G. J. Milburn, H. B. Sun, and H. Wiseman, (to be published). Home/Search Document Not in Database Summary Related Articles Check |
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The Trouble with Quantum Bit Commitment - Mayers (1999) (11 citations) (Correct)
.... 0 = j) Gamma Pr(J 1 = j) X j2A 1 Pr(J 1 = j) Gamma Pr(J 0 = j) Pr(J 0 2 A 0 ) Gamma Pr(J 1 2 A 0 ) Pr(J 1 2 A 1 ) Gamma Pr(J 0 2 A 1 ) j(Pr(X 0 = 0) Gamma Pr(X 1 = 0) j j(Pr(X 1 = 1) Gamma Pr(X 0 = 1) j 4ffl Now, let us consider the Bhattacharyya Wootters distance [7,15,18] BW = X j2A Pr(J 0 = j) 1 2 Pr(J 1 = j) 1 2 : It is explained in [15] that (1 Gamma BW ) K=2. Therefore, we have BW (1 Gamma 2ffl) Furthermore, in [7,18] it is shown that the minimum of BW over all possible measurement is the fidelity F between ae 0 and ae 1 . So, we have 1 F (1 ....
....0) Gamma Pr(X 1 = 0) j j(Pr(X 1 = 1) Gamma Pr(X 0 = 1) j 4ffl Now, let us consider the Bhattacharyya Wootters distance [7,15,18] BW = X j2A Pr(J 0 = j) 1 2 Pr(J 1 = j) 1 2 : It is explained in [15] that (1 Gamma BW ) K=2. Therefore, we have BW (1 Gamma 2ffl) Furthermore, in [7,18] it is shown that the minimum of BW over all possible measurement is the fidelity F between ae 0 and ae 1 . So, we have 1 F (1 Gamma 2ffl) A purification of ae b is simply a pure state of the overall system that has ae b for density matrix on Bob s side. A theorem due to Uhlmann [9,16] says ....
C. A. Fuchs and C. M. Caves, Open Systems and Information Dynamics, vol. 3(3), pp. 1 -- 12, to be published.
Single Spin Measurement using Single Electron Transistors - To Probe Two Self-citation (Milburn Sun Wiseman) (Correct)
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G. J. Milburn, H. B. Sun, and H. Wiseman, (to be published).
Entanglement Purification of Unknown Quantum States - Brun, Caves, Schack (2000) Self-citation (Caves Schack) (Correct)
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C. M. Caves, C. A. Fuchs, and R. Schack, to be published.
Explicit Product Ensembles for Separable Quantum States - Schack, Caves (2000) Self-citation (Caves) (Correct)
....ensembles 2. 1 Superoperator formalism The set of linear operators acting on a D dimensional Hilbert space H is a D 2 dimensional complex vector space L(H) Let us introduce operator kets jA) A and bras (Aj = A y , distinguished from vector kets and bras by the use of round brackets [9]. Then the natural inner product on L(H) the trace norm inner product, can be written as (AjB) tr(A y B) The notation S = jA) Bj de nes a superoperator S acting like SjX) jA) BjX) tr(B y X)A : 1) Now let the set fjN j )g constitute a (complete or overcomplete) operator basis; i.e. ....
C. M. Caves, J. Superconductivity, to be published (quant-ph/9811082).
Qudit Entanglement - Rungta, Munro, Nemoto, Deuar.. (2000) Self-citation (Caves) (Correct)
....Before turning to the lower and upper bounds, it is useful to develop some mathematical apparatus that will be used in deriving the bounds. 4.1. 1 Superoperator formalism We begin by reviewing a formalism for handling superoperators, introduced by Caves [16] and used by Schack and Caves [17] to generate product ensembles for separable N qubit states. The space of linear operators acting on a D dimensional complex vector space is a D 2 dimensional complex vector space. In this space we introduce operator kets jA) A and bras (Aj = A y , distinguished from vector kets and ....
R. Schack and C. M. Caves, J. Mod. Opt., to be published, quant-ph/9904109.
Qudit Entanglement - Rungta, Munro, Nemoto, Deuar.. (2000) Self-citation (Caves Milburn) (Correct)
....of N qudits near the maximally mixed state. We nd both lower and upper bounds on the size of the neighborhood of separable states around the maximally mixed state. Our results generalize and extend the results obtained by Braunstein et al. for qubits [14] and by Caves and Milburn for qutrits [15]. Before tackling the upper and lower bounds, we present, in Sect. 4.1, various mathematical results which are used to obtain the lower bound, but which might prove useful in other contexts as well. 2 Operator representation of qudit states In this section we review an operator representation of ....
.... (35) all states of the form (34) are separable and, second, that for 1 1 D N 1 ; 36) there are states of the form (34) that are not separable (i.e. they are entangled) These results generalize and extend the work of Braunstein et al. for qubits [14] and of Caves and Milburn for qutrits [15]. 6 4.1 Mathematical preliminaries Before turning to the lower and upper bounds, it is useful to develop some mathematical apparatus that will be used in deriving the bounds. 4.1.1 Superoperator formalism We begin by reviewing a formalism for handling superoperators, introduced by Caves [16] ....
C. M. Caves and G. J. Milburn, Opt. Commun., to be published, quant-ph/9910001.
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