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

Alternative model of the Antonov problem

Astrophysical systems will never be in a real Thermodynamic equilibrium: they undergo an evaporation process due to the fact that the gravity is not able to confine the particles. Ordinarily, this difficulty is overcome by enclosing the system in a rigid container which avoids the evaporation. We proposed an energetic prescription which is able to confine the particles, leading in this way to an alternative version of the Antonov isothermal model which unifies the well-known isothermal and polytropic profiles. Besides of the main features of the isothermal sphere model: the existence of the gravitational collapse and the energetic region with a negative specific heat, this alternative model has the advantage that the system size naturally appears as a consequence of the particles evaporation.Comment: RevTex4, 9 pages, 10 figures, Version Submitted to PR

Global entanglement in multiparticle systems

We define a polynomial measure of multiparticle entanglement which is scalable, i.e., which applies to any number of spin-1/2 particles. By evaluating it for three particle states, for eigenstates of the one dimensional Heisenberg antiferromagnet and on quantum error correcting code subspaces, we illustrate the extent to which it quantifies global entanglement. We also apply it to track the evolution of entanglement during a quantum computation.Comment: 9 pages, plain TeX, 1 PostScript figure included with epsf.tex (ignore the under/overfull \vbox error messages); for related work see http://math.ucsd.edu/~dmeyer/research.html or http://www.math.ucsd.edu/~nwallach

Three-qubit pure-state canonical forms

In this paper we analyze the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete classification of pure three-qubit states. This classification is related to the values of the polynomial invariants under local unitary transformations by a one-to-one correspondence.Comment: REVTEX, 9 pages, 1 figur

Thermodynamic entropy of a many body energy eigenstate

It is argued that a typical many body energy eigenstate has a well defined thermodynamic entropy and that individual eigenstates possess thermodynamic characteristics analogous to those of generic isolated systems. We examine large systems with eigenstate energies equivalent to finite temperatures. When quasi-static evolution of a system is adiabatic (in the quantum mechanical sense), two coupled subsystems can transfer heat from one subsystem to another yet remain in an energy eigenstate. To explicitly construct the entropy from the wave function, degrees of freedom are divided into two unequal parts. It is argued that the entanglement entropy between these two subsystems is the thermodynamic entropy per degree of freedom for the smaller subsystem. This is done by tracing over the larger subsystem to obtain a density matrix, and calculating the diagonal and off-diagonal contributions to the entanglement entropy.Comment: 18 page

Local symmetry properties of pure 3-qubit states

Entanglement types of pure states of 3 qubits are classified by means of their stabilisers in the group of local unitary operations. It is shown that the stabiliser is generically discrete, and that a larger stabiliser indicates a stationary value for some local invariant. We describe all the exceptional states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published version, with minor correction

Accessing the dynamics of large many-particle systems using Stochastic Series Expansion

The Stochastic Series Expansion method (SSE) is a Quantum Monte Carlo (QMC) technique working directly in the imaginary time continuum and thus avoiding "Trotter discretization" errors. Using a non-local "operator-loop update" it allows treating large quantum mechanical systems of many thousand sites. In this paper we first give a comprehensive review on SSE and present benchmark calculations of SSE's scaling behavior with system size and inverse temperature, and compare it to the loop algorithm, whose scaling is known to be one of the best of all QMC methods. Finally we introduce a new and efficient algorithm to measure Green's functions and thus dynamical properties within SSE.Comment: 11 RevTeX pages including 7 figures and 5 table

Properties of Entanglement Monotones for Three-Qubit Pure States

Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked at. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state under local unitary transformations. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [Phys. Rev. A 60, 910 (1999)]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.Comment: 14 pages, REVTe

Classification of multi-qubit mixed states: separability and distillability properties

We give a complete, hierarchic classification for arbitrary multi-qubit mixed states based on the separability properties of certain partitions. We introduce a family of N-qubit states to which any arbitrary state can be depolarized. This family can be viewed as the generalization of Werner states to multi-qubit systems. We fully classify those states with respect to their separability and distillability properties. This provides sufficient conditions for nonseparability and distillability for arbitrary states.Comment: 12 pages, 2 figure