Noncommuting observables in quantum detection and estimation theory
نویسندگان
چکیده
In quantum detection theory the optimum detection operators must commute; admitting simultaneous approximate measurement of noncommuting observables cannot yield a lower Bayes cost. The lower bounds on mean square errors of parameter estimates predicted by the quantum-mechanical Cramer-Rao inequality can also not be reduced by such means.
منابع مشابه
Joint Probabilities Reproducing Three EPR Experiments On Two Qubits
Probabilities and correlations in EPR experiments. The EPR-Bohm-Aharonov [1] system of two correlated spin-half particles or qubits observed by spatially separated observers has often been used as an arena in which to probe fundamental questions about quantum theory. Typically there are four different configurations corresponding to four different experiments and one obtains no-go theorems on (...
متن کاملTowards a skew lattice approach to quantum (computational) logic
In quantum mechanics, each observable is assigned a collection of projections. Two observables are compatible (can be measured simultaneously) if and only if any two projections that are assigned to them commute. This led to the study of noncommuting sets of idempotents which further led to the skew lattice theory that was founded and explored by Jonathan Leech. In the present paper we shall se...
متن کاملJoint Measurements on Qubits and Cloning of Observables
Cloning of observables, unlike standard cloning of states, aims at copying the information encoded in the statistics of a class of observables rather then on quantum states themselves. In such a process the emphasis is on the quantum operation (evolution plus measurement) necessary to retrieve the original information. We analyze, for qubit systems, the cloning of a class generated by two nonco...
متن کاملIndividual ergodic theorem for intuitionistic fuzzy observables using intuitionistic fuzzy state
The classical ergodic theory hasbeen built on σ-algebras. Later the Individual ergodictheorem was studied on more general structures like MV-algebrasand quantum structures. The aim of this paper is to formulate theIndividual ergodic theorem for intuitionistic fuzzy observablesusing m-almost everywhere convergence, where m...
متن کاملOn the Notion of Coexistence in Quantum Mechanics
The notion coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- IEEE Trans. Information Theory
دوره 20 شماره
صفحات -
تاریخ انتشار 1974