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

On the fidelity of two pure states

The fidelity of two pure states (also known as transition probability) is a symmetric function of two operators, and well-founded operationally as an event probability in a certain preparation-test pair. Motivated by the idea that the fidelity is the continuous quantum extension of the combinatorial equality function, we enquire whether there exists a symmetric operational way of obtaining the fidelity. It is shown that this is impossible. Finally, we discuss the optimal universal approximation by a quantum operation.Comment: LaTeX2e, 8 pages, submitted to J. Phys. A: Math. and Ge

Activating NPPT distillation with an infinitesimal amount of bound entanglement

We show that bipartite quantum states of any dimension, which do not have a positive partial transpose, become 1-distillable when one adds an infinitesimal amount of bound entanglement. To this end we investigate the activation properties of a new class of symmetric bound entangled states of full rank. It is shown that in this set there exist universal activator states capable of activating the distillation of any NPPT state.Comment: 4 pages, revtex4, 1 figure, references correcte

Neotectonic markers in the Panafrican belt formations of Cameroon: elements of interpretation and their environmental impacts

The North equatorial Panafrican Belt, whose Cameroonian formations are dated between 650 and 400 million years, and which are located in the North of the Congo Craton, is subdivided in to three major geodynamic domains: a north Cameroon domain, a central Cameroon domain and a south Cameroon domain. These major domains are generally, particularly the central domain, affected by great strikeslip faults in which the most important are the central cameroonian shear zone and the Sanaga fault. Studies that establish the order of occurrence of geological events, generally performed in these domains and particularly at Banefo area (West Cameroon) reveal markers of recent tectonics (post panafrican) that affect the granitogneissic basement...conferenc

Concurrence Vectors in Arbitrary Multipartite Quantum Systems

For a given pure state of multipartite system, the concurrence vector is defined by employing the defining representation of generators of the corresponding rotation groups. The norm of concurrence vector is considered as a measure of entanglement. For multipartite pure state, the concurrence vector is regarded as the direct sum of concurrence subvectors in the sense that each subvector is associated with a pair of particles. It is proposed to use the norm of each subvector as the contribution of the corresponding pair in entanglement of the system.Comment: 9 pages, v3, section 3 is revise

Conversion of a general quantum stabilizer code to an entanglement distillation protocol

We show how to convert a quantum stabilizer code to a one-way or two-way entanglement distillation protocol. The proposed conversion method is a generalization of those of Shor-Preskill and Nielsen-Chuang. The recurrence protocol and the quantum privacy amplification protocol are equivalent to the protocols converted from [[2,1]] stabilizer codes. We also give an example of a two-way protocol converted from a stabilizer better than the recurrence protocol and the quantum privacy amplification protocol. The distillable entanglement by the class of one-way protocols converted from stabilizer codes for a certain class of states is equal to or greater than the achievable rate of stabilizer codes over the channel corresponding to the distilled state, and they can distill asymptotically more entanglement from a very noisy Werner state than the hashing protocol.Comment: LaTeX2e, 18 pages, 1 figure. Version 4 added an example of two-way protocols better than the recurrence protocol and the quantum privacy amplification protocol. Version 2 added the quantum privacy amplification protocol as an example converted from a stabilizer code, and corrected many errors. Results unchanged from V