Fragility of a class of highly entangled states of many quantum-bits

We consider a Quantum Computer with n quantum-bits (`qubits'), where each qubit is coupled independently to an environment affecting the state in a dephasing or depolarizing way. For mixed states we suggest a quantification for the property of showing {\it quantum} uncertainty on the macroscopic level. We illustrate in which sense a large parameter can be seen as an indicator for large entanglement and give hypersurfaces enclosing the set of separable states. Using methods of the classical theory of maximum likelihood estimation we prove that this parameter is decreasing with 1/\sqrt{n} for all those states which have been exposed to the environment. Furthermore we consider a Quantum Computer with perfect 1-qubit gates and 2-qubit gates with depolarizing error and show that any state which can be obtained from a separable initial state lies inbetween a family of pairs of certain hypersurfaces parallel to those enclosing the separable ones.Comment: 9 Pages, RevTe

Topologically non--trivial chiral transformations: The chiral invariant elimination of the axial vector meson

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu--Jona--Lasinio model the hidden gauge and massive Yang--Mills approaches to vector mesons are demonstrated to be linked by a special chiral transformation which removes the chiral field from the scalar--pseudoscalar sector. The chirally rotated axial vector meson field ($\tilde A_\mu$) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu--Jona--Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important physical property which is usually generated only by non--vanishing axial vector is thus carried over by the simplification $\tilde A_\mu=0$.Comment: 28 pages LaTeX, 4 figures appended as postscript files, UNITU-THEP-12/199

The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations

We represent generalized density matrices of a $d$-complex dimensional quantum system as a subcone of a real pointed cone of revolution in $\mathbb{R}^{d^2}$, or indeed a Minkowskian cone in $\mathbb{E}^{1,d^2-1}$. Generalized pure states correspond to certain future-directed light-like vectors of $\mathbb{E}^{1,d^2-1}$. This extension of the Generalized Bloch Sphere enables us to cater for non-trace-preserving quantum operations, and in particluar to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulae for the one qubit case and express the post-measurement states in terms of the initial state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance tradeoff in the case of two equiprobable pure states. Thus we recover Fuchs and Peres' formula in an elegant manner.Comment: 11 pages, revtex, v3: some typos correcte

Local filtering operations on two qubits

We consider one single copy of a mixed state of two qubits and investigate how its entanglement changes under local quantum operations and classical communications (LQCC) of the type $\rho'\sim (A\otimes B)\rho(A\otimes B)^{\dagger}$. We consider a real matrix parameterization of the set of density matrices and show that these LQCC operations correspond to left and right multiplication by a Lorentz matrix, followed by normalization. A constructive way of bringing this matrix into a normal form is derived. This allows us to calculate explicitly the optimal local filterin operations for concentrating entanglement. Furthermore we give a complete characterization of the mixed states that can be purified arbitrary close to a Bell state. Finally we obtain a new way of calculating the entanglement of formation.Comment: 4 page

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.Comment: 4 pages, Revtex. Published version, minor changes and new references adde

Distillation of GHZ states by selective information manipulation

Methods for distilling maximally entangled tripartite (GHZ) states from arbitrary entangled tripartite pure states are described. These techniques work for virtually any input state. Each technique has two stages which we call primary and secondary distillation. Primary distillation produces a GHZ state with some probability, so that when applied to an ensemble of systems, a certain percentage is discarded. Secondary distillation produces further GHZs from the discarded systems. These protocols are developed with the help of an approach to quantum information theory based on absolutely selective information, which has other potential applications.Comment: minor corrections, especially of some numerical values; conclusions unaffecte

The Nambu-Jona-Lasinio Chiral Soliton with Constrained Baryon Number

A regularization for the baryon number consistent with the energy in the Nambu-Jona-Lasinio model is introduced. The soliton solution is constructed with the regularized baryon number constrained to unity. It is furthermore demonstrated that this constraint prevents the soliton from collapsing when scalar fields are allowed to be space dependent. In this scheme the scalar fields actually vanish at the origin reflecting a partial restoration of chiral symmetry. Also the influence of this constraint on some static properties of baryons is discussed.Comment: 10 LaTeX pages 4 figures, report no UNITU-THEP-7/199

Experimental Demonstration of Greenberger-Horne-Zeilinger Correlations Using Nuclear Magnetic Resonance

The Greenberger-Horne-Zeilinger (GHZ) effect provides an example of quantum correlations that cannot be explained by classical local hidden variables. This paper reports on the experimental realization of GHZ correlations using nuclear magnetic resonance (NMR). The NMR experiment differs from the originally proposed GHZ experiment in several ways: it is performed on mixed states rather than pure states; and instead of being widely separated, the spins on which it is performed are all located in the same molecule. As a result, the NMR version of the GHZ experiment cannot entirely rule out classical local hidden variables. It nonetheless provides an unambiguous demonstration of the "paradoxical" GHZ correlations, and shows that any classical hidden variables must communicate by non-standard and previously undetected forces. The NMR demonstration of GHZ correlations shows the power of NMR quantum information processing techniques for demonstrating fundamental effects in quantum mechanics.Comment: Latex2.09, 8 pages, 1 eps figur

On local invariants of pure three-qubit states

We study invariants of three-qubit states under local unitary transformations, i.e. functions on the space of entanglement types, which is known to have dimension 6. We show that there is no set of six independent polynomial invariants of degree less than or equal to 6, and find such a set with maximum degree 8. We describe an intrinsic definition of a canonical state on each orbit, and discuss the (non-polynomial) invariants associated with it.Comment: LateX, 13 pages. Minor typoes corrected. Published versio