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Indirect Measurement Process Parameterized by Nonunitary System- Pointer Interaction

Alexander Trifanov, George P. Miroshnichenko

Published Aug 16, 2016• 0 citations
OpenAlex

Abstract

Abstract. An indirect quantum state measurement process is under investigation. Common evolution of detector’s microscopic part (pointer) and measured system (target) is considered to be nonunitary due to the interaction between pointer and environment. System of differential equations for superoperators (operations), which map initial target state to it’s conditional final state is obtained. Developed formalism is applied to the problem of cavity quantum mode photodetection to investigate basic information characteristics of this measurement process. ar X iv

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Abstract. An indirect quantum state measurement process is under investigation. Common evolution of detector’s microscopic part (pointer) and measured system (target) is considered to be nonunitary due to the interaction between pointer and environment. System of differential equations for superoperators (operations), which map initial target state to it’s conditional final state is obtained. Developed formalism is applied to the problem of cavity quantum mode photodetection to investigate basic information characteristics of this measurement process. ar X iv
An indirect quantum state measurement process is under investigation. Common evolution of detector's microscopic part (pointer) and measured system (target) is considered to be nonunitary due to the interaction between pointer and environment. System of differential equations for superoperators, which map initial target state to it's conditional final state is obtained. Developed formalism is applied to the problem of cavity quantum mode photodetection to investigate basic information characteristics of this measurement process.
In this report, we study the reduced conditional dynamics of a quantum system in the case of indirect quantum measurement. The detectors microscopic part (pointer) interacts with the measured system (target) and the environment, which results in a nonunitary interaction between target and pointer. The quantum state evolution conditioned by the measurement result is under investigation. Particularly, we are interested in explicit analytical expressions for the conditional evolution superoperators and basic information characteristics of this measurement process, which is applied to the cavity mode photodetection problem.
The process of cavity mode quantum state photodetection subject to a nonideal measurement device is under consideration. A set of nonorthogonal probabilistic operator valued measures (POVMs) describing the photodetection process is suggested. The superoperators of conditional system evolution and their Kraus representations are obtained. Developed formalism is used to the quantum state reconstruction problem. We recalculate the probabilities of hypotheses about the initial state of cavity quantum mode in the case of unknown superposition of vacuum and single photon states.
We present an exact derivation of a process in which a microscopic measured system interacts with “heat bath ” and pointer modes of a measuring device, via a linear coupling involving Hermitian operator Λ of the system. In the limit of strong interaction with these modes, over a small time interval, we show that the measured system and the “pointer ” part of the measuring device evolve into a statistical mixture of direct-product states such that the system is in each eigenstate of Λ with the correct quantummechanical probability, whereas the expectation values of pointer-space operators retain amplified information of the system’s eigenstate. PACS: 03.65.Bz, 03.65.Ca – 1 – The problem of quantum measurement has fascinated scientists for a long time [1]. It has been argued that a large “bath ” is an essential ingredient of the measurement process. Interaction with the bath, which might be a “heat bath ” in thermal equilibrium, causes decoherence which is
Quantum Measurement problem studied in Information Theory approach of systems selfdescription which exploits the information acquisition incompleteness for the arbitrary information system. The studied model of measuring system (MS) consist of measured state S environment E and observer OOO processing input S signal. OOO considered as the quantum object which interaction with S,E obeys to Schrodinger equation (SE). MS incomplete or restricted states for OOO derived by the algebraic QM formalism which exploits Segal and C∗C^*C∗-algebras. From Segal theorem for systems subalgebras it's shown that such restricted states VO=∣Oj><Oj∣V^O=|O_j> < O_j|VO=∣Oj​><Oj​∣ describes the classical random 'pointer' outcomes OjO_jOj​ observed by OOO in the individual events. The 'preferred' basis ∣Oj>|O_j>∣Oj​> defined by OOO state decoherence via OOO - E interactions.