AMATHProblemSet5-2010

AMATHProblemSet5-201 - Advanced Quantum Theory Amath 473 673 Phys 454 Problem Set 5 This assignment is due at the beginning of class on Monday Dec

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Advanced Quantum Theory Amath 473, 673 / Phys 454 Problem Set 5 This assignment is due at the beginning of class on Monday Dec 6th, 2010. 1. Unitary Evolution vs Collapse Process. In this problem you will prove that the collapse postulate can not be derived from unitary evolution acting on (any) Hilbert space. To do this assume an initial system state | ψ i S ∈ H S , an initial measurement apparatus state | ready i A ∈ H A and an initial environment state | χ i E ∈ H E (describing any other degrees of freedom of possible relevance). For simplicity, assume that all initial states are pure and that the system state is a two-level system H S = C 2 , e.g., a spin, with orthonormal basis states | up i S and | down i S . A measurement device that is ideal performs perfectly faithful measurements , which means that distinct input basis states produce perfectly distinguishable final detector states, i.e., a macroscopic pointer is moved to the ‘left’ if the particle is prepared in the ‘up’ state and to the ‘right’ if the particle is prepared in the ‘down’ state. Perfectly distinguishable here means that the detector states (i.e., the states associated with ‘left’ and ‘right’) are orthogonal.
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This note was uploaded on 01/17/2011 for the course AMATH 454 taught by Professor Joseph during the Fall '10 term at Waterloo.

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AMATHProblemSet5-201 - Advanced Quantum Theory Amath 473 673 Phys 454 Problem Set 5 This assignment is due at the beginning of class on Monday Dec

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