We investigate the entanglement between two spatially separated intervals in the vacuum state of a free 1D Klein-Gordon field by means of explicit computations in the continuum limit of the linear harmonic chain. We demonstrate that the entanglement, which we quantify by the logarithmic negativity, is finite with no further need for renormalization. We find that the quantum correlations are scale-invariant and are determined by a function depending on the ratio of distance to length only. They decay much faster than the classical correlations as in the critical limit long range entanglement decays exponentially for separations larger than the size of the blocks, while classical correlations follow a power law decay. With decreasing distance of the blocks, the entanglement diverges as a power law in the distance. The noncritical regime manifests richer behavior, as the entanglement depends both on the size of the blocks and on their separation. In correspondence with the von Neumann entropy also long-range entanglement distinguishes critical from noncritical systems.

We propose to realize quantized discrete kinks with cold trapped ions. We show that long-lived solitonlike configurations are manifested as deformations of the zigzag structure in the linear Paul trap, and are topologically protected in a circular trap with an odd number of ions. We study the quantum-mechanical time evolution of a high-frequency, gap separated internal mode of a static kink and find long coherence times when the system is cooled to the Doppler limit. The spectral properties of the internal modes make them ideally suited for manipulation using current technology. This suggests that ion traps can be used to test quantum-mechanical effects with solitons and explore ideas for the utilization of the solitonic internal-modes as carriers of quantum information.Solitons are localized configurations of nonlinear systems which are nonperturbative and topologically protected [1]. Quantum-mechanical properties of solitons, such as squeezing, have been predicted and measured in optical systems [2]. Quantum dynamics has been observed with a single Josephson junction soliton [3]. In waveguide arrays [4,5] and Bose-Einstein condensates [6] solitons are mean field solutions, localized to a few sites of a periodic potential. In chains of coupled particles, solitons are discrete spatial configurations, as in the Frenkel-Kontorova (FK) model [7,8].Discrete solitons of the FK model and its generalizations are referred to as kinks. An important property of kinks is the existence of localized modes. One mode is the kink's translational 'zero-mode', whose frequency generally rises above zero. Other localized modes are known as 'internal modes' [9,10]. Physically they describe 'shapechange' excitations of the kink and typically they are separated by an energy gap from other long-wavelength phononic modes. It was suggested to use the internal mode as a carrier of quantum information [11].Quantum information processing in ion traps [12] has dramatically improved over the last decades [13,14]. Recently there has been a considerable interest in using trapped ions for quantum simulation of various systems such as spin-chains [15][16][17] In this Letter we demonstrate that quantum coherence in static discrete kinks can be observed with ordinary Paul traps without external additions. We explore quasi-2D discrete kinks resembling those of the zigzag model [23]. In the linear trap we find local metastable deformations of the zigzag structure [24], as depicted in Fig. 1, which are long-lived already with a moderate number of ions, N 20. In a circular trap with an odd number of ions, similar configurations form the ground state. We study the robustness of a high-frequency internal mode of the kink against decoherence in the thermal environment of all the other modes. With all nonlinear interactions accounted for, we numerically integrate a non-Markovian master equation, which leads us to our main result: already at the standard Doppler cooling limit coherence persists in the internal mode for many oscillations. This could allow ...

We consider quantum ensembles which are determined by pre-and post-selection. Unlike the case of only pre-selected ensembles, we show that in this case the probabilities for measurement outcomes at intermediate times satisfy causality only rarely; such ensembles can in general be used to signal between causally disconnected regions. We show that under restrictive conditions, there are certain non-trivial bi-partite ensembles which do satisfy causality. These ensembles give rise to a violation of the CHSH inequality, which exceeds the maximal quantum violation given by Tsirelson's bound, BCHSH ≤ 2 √ 2, and obtains the Popescu-Rohrlich bound for the maximal violation, BCHSH ≤ 4. This may be regarded as an a posteriori realization of super-correlations, which have recently been termed Popescu-Rohrlich boxes.

We investigate entanglement of solitons in the continuum-limit of the nonlinear Frenkel-Kontorova chain. We find that the entanglement of solitons manifests particle-like behavior as they are characterized by localization of entanglement. The von-Neumann entropy of solitons mixes critical with noncritical behaviors. Inside the core of the soliton the logarithmic increase of the entropy is faster than the universal increase of a critical field, whereas outside the core the entropy decreases and saturates the constant value of the corresponding massive noncritical field. In addition, two solitons manifest long-range entanglement that decreases with the separation of the solitons more slowly than the universal decrease of the critical field. Interestingly, in the noncritical regime of the Frenkel-Kontorova model, entanglement can even increase with the separation of the solitons. We show that most of the entanglement of the so-called internal modes of the solitons is saturated by local degrees of freedom inside the core, and therefore we suggest using the internal modes as carriers of quantum information.

We present a class of noisy N-partite nonlocal boxes which reduces all communication complexity problems of N parties to triviality. The noise level is constant for any number of parties and gives a probability of simulating the nonlocal box only slightly higher than that of quantum mechanics. Intriguingly, this class of multipartite nonlocal boxes corresponds to the Bell-Svetlichny inequality, which manifests genuine multipartite nonseparability. These results provide further support for the recent conjecture by Brassard et al., ͓Phys. Rev. Lett. 96, 250401 ͑2006͔͒ that had nature been more nonlocal than quantum mechanics allows, communication complexity would have been trivial.