qitd122 - qitd122 Measurements Robert B. Griffiths Version...

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Unformatted text preview: qitd122 Measurements Robert B. Griffiths Version of 2 Feb. 2010 References: CQT = Consistent Quantum Theory by Griffiths (Cambridge, 2002) QCQI = Quantum Computation and Quantum Information by Nielsen and Chuang (Cambridge, 2000). Contents 1 Introduction 1 1.1 Scope of these notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Measurements and histories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2 Destructive Measurements 2 2.1 Standard measuring device . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Competent experimentalist principle (CEP) . . . . . . . . . . . . . . . . . . . . . . . 3 2.3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.4 Using the right basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.5 The counterfactual error . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3 Partial measurements 7 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.2 Two qubit example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 General H a H b . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.4 Wave function collapse . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.5 Measurements in QCQI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4 Nondestructive Measurements 11 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.2 One qubit example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 General case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 1 Intr oduc tion 1.1 Scope of these notes In quantum foundations, the study of the conceptual basis of quantum mechanics, mea- surements are an enormous conceptual headache. They have given rise to endless arguments. To resolve the arguments one needs to adopt a consistent approach in which the measuring apparatus itself is treated in quantum mechanical, not classical, terms, and probabilities are prop- erly defined. This is discussed at some length in CQT Chs. 17 and 18. However, the reader who wants to delve into this would do well to begin with toy models in Sec. 7.4 of CQT. The axiomatic approach found in QCQI can be regarded as a recipe for making calculations. When properly applied it gives the right answers. The danger comes from mistaking calculational 1 rules, such as wave function collapse, for real physical processes. This mistake leads to all sorts of magic, mystery, and misguided notions of what the quantum world is like (e.g., the idea of long-range superluminal influences)....
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qitd122 - qitd122 Measurements Robert B. Griffiths Version...

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