Natural multiparticle entanglement in a Fermi gas

We investigate multipartite entanglement in a non-interacting fermion gas, as a function of fermion separation, starting from the many particle fermion density matrix. We prove that all multiparticle entanglement can be built only out of two-fermion entanglement. Although from the Pauli exclusion principle we would always expect entanglement to decrease with fermion distance, we surprisingly find the opposite effect for certain fermion configurations. The von Neumann entropy is found to be proportional to the volume for a large number of particles even when they are arbitrarily close to each other. We will illustrate our results using different configurations of two, three, and four fermions at zero temperature although all our results can be applied to any temperature and any number of particles.Comment: Replaced with revised editio

Magnetic Susceptibility as a Macrosopic Entaglement Witness

We show that magnetic susceptibility can reveal spin entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between spin entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be a macroscopic spin entanglement witness that can be applied without complete knowledge of the specific model (Hamiltonian) of the solid.Comment: 6 Pages, 2 figures, revtex

Equation of state for Entanglement in a Fermi gas

Entanglement distance is the maximal separation between two entangled electrons in a degenerate electron gas. Beyond that distance, all entanglement disappears. We relate entanglement distance to degeneracy pressure both for extreme relativistic and non-relativistic systems, and estimate the entanglement distance in a white dwarf. Treating entanglement as a thermodynamical quantity, we relate the entropy of formation and concurrence to relative electron distance, pressure, and temperature, to form a new equation of state for entanglement.Comment: To appear in Phys. Rev. A., 4 pages, 1 figur

A scheme for entanglement extraction from a solid

Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact of the typical symmetrization procedure of many-body wave function in solid state physics. Here we show that this entanglement is physical demonstrating the principles of its extraction from a typical solid state system by scattering two particles off the system. Moreover we show how to simulate this process using present-day optical lattices technology. This demonstrates not only that entanglement exists in solids but also that it can be used for quantum information processing or for test of Bell's inequalities.Comment: 10 pages, 3 figures, published versio

Macroscopic Observables Detecting Genuine Multipartite Entanglement and Partial Inseparability in Many-Body Systems

We show a general approach for detecting genuine multipartite entanglement (GME) and partial inseparability in many-body-systems by means of macroscopic observables (such as the energy) only. We show that the obtained criteria, the "GME gap" and "the k-entanglement gap", detect large areas of genuine multipartite entanglement and partial entanglement in typical many body states, which are not detected by other criteria. As genuine multipartite entanglement is a necessary property for several quantum information theoretic applications such as e.g. secret sharing or certain kinds of quantum computation, our methods can be used to select or design appropriate condensed matter systems.Comment: 4 pages, 3 figures, published version, title extende

Entanglement as a quantum order parameter

We show that the quantum order parameters (QOP) associated with the transitions between a normal conductor and a superconductor in the BCS and eta-pairing models and between a Mott-insulator and a superfluid in the Bose-Hubbard model are directly related to the amount of entanglement existent in the ground state of each system. This gives a physical meaningful interpretation to these QOP, which shows the intrinsically quantum nature of the phase transitions considered.Comment: 5 pages. No figures. Revised version. References adde

Entanglement in spin-one Heisenberg chains

By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.Comment: 7 pages and 4 figure

Survival of entanglement in thermal states

We present a general sufficiency condition for the presence of multipartite entanglement in thermal states stemming from the ground state entanglement. The condition is written in terms of the ground state entanglement and the partition function and it gives transition temperatures below which entanglement is guaranteed to survive. It is flexible and can be easily adapted to consider entanglement for different splittings, as well as be weakened to allow easier calculations by approximations. Examples where the condition is calculated are given. These examples allow us to characterize a minimum gapping behavior for the survival of entanglement in the thermodynamic limit. Further, the same technique can be used to find noise thresholds in the generation of useful resource states for one-way quantum computing.Comment: 6 pages, 2 figures. Changes made in line with publication recommendations. Motivation and concequences of result clarified, with the addition of one more example, which applies the result to give noise thresholds for measurement based quantum computing. New author added with new result

Quantum correlations in the temporal CHSH scenario

We consider a temporal version of the CHSH scenario using projective measurements on a single quantum system. It is known that quantum correlations in this scenario are fundamentally more general than correlations obtainable with the assumptions of macroscopic realism and non-invasive measurements. In this work, we also educe some fundamental limitations of these quantum correlations. One result is that a set of correlators can appear in the temporal CHSH scenario if and only if it can appear in the usual spatial CHSH scenario. In particular, we derive the validity of the Tsirelson bound and the impossibility of PR-box behavior. The strength of possible signaling also turns out to be surprisingly limited, giving a maximal communication capacity of approximately 0.32 bits. We also find a temporal version of Hardy's nonlocality paradox with a maximal quantum value of 1/4.Comment: corrected versio

Hybrid cluster state proposal for a quantum game

We propose an experimental implementation of a quantum game algorithm in a hybrid scheme combining the quantum circuit approach and the cluster state model. An economical cluster configuration is suggested to embody a quantum version of the Prisoners' Dilemma. Our proposal is shown to be within the experimental state-of-art and can be realized with existing technology. The effects of relevant experimental imperfections are also carefully examined.Comment: 4 pages, 3 figures, RevTeX