Physical accessibility of non-completely positive maps

Maps that are not completely positive (CP) are often useful to describe the dynamics of open systems. An apparent violation of complete positivity can occur because there are prior correlations of the principal system with the environment, or if the applied transformation is correlated with the state of the system. We provide a physically motivated definition of accessible non-CP maps and derive two necessary conditions for a map to be accessible. We also show that entanglement between the system and the environment is not necessary to generate a non-CP dynamics. We describe two simple approximations that may be sufficient for some problems in process tomography, and then outline what these methods may be able to tell us in other situations where non-CP dynamics naturally arise.Comment: 8 pages, 1 eps figure. Final versio

Evanescence in Coined Quantum Walks

In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the "exponential decay'' regions at the leading edges of the main peaks in the Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to generalise the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response to referee comments, including some additional references. v3: typos fixed in equations (131), (133) and (134). v5: published versio

Maximum Power Efficiency and Criticality in Random Boolean Networks

Random Boolean networks are models of disordered causal systems that can occur in cells and the biosphere. These are open thermodynamic systems exhibiting a flow of energy that is dissipated at a finite rate. Life does work to acquire more energy, then uses the available energy it has gained to perform more work. It is plausible that natural selection has optimized many biological systems for power efficiency: useful power generated per unit fuel. In this letter we begin to investigate these questions for random Boolean networks using Landauer's erasure principle, which defines a minimum entropy cost for bit erasure. We show that critical Boolean networks maximize available power efficiency, which requires that the system have a finite displacement from equilibrium. Our initial results may extend to more realistic models for cells and ecosystems.Comment: 4 pages RevTeX, 1 figure in .eps format. Comments welcome, v2: minor clarifications added, conclusions unchanged. v3: paper rewritten to clarify it; conclusions unchange

The meeting problem in the quantum random walk

We study the motion of two non-interacting quantum particles performing a random walk on a line and analyze the probability that the two particles are detected at a particular position after a certain number of steps (meeting problem). The results are compared to the corresponding classical problem and differences are pointed out. Analytic formulas for the meeting probability and its asymptotic behavior are derived. The decay of the meeting probability for distinguishable particles is faster then in the classical case, but not quadratically faster. Entangled initial states and the bosonic or fermionic nature of the walkers are considered

Decomposition of pure states of quantum register

The generalization of Schmidt decomposition due to Cartelet-Higuchi-Sudbery applied to quantum register (a system of N qubits) is shown to acquire direct geometrical meaning: any pure state is canonically associated with a chain of a simplicial complex. A leading vector method is presented to calculate the values of the coefficients of appropriate chain

Implementation of NMR quantum computation with para-hydrogen derived high purity quantum states

We demonstrate the first implementation of a quantum algorithm on a liquid state nuclear magnetic resonance (NMR) quantum computer using almost pure states. This was achieved using a two qubit device where the initial state is an almost pure singlet nuclear spin state of a pair of 1H nuclei arising from a chemical reaction involving para-hydrogen. We have implemented Deutsch's algorithm for distinguishing between constant and balanced functions with a single query.Comment: 7 pages RevTex including 6 figures. Figures 4-6 are low quality to save space. Submitted to Phys Rev

Pairwise entanglement in the XX model with a magnetic impurity

For a 3-qubit Heisenberg model in a uniform magnetic field, the pairwise thermal entanglement of any two sites is identical due to the exchange symmetry of sites. In this paper we consider the effect of a non-uniform magnetic field on the Heisenberg model, modeling a magnetic impurity on one site. Since pairwise entanglement is calculated by tracing out one of the three sites, the entanglement clearly depends on which site the impurity is located. When the impurity is located on the site which is traced out, that is, when it acts as an external field of the pair, the entanglement can be enhanced to the maximal value 1; while when the field acts on a site of the pair the corresponding concurrence can only be increased from 1/3 to 2/3.Comment: 9 Pages, 4 EPS figures, LaTeX 2

Three-tangle for mixtures of generalized GHZ and generalized W states

We give a complete solution for the three-tangle of mixed three-qubit states composed of a generalized GHZ state, a|000>+b|111>, and a generalized W state, c|001>+d|010>+f|100>. Using the methods introduced by Lohmayer et al. we provide explicit expressions for the mixed-state three-tangle and the corresponding optimal decompositions for this more general case. Moreover, as a special case we obtain a general solution for a family of states consisting of a generalized GHZ state and an orthogonal product state

Properties of Entanglement Monotones for Three-Qubit Pure States

Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked at. It is shown that the entanglement monotones of any multipartite pure state uniquely determine the orbit of that state under local unitary transformations. It follows that there must be an entanglement monotone for three-qubit pure states which depends on the Kempe invariant defined in [Phys. Rev. A 60, 910 (1999)]. A form for such an entanglement monotone is proposed. A theorem is proved that significantly reduces the number of entanglement monotones that must be looked at to find the maximal probability of transforming one multipartite state to another.Comment: 14 pages, REVTe

Constraint on teleportation over multipartite pure states

We first define a quantity exhibiting the usefulness of bipartite quantum states for teleportation, called the quantum teleportation capability, and then investigate its restricted shareability in multi-party quantum systems. In this work, we verify that the quantum teleportation capability has a monogamous property in its shareability for arbitrary three-qutrit pure states by employing the monogamy inequality in terms of the negativity.Comment: 4 pages, 1 figur