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## State Estimation for Large Ensembles (2000)

Venue: | Phys. Review A |

Citations: | 23 - 9 self |

### Citations

579 |
Quantum Detection and Estimation Theory
- Helstrom
- 1976
(Show Context)
Citation Context ...of the problem is that we may dispose of a finite number N of copies of an unknown quantum state ae (pure or mixed). Our task is to determine ae as well as possible. This is by now a classical problem=-=[9]-=-[10]. A common approach is first to specify a cost function which numerically quantifies the deviation of the estimate from the true state. One then tries to devise a measurement and estimation strate... |

461 | Probabilistic and statistical aspects of quantum theory - Holevo - 1982 |

143 |
Trees, Detection, Estimation, and Modulation Theory Part IV: Optimum Array Processing,
- Van
- 2002
(Show Context)
Citation Context ...nterested in averaging the mean cost over possible values of ` with respect to a given prior distribution (`), then there is a Bayesian version of the Cram'er-Rao inequality, the van Trees inequality =-=[20]-=-[21]. In the multivariate case, upon giving oneself a quadratic cost function determined by a matrix C(`), one can derive the inequality Z d`(`)tr C(`)V N (`)sR d`(`)tr C(`)I \Gamma1 (`) N \Gamma ff N... |

28 |
Nature 386
- Kurtsiefer, Pfau, et al.
- 1997
(Show Context)
Citation Context ... Indeed there are now several beautiful experimental realizations of quantum state reconstruction in such diverse systems as quantum optics[1], molecular states[2], trapped ions[3] and atoms in motion=-=[4]-=-. The theoretical work which is the basis for these experiments is concerned with devising measurement strategies that are simple to realize experimentally and which allow an unambiguous reconstructio... |

5 |
Quantum tomography as a normalization of incompatible observations
- Hradil, Summhammer, et al.
- 1999
(Show Context)
Citation Context ...se works suppose that the measurements are perfect and that any operator can be measured with infinite precision. But in general the quality of the reconstruction will be limited by experimental error=-=[8]-=- or by finite statistics. The present work is devoted to studying this latter aspect when the unknown state belongs to a finite dimensional Hilbert space. Thus the setting of the problem is that we ma... |

4 |
Reconstruction of Spin States and its Conceptual Implications
- Weigert
(Show Context)
Citation Context ... of the quantum state. The best known such technique is quantum state tomography[5], adapted in [6] for the case of finite dimensional Hilbert spaces. However other techniques are also available, see =-=[7]-=- for a recent discussion in the case of finite dimensional Hilbert spaces. However, all these works suppose that the measurements are perfect and that any operator can be measured with infinite precis... |

3 | An example of non-attainability of expected quantum information xxx.lanl.gov, quant-ph/9808009 Belavkin V P 1976 Generalized uncertainty relations and efficient measurements in quantum systems Teoreticheskaya i Matematicheskaya Fizika 26 316–329 English t
- Barndorff-Nielsen, Gill
- 1998
(Show Context)
Citation Context ...problem has been solved: a bound on the variance of unbiased estimators---the quantum Cram'er-Rao bound---was given in [9], and a strategy for attaining the bound in the large N limit was proposed in =-=[15]-=-. This justifies taking the bound to induce a `distinguishability metric' on the space of states [13][14]. In the case of a multidimensional parameter however, though different bounds for the matrix W... |

2 |
R.Z Has'minskii, Statistical estimation---asymptotic theory
- Ibragimov
- 1981
(Show Context)
Citation Context ...on of super-efficiency (see [22] for a recent discussion) whereby an estimator can have mean quadratic error of smaller order than 1=N at isolated points. Modern statistical theory (see again [22] or =-=[23]-=-) has concentrated on the more difficult problem of obtaining non-Bayesian results (i.e., pointwise rather than average) making much use of the technical tool of `local asymptotic normality'. A major ... |

1 |
Optimal minimal measurements of mixed states, quantph /9812068
- Vidal, Latorre, et al.
(Show Context)
Citation Context ...ve at a single number expressing the quality of the estimation. However optimal strategies have only been found in some simple highly symmetric cases (the covariant measurements of [10], see also [11]=-=[12]-=-). However when the number of copies N becomes large one can hope that the problem becomes simpler so that one might be able to find the optimal strategies in this limit. The reason for this is that i... |

1 |
der Vaart, ch. 27 pp. 397--410 in Festschrift for
- van
- 1997
(Show Context)
Citation Context ... likelihood estimator is for large N an optimal estimator for each value of ` separately. The reason why in 2b) additional regularity is demanded is because of the phenomenon of super-efficiency (see =-=[22]-=- for a recent discussion) whereby an estimator can have mean quadratic error of smaller order than 1=N at isolated points. Modern statistical theory (see again [22] or [23]) has concentrated on the mo... |