A Simple Algorithm for Local Conversion of Pure States

We describe an algorithm for converting one bipartite quantum state into another using only local operations and classical communication, which is much simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436 (1999)]. Our algorithm uses only a single measurement by one of the parties, followed by local unitary operations which are permutations in the local Schmidt bases.Comment: 5 pages, LaTeX, reference adde

A de Finetti Representation Theorem for Quantum Process Tomography

In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for probability distributions, we give a definition of exchangeability for sequences of quantum operations. We then state and prove a representation theorem for such exchangeable sequences. The theorem leads to a simple characterization of admissible priors for quantum process tomography and solves to a Bayesian's satisfaction the problem of an unknown quantum operation.Comment: 10 page

Linear Logic Programming for Narrative Generation

Abstract. In this paper, we explore the use of Linear Logic programming for story generation. We use the language Celf to represent narrative knowledge, and its own querying mechanism to generate story instances, through a number of proof terms. Each proof term obtained is used, through a resource-flow analysis, to build a directed graph where nodes are narrative actions and edges represent inferred causality relationships. Such graphs represent narrative plots structured by narrative causality. Building on previous work evidencing the suitability of Linear Logic as a conceptual model of action and change for narratives, we explore the conditions under which these representations can be operationalized through Linear Logic Programming techniques. This approach is a candidate technique for narrative generation which unifies declarative representations and generation via query and deduction mechanisms

Optimal quantum teleportation with an arbitrary pure state

We derive the maximum fidelity attainable for teleportation using a shared pair of d-level systems in an arbitrary pure state. This derivation provides a complete set of necessary and sufficient conditions for optimal teleportation protocols. We also discuss the information on the teleported particle which is revealed in course of the protocol using a non-maximally entangled state.Comment: 10 pages, REVTe

Subjective probability and quantum certainty

In the Bayesian approach to quantum mechanics, probabilities--and thus quantum states--represent an agent's degrees of belief, rather than corresponding to objective properties of physical systems. In this paper we investigate the concept of certainty in quantum mechanics. Particularly, we show how the probability-1 predictions derived from pure quantum states highlight a fundamental difference between our Bayesian approach, on the one hand, and Copenhagen and similar interpretations on the other. We first review the main arguments for the general claim that probabilities always represent degrees of belief. We then argue that a quantum state prepared by some physical device always depends on an agent's prior beliefs, implying that the probability-1 predictions derived from that state also depend on the agent's prior beliefs. Quantum certainty is therefore always some agent's certainty. Conversely, if facts about an experimental setup could imply agent-independent certainty for a measurement outcome, as in many Copenhagen-like interpretations, that outcome would effectively correspond to a preexisting system property. The idea that measurement outcomes occurring with certainty correspond to preexisting system properties is, however, in conflict with locality. We emphasize this by giving a version of an argument of Stairs [A. Stairs, Phil. Sci. 50, 578 (1983)], which applies the Kochen-Specker theorem to an entangled bipartite system.Comment: 20 pages RevTeX, 1 figure, extensive changes in response to referees' comment

Hypersensitivity and chaos signatures in the quantum baker's maps

Classical chaotic systems are distinguished by their sensitive dependence on initial conditions. The absence of this property in quantum systems has lead to a number of proposals for perturbation-based characterizations of quantum chaos, including linear growth of entropy, exponential decay of fidelity, and hypersensitivity to perturbation. All of these accurately predict chaos in the classical limit, but it is not clear that they behave the same far from the classical realm. We investigate the dynamics of a family of quantizations of the baker's map, which range from a highly entangling unitary transformation to an essentially trivial shift map. Linear entropy growth and fidelity decay are exhibited by this entire family of maps, but hypersensitivity distinguishes between the simple dynamics of the trivial shift map and the more complicated dynamics of the other quantizations. This conclusion is supported by an analytical argument for short times and numerical evidence at later times.Comment: 32 pages, 6 figure

Quasi-probability representations of quantum theory with applications to quantum information science

This article comprises a review of both the quasi-probability representations of infinite-dimensional quantum theory (including the Wigner function) and the more recently defined quasi-probability representations of finite-dimensional quantum theory. We focus on both the characteristics and applications of these representations with an emphasis toward quantum information theory. We discuss the recently proposed unification of the set of possible quasi-probability representations via frame theory and then discuss the practical relevance of negativity in such representations as a criteria for quantumness.Comment: v3: typos fixed, references adde

Classical model for bulk-ensemble NMR quantum computation

We present a classical model for bulk-ensemble NMR quantum computation: the quantum state of the NMR sample is described by a probability distribution over the orientations of classical tops, and quantum gates are described by classical transition probabilities. All NMR quantum computing experiments performed so far with three quantum bits can be accounted for in this classical model. After a few entangling gates, the classical model suffers an exponential decrease of the measured signal, whereas there is no corresponding decrease in the quantum description. We suggest that for small numbers of quantum bits, the quantum nature of NMR quantum computation lies in the ability to avoid an exponential signal decrease.Comment: 14 pages, no figures, revte

Separability of very noisy mixed states and implications for NMR quantum computing

We give a constructive proof that all mixed states of N qubits in a sufficiently small neighborhood of the maximally mixed state are separable. The construction provides an explicit representation of any such state as a mixture of product states. We give upper and lower bounds on the size of the neighborhood, which show that its extent decreases exponentially with the number of qubits. We also discuss the implications of the bounds for NMR quantum computing.Comment: 4 pages, extensively revised, references adde