for mixed two-qubit states are characterized on the Entropy-Concurrence plane. This class of inequalities is stronger than Clauser-Horne-Shimony-Holt (CHSH) inequalities and, in particular, are violated "in toto" by the set of Type I Maximally-Entangled-Mixture States (MEMS I)

The 3D Structure of N132D in the LMC: A Late-Stage Young Supernova Remnant

We have used the Wide Field Spectrograph (WiFeS) on the 2.3m telescope at Siding Spring Observatory to map the [O III] 5007{\AA} dynamics of the young oxygen-rich supernova remnant N132D in the Large Magellanic Cloud. From the resultant data cube, we have been able to reconstruct the full 3D structure of the system of [O III] filaments. The majority of the ejecta form a ring of ~12pc in diameter inclined at an angle of 25 degrees to the line of sight. We conclude that SNR N132D is approaching the end of the reverse shock phase before entering the fully thermalized Sedov phase of evolution. We speculate that the ring of oxygen-rich material comes from ejecta in the equatorial plane of a bipolar explosion, and that the overall shape of the SNR is strongly influenced by the pre-supernova mass loss from the progenitor star. We find tantalizing evidence of a polar jet associated with a very fast oxygen-rich knot, and clear evidence that the central star has interacted with one or more dense clouds in the surrounding ISM.Comment: Accepted for Publication in Astrophysics & Space Science, 18pp, 8 figure

A device for feasible fidelity, purity, Hilbert-Schmidt distance and entanglement witness measurements

A generic model of measurement device which is able to directly measure commonly used quantum-state characteristics such as fidelity, overlap, purity and Hilbert-Schmidt distance for two general uncorrelated mixed states is proposed. In addition, for two correlated mixed states, the measurement realizes an entanglement witness for Werner's separability criterion. To determine these observables, the estimation only one parameter - the visibility of interference, is needed. The implementations in cavity QED, trapped ion and electromagnetically induced transparency experiments are discussed.Comment: 6 pages, 3 figure

Monogamy of Correlations vs. Monogamy of Entanglement

A fruitful way of studying physical theories is via the question whether the possible physical states and different kinds of correlations in each theory can be shared to different parties. Over the past few years it has become clear that both quantum entanglement and non-locality (i.e., correlations that violate Bell-type inequalities) have limited shareability properties and can sometimes even be monogamous. We give a self-contained review of these results as well as present new results on the shareability of different kinds of correlations, including local, quantum and no-signalling correlations. This includes an alternative simpler proof of the Toner-Verstraete monogamy inequality for quantum correlations, as well as a strengthening thereof. Further, the relationship between sharing non-local quantum correlations and sharing mixed entangled states is investigated, and already for the simplest case of bi-partite correlations and qubits this is shown to be non-trivial. Also, a recently proposed new interpretation of Bell's theorem by Schumacher in terms of shareability of correlations is critically assessed. Finally, the relevance of monogamy of non-local correlations for secure quantum key distribution is pointed out, although, and importantly, it is stressed that not all non-local correlations are monogamous.Comment: 12 pages, 2 figures. Invited submission to a special issue of Quantum Information Processing. v2: Published version. Open acces

Quantum state merging and negative information

We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.Comment: 23 pages, 3 figure