11,482 research outputs found

    Entanglement distribution by an arbitrarily inept delivery service

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    We consider the scenario where a company C manufactures in bulk pure entangled pairs of particles, each pair intended for a distinct pair of distant customers. Unfortunately, its delivery service is inept - the probability that any given customer pair receives its intended particles is S, and the customers cannot detect whether an error has occurred. Remarkably, no matter how small S is, it is still possible for C to distribute entanglement by starting with non-maximally entangled pairs. We determine the maximum entanglement distributable for a given S, and also determine the ability of the parties to perform nonlocal tasks with the qubits they receive.Comment: 5 pages, 3 figures. v2 includes minor change

    Sharing Polarization within Quantum Subspaces

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    Given an ensemble of n spins, at least some of which are partially polarized, we investigate the sharing of this polarization within a subspace of k spins. We assume that the sharing results in a pseudopure state, characterized by a single purity parameter which we call the bias. As a concrete example we consider ensembles of spin-1/2 nuclei in liquid-state nuclear magnetic resonance (NMR) systems. The shared bias levels are compared with some current entanglement bounds to determine whether the reduced subspaces can give rise to entangled states.Comment: 7 pages, 3 figure

    Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond

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    This paper concentrates on a particular example of a constraint imposed by superselection rules (SSRs): that which applies when the parties (Alice and Bob) cannot distinguish among certain quantum objects they have. This arises naturally in the context of ensemble quantum information processing such as in liquid NMR. We discuss how a SSR for the symmetric group can be applied, and show how the extractable entanglement can be calculated analytically in certain cases, with a maximum bipartite entanglement in an ensemble of N Bell-state pairs scaling as log(N) as N goes to infinity . We discuss the apparent disparity with the asymptotic (N >> 1) recovery of unconstrained entanglement for other sorts of superselection rules, and show that the disparity disappears when the correct notion of applying the symmetric group SSR to multiple copies is used. Next we discuss reference frames in the context of this SSR, showing the relation to the work of von Korff and Kempe [Phys. Rev. Lett. 93, 260502 (2004)]. The action of a reference frame can be regarded as the analog of activation in mixed-state entanglement. We also discuss the analog of distillation: there exist states such that one copy can act as an imperfect reference frame for another copy. Finally we present an example of a stronger operational constraint, that operations must be non-collective as well as symmetric. Even under this stronger constraint we nevertheless show that Bell-nonlocality (and hence entanglement) can be demonstrated for an ensemble of N Bell-state pairs no matter how large N is. This last work is a generalization of that of Mermin [Phys. Rev. D 22, 356 (1980)].Comment: 16 pages, 6 figures. v2 updated version published in Phys Rev

    Global Optical Control of a Quantum Spin Chain

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    Quantum processors which combine the long decoherence times of spin qubits together with fast optical manipulation of excitons have recently been the subject of several proposals. I show here that arbitrary single- and entangling two-qubit gates can be performed in a chain of perpetually coupled spin qubits solely by using laser pulses to excite higher lying states. It is also demonstrated that universal quantum computing is possible even if these pulses are applied {\it globally} to a chain; by employing a repeating pattern of four distinct qubit units the need for individual qubit addressing is removed. Some current experimental qubit systems would lend themselves to implementing this idea.Comment: 5 pages, 3 figure

    Geometric Aspects of Composite Pulses

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    Unitary operations acting on a quantum system must be robust against systematic errors in control parameters for reliable quantum computing. Composite pulse technique in nuclear magnetic resonance (NMR) realises such a robust operation by employing a sequence of possibly poor quality pulses. In this article, we demonstrate that two kinds of composite pulses, one compensates for a pulse length error in a one-qubit system and the other compensates for a J-coupling error in a twoqubit system, have vanishing dynamical phase and thereby can be seen as geometric quantum gates, which implement unitary gates by the holonomy associated with dynamics of cyclic vectors defined in the text.Comment: 20 pages, 4 figures. Accepted for publication in Philosophical Transactions of the Royal Society

    Implementation of quantum gates based on geometric phases accumulated in the eigenstates of periodic invariant operators

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    We propose a new strategy to physically implement a universal set of quantum gates based on geometric phases accumulated in the nondegenerate eigenstates of a designated invariant operator in a periodic physical system. The system is driven to evolve in such a way that the dynamical phase shifts of the invariant operator eigenstates are the same (or {\it mod} 2π2\pi) while the corresponding geometric phases are nontrivial. We illustrate how this strategy to work in a simple but typical NMR-type qubit system.Comment: 4 page

    Practical Implementations of Twirl Operations

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    Twirl operations, which convert impure singlet states into Werner states, play an important role in many schemes for entanglement purification. In this paper we describe strategies for implementing twirl operations, with an emphasis on methods suitable for ensemble quantum information processors such as nuclear magnetic resonance (NMR) quantum computers. We implement our twirl operation on a general two-spin mixed state using liquid state NMR techniques, demonstrating that we can obtain the singlet Werner state with high fidelity.Comment: 6 pages RevTex4 including 2 figures (fig 1 low quality to save space

    Polarization Requirements for Ensemble Implementations of Quantum Algorithms with a Single Bit Output

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    We compare the failure probabilities of ensemble implementations of quantum algorithms which use pseudo-pure initial states, quantified by their polarization, to those of competing classical probabilistic algorithms. Specifically we consider a class algorithms which require only one bit to output the solution to problems. For large ensemble sizes, we present a general scheme to determine a critical polarization beneath which the quantum algorithm fails with greater probability than its classical competitor. We apply this to the Deutsch-Jozsa algorithm and show that the critical polarization is 86.6%.Comment: 11 pages, 3 figure
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