翻訳と辞書 Words near each other ・ No. 106 Fuze ・ No. 106 Squadron IAF ・ No. 106 Squadron RAF ・ No. 107 Squadron RAAF ・ No. 107 Squadron RAF ・ No. 108 Squadron RAF ・ No. 109 Helicopter Unit, IAF ・ No. 109 Squadron IqAF ・ No. 109 Squadron RAF ・ No. 11 (Scottish) Commando ・ No. 11 Elementary Flying Training School RAAF ・ No. 11 Flight SLAF ・ No-Cal (model aircraft) ・ No-Cal Soda ・ No-carbohydrate diet ・ No-cloning theorem ・ No-communication theorem ・ No-Conscription Fellowship ・ No-contest clause ・ No-cost campaign ・ No-dig gardening ・ No-disc crack ・ No-Do ・ No-drive zone ・ No-fault ・ No-fault divorce ・ No-fault insurance ・ No-FEAR Act ・ No-Fi ・ No-Fi Soul Rebellion Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク No-cloning theorem ： ウィキペディア英語版 No-cloning theorem In physics, the no-cloning theorem states that it is impossible to create an identical copy of an arbitrary unknown quantum state. This no-go theorem of quantum mechanics was articulated by Wootters and Zurek and Dieks in 1982, and has profound implications in quantum computing and related fields. The state of one system can be entangled with the state of another system. For instance, one can use the controlled NOT gate and the Walsh–Hadamard gate to entangle two qubits. This is not cloning. No well-defined state can be attributed to a subsystem of an entangled state. Cloning is a process whose result is a separable state with identical factors. According to Asher Peres and David Kaiser, the publication of the no-cloning theorem was prompted by a proposal of Nick Herbert for a superluminal communication device using quantum entanglement. The no-cloning theorem is normally stated and proven for pure states; the no-broadcast theorem generalizes this result to mixed states. The no-cloning theorem has a time-reversed dual, the no-deleting theorem. Together, these underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger compact category.〔John Baez, Mike Stay, ''(Physics, Topology, Logic and Computation: A Rosetta Stone )'' (2009)〕〔Bob Coecke, ''Quantum Picturalism'', (2009) (ArXiv 0908.1787 )〕 This formulation, known as categorical quantum mechanics, allows, in turn, a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in the same sense that classical logic arises from Cartesian closed categories). == Theorem and proof == Suppose the state of a quantum system A, which we wish to copy, is $|\backslash phi\backslash rangle\_A$ (see bra–ket notation). In order to make a copy, we take a system B with the same state space and initial state $|e\backslash rangle\_B$. The initial, or blank, state must be independent of $|\backslash phi\backslash rangle\_A$, of which we have no prior knowledge. The state of the composite system is then described by the following tensor product: :$|\backslash phi\backslash rangle\_A\; \backslash otimes\; |e\backslash rangle\_B\; \backslash ,$. (in the following we will omit the $\backslash otimes$ symbol and keep it implicit) There are only two permissible quantum operations with which we may manipulate the composite system. We could perform an observation, which irreversibly collapses the system into some eigenstate of an observable, corrupting the information contained in the qubit(s). This is obviously not what we want. Alternatively, we could control the Hamiltonian of the system, and thus the time-evolution operator ''U'' (for a time independent Hamiltonian, $U(t)=e^$, where $-H/\backslash hbar$ is called the generator of translations in time) up to some fixed time interval, which yields a unitary operator ''U''. Then ''U'' acts as a copier provided that :$U\; |\backslash phi\backslash rangle\_A\; |e\backslash rangle\_B\; =\; |\backslash phi\backslash rangle\_A\; |\backslash phi\backslash rangle\_B\; \backslash ,$ for all possible states $|\; \backslash phi\; \backslash rangle$ in the state space. We now select an arbitrary pair of states $|\backslash phi\backslash rangle\_A$ and $|\backslash psi\backslash rangle\_A$ drawn from the Hilbert space. Because ''U'' is unitary, it preserves the inner product: :$$ \langle e|_B \langle \phi|_A |\psi\rangle_A |e\rangle_B = \langle e|_B \langle \phi|_A U^ U |\psi\rangle_A |e\rangle_B = \langle \phi|_B \langle \phi|_A |\psi\rangle_A |\psi\rangle_B, and because quantum mechanical states are assumed to be normalized, it follows that :$\backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; =\; \backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; ^2.\; \backslash ,$ This implies that either $\backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; =\; 1$ or $\backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; =\; 0$, so we obtain either $\backslash phi=\backslash psi$ or $\backslash phi$ is orthogonal to $\backslash psi$. However, this cannot be the case for two ''arbitrary'' states. Therefore a single universal ''U'' cannot clone a ''general'' quantum state. This proves the no-cloning theorem. Note that it is possible to find specific pairs that satisfy the algebraic requirement above. An example is given by the orthogonal states :$|\; \backslash phi\; \backslash rangle\; =\; \}\; \backslash bigg(\; |\; 0\; \backslash rangle\; -\; |\; 1\; \backslash rangle\; \backslash bigg)$ and one verifies that $\backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; =\; 0\; =\; \backslash langle\; \backslash phi\; |\; \backslash psi\; \backslash rangle\; ^2$ in this special case. But this relationship does not hold for more general quantum states. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「No-cloning theorem」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.