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endobj 17 0 obj Chapters 2 and 3 depend on Section 1 but not on each other, so the reader who is interested in quantum computation can go directly from Chap- In order to describe incomplete knowledge about a quantum physical system, instead of a probability … endobj 4 0 obj x�uXKs�6��W��bH��{2��VkO�I�B$la�"i>��߯�AY�h.�h4_?��ۋ��*�C��nge��|��Q�&��^��9�v��`��덎T��m��5n"��Me�U+��Э7빚\׮��T��LSE��u��B�r��(��Ǭ��(²ЫM��I��5��h\sm�ʙ{��}�D�NVyX�Q��0�WI��?�|��2�4^mt�Q*�q"w�[q`��l�g��{"&�a��LK�B�"�c%rnwHe��]%��N��C This article is a concise introduction to quantum probability theory, quantum mechanics, and quan-tum computation for the mathematically prepared reader. << /S /GoTo /D (section.2) >> Copenhagen interpretation of quantum mechanics, it became clear that quantum mechanics, at its heart, is a theory about probabilities, and that these probabilities do not t into Kolmogorov’s scheme. (Non-embeddability $and no-hidden-variables$) endobj 24 0 obj stream endobj << /S /GoTo /D (section.3) >> << /S /GoTo /D (section.5) >> Quantum Probability: An Introduction Guido Bacciagaluppiy 14 February 2014 The topic of probabilty in quantum mechanics is rather vast, and in this article, we shall choose to discuss it from the perspective of whether and in what sense quantum mechanics requires a generalisation of the usual (Kolmogorovian) concept of probability. (Quantum mechanics $once over gently$) 25 0 obj This is just another way of saying that there is no 29 0 obj << 73{100. 12 0 obj 9 0 obj To summarize, quantum probability is the most natural non-commutative generalization of classical probability. tum Probability, Quantum Probability Communications, X pp. (Classical probability $with an eye to quantum mechanics$) 16 0 obj (Is probability empirical $and quantum$?) 21 0 obj endobj 13 0 obj endobj the basic ideas of quantum probability, just as ﬁnite or combinatorial probability is enough to show most of the basic ideas of classical probability. So formula (1) only holds on the average, i.e., for large numbers of photons. Inﬁnite-dimensional quantum systems are discussed in Sec-tion ??. (Quantum mechanics $with an eye to probability$) 5. a probability cos2 to pass through the second. %PDF-1.5 14.1.2 Expectation Value We can now use this result to arrive at an expression for the average or mean value of all these results. /Filter /FlateDecode << /S /GoTo /D (section.1) >> If we think along the lines of classical probability, then we may attach to a ‘probability as frequency’ interpretation of quantum probabilities is the interpretation that is still most commonly to be found in quantum mechanics. endobj >> 5 0 obj << /S /GoTo /D (section.4) >> endobj 8 0 obj << /S /GoTo /D [26 0 R /Fit] >> (Generalised probability $a sketch$) D��4��V�ޙ�U��`��d��N��%�e��>ȅ�P2K�c԰u):N;��K�X�w�id*z��Ѩ�ڍ�. 20 0 obj The probability is zero if no systems exhibit the outcome X, even when the number of systems goes to inﬁnity. endobj endobj << /S /GoTo /D (section.6) >> /Length 2118 endobj endobj endobj 1 0 obj %��