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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Quantum no-deleting theorem ： ウィキペディア英語版 Quantum no-deleting theorem In physics, the no-deleting theorem of quantum information theory is a no-go theorem which states that, in general, given two copies of some arbitrary quantum state, it is impossible to delete one of the copies.〔A. K. Pati and S. L. Braunstein, "Impossibility of Deleting an Unknown Quantum State", ''Nature'' 404 (2000), p104.〕 It is a time-reversed dual to the no-cloning theorem,〔W.K. Wootters and W.H. Zurek, "A Single Quantum Cannot be Cloned", ''Nature'' 299 (1982), p802.〕〔D. Dieks, "Communication by EPR devices", ''Physics Letters A'', vol. 92(6) (1982), p271.〕 which states that arbitrary states cannot be copied. This theorem seems remarkable, because, in many senses, quantum states are fragile; the theorem asserts that, in a particular case, they are also robust. The no-deleting theorem, together with the no-cloning theorem, underpin the interpretation of quantum mechanics in terms of category theory, and, in particular, as a dagger symmetric monoidal category.〔John Baez, ''(Physics, Topology, Logic and Computation: A Rosetta Stone )'' (2009)〕〔Bob Coecke, ''Quantum Picturalism'', (2009) (ArXiv 0908.1787 )〕 This formulation, known as categorical quantum mechanics, in turn allows a connection to be made from quantum mechanics to linear logic as the logic of quantum information theory (in exact analogy to classical logic being founded on Cartesian closed categories.) ==Overview of quantum deletion== Suppose that there are two copies of an unknown quantum state. A pertinent question in this context is to ask if it is possible, given two identical copies, to delete one of them using quantum mechanical operations? It turns out that one cannot. The no-deleting theorem is a consequence of linearity of quantum mechanics. Like the no-cloning theorem this has important implications in quantum computing, quantum information theory and quantum mechanics in general. The process of quantum deleting takes two copies of an arbitrary, unknown quantum state at the input port and outputs a blank state along with the original. Mathematically, this can be described by: :$U\; |\backslash psi\backslash rangle\_A\; |\backslash psi\backslash rangle\_B\; |A\backslash rangle\_C\; =\; |\backslash psi\backslash rangle\_A\; |0\backslash rangle\_B\; |A\text{'}\backslash rangle\_C$ where $U$ is the deleting operation which is not necessarily unitary (but a linear operator), $|\backslash psi\backslash rangle\_A$ is the unknown quantum state, $|0\backslash rangle\_B$ is the blank state, $|A\backslash rangle\_C$ is the initial state of the deleting machine and $|A\text{'}\backslash rangle\_C$ is the final state of the machine. It may be noted that classical bits can be copied and deleted, as can qubits in orthogonal states. For example, if we have two identical qubits $|00\; \backslash rangle$ and $|11\; \backslash rangle$ then we can transform to $|00\; \backslash rangle$ and $|10\; \backslash rangle$. In this case we have deleted the second copy. However, it follows from linearity of quantum theory that there is no $U$ that can perform the deleting operation for any arbitrary state $|\backslash psi\backslash rangle$. 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「Quantum no-deleting 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.