Frontier between separability and quantum entanglement in a many spin system

We discuss the critical point $x_c$ separating the quantum entangled and separable states in two series of N spins S in the simple mixed state characterized by the matrix operator $\rho=x|\tilde{\phi}><\tilde{\phi}| + \frac{1-x}{D^N} I_{D^N}$ where $x \in [0,1]$, $D =2S+1$, ${\bf I}_{D^N}$ is the $D^N \times D^N$ unity matrix and $|\tilde {\phi}>$ is a special entangled state. The cases x=0 and x=1 correspond respectively to fully random spins and to a fully entangled state. In the first of these series we consider special states $|\tilde{\phi}>$ invariant under charge conjugation, that generalizes the N=2 spin S=1/2 Einstein-Podolsky-Rosen state, and in the second one we consider generalizations of the Weber density matrices. The evaluation of the critical point $x_c$ was done through bounds coming from the partial transposition method of Peres and the conditional nonextensive entropy criterion. Our results suggest the conjecture that whenever the bounds coming from both methods coincide the result of $x_c$ is the exact one. The results we present are relevant for the discussion of quantum computing, teleportation and cryptography.Comment: 4 pages in RevTeX forma

Separable-entangled frontier in a bipartite harmonic system

We consider a statistical mixture of two identical harmonic oscillators which is characterized by four parameters, namely, the concentrations (x and y) of diagonal and nondiagonal bipartite states, and their associated thermal-like noises (T/a and T, respectively). The fully random mixture of two spins 1/2 as well as the Einstein-Podolsky-Rosen (EPR) state are recovered as particular instances. By using the conditional nonextensive entropy as introduced by Abe and Rajagopal, we calculate the separable-entangled frontier. Although this procedure is known to provide a necessary but in general not sufficient condition for separability, it does recover, in the particular case x=T=0 (for all a), the 1/3 exact result known as Peres' criterion. This is an indication of reliability of the calculation of the frontier in the entire parameter space. The x=0 frontier remarkably resembles to the critical line associated with standard diluted ferromagnetism where the entangled region corresponds to the ordered one and the separable region to the paramagnetic one. The entangled region generically shrinks for increasing T or increasing a.Comment: 6 pages, 5 figure

Evidence for entanglement at high temperatures in an engineered molecular magnet

The molecular compound [Fe$_{2}$($\mu_{2}$-oxo)(C$_{3}$H$_{4}$N$_{2}$)$_{6}$(C$_{2}$O$_{4}$)$_{2}$] was designed and synthesized for the first time and its structure was determined using single-crystal X-ray diffraction. The magnetic susceptibility of this compound was measured from 2 to 300 K. The analysis of the susceptibility data using protocols developed for other spin singlet ground-state systems indicates that the quantum entanglement would remain at temperatures up to 732 K, significantly above the highest entanglement temperature reported to date. The large gap between the ground state and the first-excited state (282 K) suggests that the spin system may be somewhat immune to decohering mechanisms. Our measurements strongly suggest that molecular magnets are promising candidate platforms for quantum information processing

Decoherence and wave function collapse

The possibility of consistency between the basic quantum principles of quantum mechanics and wave function collapse is reexamined. A specific interpretation of environment is proposed for this aim and applied to decoherence. When the organization of a measuring apparatus is taken into account, this approach leads also to an interpretation of wave function collapse, which would result in principle from the same interactions with environment as decoherence. This proposal is shown consistent with the non-separable character of quantum mechanics

Qualitative individuation in permutation-invariant quantum mechanics

In this article I expound an understanding of the quantum mechanics of so-called "indistinguishable" systems in which permutation invariance is taken as a symmetry of a special kind, namely the result of representational redundancy. This understanding has heterodox consequences for the understanding of the states of constituent systems in an assembly and for the notion of entanglement. It corrects widespread misconceptions about the inter-theoretic relations between quantum mechanics and both classical particle mechanics and quantum field theory. The most striking of the heterodox consequences are: (i) that fermionic states ought not always to be considered entangled; (ii) it is possible for two fermions or two bosons to be discerned using purely monadic quantities; and that (iii) fermions (but not bosons) may always be so discerned.Comment: 58 pages, 5 figure

Multipartite positive-partial-transpose inequalities exponentially stronger than local reality inequalities

We show that positivity of {\it every} partial transpose of $N$-partite quantum states implies new inequalities on Bell correlations which are stronger than standard Bell inequalities by a factor of $2^{(N-1)/2}$. A violation of the inequality implies the system is in a bipartite distillable entangled state. It turns out that a family of $N$-qubit bound entangled states proposed by D\"ur {[Phys. Rev. Lett. {\bf 87}, 230402 (2001)]} violates the inequality for $N\geq 4$.Comment: 4 pages, To appear in Phys. Rev.