Preparation of Indole

Tyson, Floyd T.

doi:10.1021/ja01162a540

Cited by 14 publications

(7 citation statements)

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“…Another future direction, in which we have made recent progress [93], is to employ matrix monotonicity to obtain bounds for the maximum overlap problem, including its special cases of channel reversibility and quantum conditional min-entropy.…”

Section: Discussionmentioning

confidence: 99%

Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates

Tyson

2010

Journal of Mathematical Physics

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In a unified framework, we estimate the following quantities of interest in quantum information theory:1. The minimum-error distinguishability of arbitrary ensembles of mixed quantum states.2. The approximate reversibility of quantum dynamics in terms of entanglement fidelity.(This is referred to as "channel-adapted quantum error recovery" when applied to the composition of an encoding operation and a noise channel.)3. The maximum overlap between a bipartite pure quantum state and a bipartite mixed state that may be achieved by applying a local quantum operation to one part of the mixed state.4. The conditional min-entropy of bipartite quantum states.A refined version of the author's techniques [J. Math. Phys. 50, 032016] for bounding the first quantity is employed to give two-sided estimates of the remaining three quantities. We obtain a closed-form approximate reversal channel. Using a state-dependent Kraus decomposition, our reversal may be interpreted as a quadratically-weighted version of that of Barnum and Knill [J. Math. Phys. 43, 2097]. The relationship between our reversal and Barnum and Knill's is therefore similar to the relationship between Holevo's asymptoticallyoptimal measurement [Theor. Probab. Appl. 23, 411] and the "pretty good" measurement of Belavkin [Stochastics 1, 315] and Hausladen & Wootters [J. Mod. Optic. 41, 2385]. In particular, we obtain relatively simple reversibility estimates without negative matrix powers at no cost in tightness of our bounds. Our recovery operation is found to significantly outperform the so-called "transpose channel" in the simple case of depolarizing noise acting on half of a maximally-entangled state. Furthermore, our overlap results allow the entangled input state and the output target state to differ, thus obtaining estimates in a somewhat more general setting.Using a result of König, Renner, and Schaffner [IEEE. Trans. Inf. Th. 55, 4337], our maximum overlap estimate is used to bound the conditional min-entropy of arbitrary bipartite states.Our primary tool is "small angle" initialization of an abstract generalization of the iterative schemes of Ježek-

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Section: Discussionmentioning

confidence: 99%

Two-sided bounds on minimum-error quantum measurement, on the reversibility of quantum dynamics, and on maximum overlap using directional iterates

Tyson

2010

Journal of Mathematical Physics

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“…A proper setting to explore such questions is in the theory of approximate quantum channel reversals, which Barnum and Knill [24] have already investigated using a generalization of the "pretty good" measurement. We will consider an abstract form of JRF iteration, study its convergence properties, and construct bounds on channel reversibility and relative min-entropy in future work [52,56]. We will also attempt to reconsider Holevo's notion of asymptotic optimality in this setting.…”

Section: Discussionmentioning

confidence: 99%

Two-sided estimates of minimum-error distinguishability of mixed quantum states via generalized Holevo–Curlander bounds

Tyson

2009

Journal of Mathematical Physics

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We prove a concise factor-of-two estimate for the failure-rate of optimally distinguishing an arbitrary ensemble of mixed quantum states, generalizing work of Holevo [Theor. Probab. Appl. 23, 411 (1978)] and Curlander [Ph.D. Thesis, MIT, 1979]. A modification of the minimal principle of Concha and Poor [Proceedings of the 6th International Conference on Quantum Communication, Measurement, and Computing (Rinton, Princeton, NJ, 2003)] is used to derive a sub-optimal measurement which has an error rate within a factor of two of the optimal by construction. This measurement is quadratically weighted, and has appeared as the first iterate of a sequence of measurements proposed by Ježek,Řeháček, and Fiurášek [Phys. Rev. A 65, 060301]. Unlike the so-called "pretty good" measurement, it coincides with Holevo's asymptotically-optimal measurement in the case of non-equiprobable pure states. A quadraticallyweighted version of the measurement bound by Barnum and Knill [J. Math. Phys. 43, 2097 (2002)] is proven. Bounds on the distinguishability of syndromes in the sense of Schumacher and Westmoreland [Phys. Rev. A 56, 131 (1997)] appear as a corollary. An appendix relates our bounds to the trace-Jensen inequality. * jonetyson@X.Y.Z, where X=post, Y=Harvard, Z=edu

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“…The Madelung indole synthesis is a method for producing indoles from a base-catalyzed thermal cyclization of -acyl-o-toluidides [31,32], and is one of the few known reactions by which the simple indole compound 15 (Scheme 5) can be obtained [33][34][35].…”

Section: Resultsmentioning

confidence: 99%