Entanglement flow in multipartite systems

We investigate entanglement dynamics in multipartite systems, establishing a quantitative concept of entanglement flow: both flow through individual particles, and flow along general networks of interacting particles. In the former case, the rate at which a particle can transmit entanglement is shown to depend on that particle's entanglement with the rest of the system. In the latter, we derive a set of entanglement rate equations, relating the rate of entanglement generation between two subsets of particles to the entanglement already present further back along the network. We use the rate equations to derive a lower bound on entanglement generation in qubit chains, and compare this to existing entanglement creation protocols.Comment: 13 pages, 5 figures, REVTeX format. Proof of lemma 3 corrected. Restructured and expande

Stochastic Matrix Product States

The concept of stochastic matrix product states is introduced and a natural form for the states is derived. This allows to define the analogue of Schmidt coefficients for steady states of non-equilibrium stochastic processes. We discuss a new measure for correlations which is analogous to the entanglement entropy, the entropy cost $S_C$, and show that this measure quantifies the bond dimension needed to represent a steady state as a matrix product state. We illustrate these concepts on the hand of the asymmetric exclusion process

Faster Methods for Contracting Infinite 2D Tensor Networks

We revisit the corner transfer matrix renormalization group (CTMRG) method of Nishino and Okunishi for contracting two-dimensional (2D) tensor networks and demonstrate that its performance can be substantially improved by determining the tensors using an eigenvalue solver as opposed to the power method used in CTMRG. We also generalize the variational uniform matrix product state (VUMPS) ansatz for diagonalizing 1D quantum Hamiltonians to the case of 2D transfer matrices and discuss similarities with the corner methods. These two new algorithms will be crucial to improving the performance of variational infinite projected entangled pair state (PEPS) methods.Comment: 20 pages, 5 figures, V. Zauner-Stauber previously also published under the name V. Zaune

Quantum Metropolis Sampling

The original motivation to build a quantum computer came from Feynman who envisaged a machine capable of simulating generic quantum mechanical systems, a task that is believed to be intractable for classical computers. Such a machine would have a wide range of applications in the simulation of many-body quantum physics, including condensed matter physics, chemistry, and high energy physics. Part of Feynman's challenge was met by Lloyd who showed how to approximately decompose the time-evolution operator of interacting quantum particles into a short sequence of elementary gates, suitable for operation on a quantum computer. However, this left open the problem of how to simulate the equilibrium and static properties of quantum systems. This requires the preparation of ground and Gibbs states on a quantum computer. For classical systems, this problem is solved by the ubiquitous Metropolis algorithm, a method that basically acquired a monopoly for the simulation of interacting particles. Here, we demonstrate how to implement a quantum version of the Metropolis algorithm on a quantum computer. This algorithm permits to sample directly from the eigenstates of the Hamiltonian and thus evades the sign problem present in classical simulations. A small scale implementation of this algorithm can already be achieved with today's technologyComment: revised versio

Intra- and Extra-articular Features of Temporomandibular Joint Ankylosis in the Cat (Felis catus).

Temporomandibular joint (TMJ) ankylosis is an uncommon clinical entity in human and veterinary medicine. However, the condition is severely debilitating and is life-limiting if not treated. This study sought to characterize the intra- and extra-articular features of naturally occurring TMJ ankylosis in cats. TMJs from client-owned cats (n = 5) that underwent bilateral TMJ gap arthroplasty were examined and compared with TMJs from healthy, age-matched feline cadavers (n = 2) by cone-beam computed tomography (CBCT), micro-computed tomography (μCT) and histologically. Features of bilateral intra- and extra-articular ankylosis compounded by degenerative joint lesions were identified radiographically and histologically in all affected cats. Features of TMJ 'true' ankylosis included variable intracapsular fibro-osseous bridging, degeneration of the disc and the articular surfaces, narrowing of the joint space and flattening of the condylar process of the mandible. Extra-articular features of TMJ ankylosis included periarticular bone formation and fibro-osseous bridging between the mandible, zygomatic arch and coronoid process. In addition, subchondral bone loss or sclerosis, irregular and altered joint contours and irregularly increased density of the medullary bone characterized the degenerative changes of the osseous components of the TMJ. Complex radiological and histological features of both ankylosis and pseudoankylosis were identified that clinically manifested in complete inability to open the mouth

Nonlocal resources in the presence of Superselection Rules

Superselection rules severely alter the possible operations that can be implemented on a distributed quantum system. Whereas the restriction to local operations imposed by a bipartite setting gives rise to the notion of entanglement as a nonlocal resource, the superselection rule associated with particle number conservation leads to a new resource, the \emph{superselection induced variance} of local particle number. We show that, in the case of pure quantum states, one can quantify the nonlocal properties by only two additive measures, and that all states with the same measures can be asymptotically interconverted into each other by local operations and classical communication. Furthermore we discuss how superselection rules affect the concepts of majorization, teleportation and mixed state entanglement.Comment: 4 page

Separable states can be used to distribute entanglement

We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.Comment: 4 pages, 2 figures. Slight modification

Binegativity and geometry of entangled states in two qubits

We prove that the binegativity is always positive for any two-qubit state. As a result, as suggested by the previous works, the asymptotic relative entropy of entanglement in two qubits does not exceed the Rains bound, and the PPT-entanglement cost for any two-qubit state is determined to be the logarithmic negativity of the state. Further, the proof reveals some geometrical characteristics of the entangled states, and shows that the partial transposition can give another separable approximation of the entangled state in two qubits.Comment: 5 pages, 3 figures. I made the proof more transparen

Quantum entanglement theory in the presence of superselection rules

Superselection rules severly constrain the operations which can be implemented on a distributed quantum system. While the restriction to local operations and classical communication gives rise to entanglement as a nonlocal resource, particle number conservation additionally confines the possible operations and should give rise to a new resource. In [Phys. Rev. Lett. 92, 087904 (2004), quant-ph/0310124] we showed that this resource can be quantified by a single additional number, the superselection induced variance (SiV) without changing the concept of entanglement. In this paper, we give the results on pure states in greater detail; additionally, we provide a discussion of mixed state nonlocality with superselection rules where we consider both formation and distillation. Finally, we demonstrate that SiV is indeed a resource, i.e., that it captures how well a state can be used to overcome the restrictions imposed by the superselection rule.Comment: 16 pages, 5 figure