3,128 research outputs found
Efficiency of Deterministic Entanglement Transformation
We prove that sufficiently many copies of a bipartite entangled pure state
can always be transformed into some copies of another one with certainty by
local quantum operations and classical communication. The efficiency of such a
transformation is characterized by deterministic entanglement exchange rate,
and it is proved to be always positive and bounded from top by the infimum of
the ratios of Renyi's entropies of source state and target state. A careful
analysis shows that the deterministic entanglement exchange rate cannot be
increased even in the presence of catalysts. As an application, we show that
there can be two incomparable states with deterministic entanglement exchange
rate strictly exceeding 1.Comment: 7 pages, RevTex4. Journal versio
An Algebra of Quantum Processes
We introduce an algebra qCCS of pure quantum processes in which no classical
data is involved, communications by moving quantum states physically are
allowed, and computations is modeled by super-operators. An operational
semantics of qCCS is presented in terms of (non-probabilistic) labeled
transition systems. Strong bisimulation between processes modeled in qCCS is
defined, and its fundamental algebraic properties are established, including
uniqueness of the solutions of recursive equations. To model sequential
computation in qCCS, a reduction relation between processes is defined. By
combining reduction relation and strong bisimulation we introduce the notion of
strong reduction-bisimulation, which is a device for observing interaction of
computation and communication in quantum systems. Finally, a notion of strong
approximate bisimulation (equivalently, strong bisimulation distance) and its
reduction counterpart are introduced. It is proved that both approximate
bisimilarity and approximate reduction-bisimilarity are preserved by various
constructors of quantum processes. This provides us with a formal tool for
observing robustness of quantum processes against inaccuracy in the
implementation of its elementary gates
Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
We apply the plaquette renormalization scheme of tensor network states [Phys.
Rev. E, 83, 056703 (2011)] to study the spin-1/2 frustrated Heisenberg J1-J2
model on a L*L square lattice with L = 8, 16 and 32. By treating tensor
elements as variational parameters, we obtain the ground states for different
J2/J1 values, and investigate the staggered magnetic order parameters, the
nearest-neighbor spin-spin correlations and the plaquette order parameters. In
addition to the well-known N\'eel-order and collinear-order at low and high
J2/J1, we observe a plaquette order at intermediate J2/J1. A continuous
transition between the N\'eel order and the plaquette order near J2 = 0.40J1 is
observed. The collinear order emerges at J2 = 0.62J1 through a first-order
phase transition.Comment: 6 pages, 5 figures total; added one figure; Revised argument in
section 3, results unchanged; added note and reference wherei
Local cloning of two product states
Local quantum operations and classical communication (LOCC) put considerable
constraints on many quantum information processing tasks such as cloning and
discrimination. Surprisingly however, discrimination of any two pure states
survives such constraints in some sense. In this paper, we show that cloning is
not that lucky; namely, conclusive LOCC cloning of two product states is
strictly less efficient than global cloning.Comment: Totally rewritten with improved result
Super-activating quantum memory with entanglement
© Rinton Press. Noiseless subsystems were proved to be an efficient and faithful approach to preserve fragile information against decoherence in quantum information processing and quantum computation. They were employed to design a general (hybrid) quantum memory cell model that can store both quantum and classical information. In this paper, we find an interesting new phenomenon that the purely classical memory cell can be super-activated to preserve quantum states, whereas the null memory cell can only be super-activated to encode classical information. Furthermore, necessary and sufficient conditions for this phenomenon are discovered so that the super-activation can be easily checked by examining certain eigenvalues of the quantum memory cell without computing the noiseless subsystems explicitly. In particular, it is found that entangled and separable stationary states are responsible for the super-activation of storing quantum and classical information, respectively
Asymptotically Efficient Quasi-Newton Type Identification with Quantized Observations Under Bounded Persistent Excitations
This paper is concerned with the optimal identification problem of dynamical
systems in which only quantized output observations are available under the
assumption of fixed thresholds and bounded persistent excitations. Based on a
time-varying projection, a weighted Quasi-Newton type projection (WQNP)
algorithm is proposed. With some mild conditions on the weight coefficients,
the algorithm is proved to be mean square and almost surely convergent, and the
convergence rate can be the reciprocal of the number of observations, which is
the same order as the optimal estimate under accurate measurements.
Furthermore, inspired by the structure of the Cramer-Rao lower bound, an
information-based identification (IBID) algorithm is constructed with adaptive
design about weight coefficients of the WQNP algorithm, where the weight
coefficients are related to the parameter estimates which leads to the
essential difficulty of algorithm analysis. Beyond the convergence properties,
this paper demonstrates that the IBID algorithm tends asymptotically to the
Cramer-Rao lower bound, and hence is asymptotically efficient. Numerical
examples are simulated to show the effectiveness of the information-based
identification algorithm.Comment: 16 pages, 3 figures, submitted to Automatic
Predicate transformer semantics of quantum programs
© Cambridge University Press 2010. This chapter presents a systematic exposition of predicate transformer semantics for quantum programs. It is divided into two parts: The first part reviews the state transformer (forward) semantics of quantum programs according to Selinger’s suggestion of representing quantum programs by superoperators and elucidates D’Hondt-Panangaden’s theory of quantum weakest preconditions in detail. In the second part, we develop a quite complete predicate transformer semantics of quantum programs based on Birkhoff–von Neumann quantum logic by considering only quantum predicates expressed by projection operators. In particular, the universal conjunctivity and termination law of quantum programs are proved, and Hoare’s induction rule is established in the quantum setting
Proof rules for the correctness of quantum programs
We apply the notion of quantum predicate proposed by D'Hondt and Panangaden to analyze a simple language fragment which may describe the quantum part of a future quantum computer in Knill's architecture. The notion of weakest liberal precondition semantics, introduced by Dijkstra for classical deterministic programs and by McIver and Morgan for probabilistic programs, is generalized to our quantum programs. To help reasoning about the correctness of quantum programs, we extend the proof rules presented by Morgan for classical probabilistic loops to quantum loops. These rules are shown to be complete in the sense that any correct assertion about the quantum loops can be proved using them. Some illustrative examples are also given to demonstrate the practicality of our proof rules. © 2007 Elsevier Ltd. All rights reserved
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