Wooters, W.K., and W.H. Zurek, A single quantum cannot be cloned," Nature, 299 (1982), pp982-983. email: Lomonaco@UMBC.EDU  Home/Search   Document Not in Database   Summary   Related Articles   Check

....small probability for a single channel, they will have order for the triple channel, because we go wrong only when two independent errors occur. Unfortunately, such a scheme cannot work in the quantum case because it involves a copying operation, which is forbidden by the No Cloning Theorem [23]. So we have to look for subtler ways of distributing quantum information among several systems and thereby reducing the probability of errors. Indeed such schemes exist [3, 20] and are the subject of the exciting new eld of quantum error correcting codes. The eciency of such a scheme is ....

W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature 299, 802-803 (1982). 23

....fault tolerant quantum computation can be used to perform multiparty secure quantum computations [8] For all of these reasons, it is interesting to study bounds on the performance of quantum error correcting codes (QECCs) in various scenarios. It is an immediate result of the no cloning theorem [15] that no quantum error correcting code of length n can fix n 2 erasures because that would imply that we could reconstruct two copies of an encoded quantum state from two halves of the full codeword. This statement is valid regardless of the dimension of the coding Hilbert space. Another well ....

W. K. Wootters and W. H. Zurek, "A single quantum cannot be cloned", Nature 299, 802, 1982 . 11

....if not for the reason to obtain new insights by disproving them. Earlier attempts [3] to utilize nonlinear optical devices for signal amplification ( photon cloning ) to construct a FLASH 1 failed, heuristically speaking, because of the impossibility of noiseless amplification [4] see also [5, 6, 7, 8]) and the reversivility (i.e. one to oneness) of the unitary quantum state evolution. In this Communication a proposal for another arrangement will be presented which at first glance seems to be able to utilize delayed choice on the basis of an EPR type configuration for faster than light ....

W. K. Wooters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299:802--803, 1982.

....that EPR pairs can not be used to reduce communication but they can be used to reduce communication complexity. In the next section we will see another feature of EPR pairs: teleportation. 3 No Cloning and Teleportation Classical bits can be copied. Qubits on the other hand can not be copied [WZ82] Theorem 1 [WZ82] Qubits can not be copied The reason for this is that the copy qubit operation is not linear and hence not unitary. Suppose we had a linear operation U c that would copy a qubit. That means on state (ffj0i fij1i) Omega j0i it would do the following: U c [ ffj0i ....

....can not be used to reduce communication but they can be used to reduce communication complexity. In the next section we will see another feature of EPR pairs: teleportation. 3 No Cloning and Teleportation Classical bits can be copied. Qubits on the other hand can not be copied [WZ82] Theorem 1 [WZ82] Qubits can not be copied The reason for this is that the copy qubit operation is not linear and hence not unitary. Suppose we had a linear operation U c that would copy a qubit. That means on state (ffj0i fij1i) Omega j0i it would do the following: U c [ ffj0i fij1i) Omega j0i] ....

W.K. Wootters and W.H. Zurek. A single quantum cannot be cloned. Nature, (299):802, 1982.

....where communication is with classical bits, but the parties have an a priori supply of entangled qubits. In the qubit model (introduced by Yao [34] and Kremer [22] the parties have no entanglement but are allowed to communicate with qubits in place of classical bits. Qubits cannot be broadcast [32], so in a multiparty setting a qubit of communication must be sent to a specific party. In this section, we show how to translate the protocols from sections 2 and 3 in the entanglement model into protocols in the qubit model. By doing so we also prove the same separation between qubit ....

W.K. Wootters and W.H. Zurek, A single quantum cannot be cloned, Nature, 299 (1982), pp. 802--803.

....(3.1.1) The state of H n 2 after decoherence is obtained using formula for Pi 1 in (2.7.10) for H n Gammat 2 Omega H t 2 Omega H env , where H (1) H n Gammat 2 Omega H t 2 (tracing over environment) 15 3. 2 Shor s error correcting scheme Because of quantum no cloning theorem [8] it was widely believed that error correction in quantum computation is impossible, because no redundancy could be obtained by duplicating qubits. If this assumption were correct, it would mean that it would be practically impossible to build a quantum computer that could work arbitrarily long. In ....

W. K. Wooters, W. H. Zurek, A Single Quantum Cannot be Cloned,

....However, these usually require more of the quantum formalism and give less insight into the di#erences between classical and quantum information. 7 3. 1 The Quantum Copier This is the machine referred to in the famous paper of Wootters and Zurek, entitled A single quantum cannot be cloned [4]. By definition, a copier would be a device taking one quantum system as input and turning out two systems of the same type. The condition for calling this a (faithful) copier is that we won t be able to distinguish the systems coming from either output from the input systems by any statistical ....

W.K. Wootters, W.H. Zurek: "A single quantum cannot be cloned", Nature 299 (1982) 802--803

....represents a collaboration with H. Barnum, C. M. Caves, R. Jozsa, and B. Schumacher) proves that there is a very general sense in which it is impossible to make a copy of an unknown 2 quantum state. This is a result that extends the now standard no cloning theorem for pure quantum states [2, 3]. Chapter 5 caps o the dissertation with a comprehensive bibliography of 527 books and articles relevant to quantum distinguishability and quantum state disturbance. 1.2 Summary of Results Mutual Information As stated already, the main focus of this work is in deriving distinguishability ....

....two separate quantum systems. That is to say, a state identical to the original should appear in each system when it is considered without regard to the other (though there may be correlation or quantum entanglement between the systems) Can such a black box be built The no cloning theorem [2, 3] insures that the answer to this question is no when the states in A are pure and nonorthogonal; for the only way to have each of the broadcast systems described separately by a pure state j i is for their joint state to be j i j i. When the states are mixed, however, things are not so clear. ....

[Article contains additional citation context not shown here]

W. K. Wootters and W. H. Zurek, \A single quantum cannot be cloned," Nature, vol. 299, pp. 802-803, 1982.

....theory, this is one of a set of mutually exclusive classical states; in quantum mechanics, a quantum state represented by a vector in a Hilbert space, or a density operator on that space. Classically, the input system may retain its original state, while the no cloning theorem and related results [1], 2] 3] 4] 5] 6] 7] 8] 9] 10] 11] 12] imply that in the quantum case the input system cannot in general remain in its initial state. Both theories allow the use of encoding and decoding operations to increase the delity with which states are transmitted. Due partly to the ....

W. K. Wootters and W. H. Zurek, \A single quantum cannot be cloned," Nature, vol. 299, pp. 802, 1982.

....qubits are completely entangled. Making an unentangled copy requires non unitary, and in fact non linear, processes since ( j0i j1i) j0i j1i) 2 j00i (j01i j10i) 2 j11i has coecients quadratic in and . This is one form of the no cloning theorem of quantum mechanics [25]. This means that disentangling or uncopying the ancillae by the end of the computation, and returning them to their initial state j0i, is a non trivial and important part of a quantum circuit. There are, however, some special cases where this can be done easily. Suppose we have a series of n ....

W.K. Wooters and W.H. Zurek, \A Single Quantum Cannot be Cloned." Nature 299 (1982) 802-803.

....the development of many equivalent ways of formulating fundamental physical principles. For example, Westmoreland and Schumacher [185] have recently argued that the physical prohibition against superluminal communication can be deduced from elementary quantum mechanics, via the no cloning theorem [196, 60]. Feynman [65] has argued that such development of new ways of looking at physical principles has great value for fundamental research. As we do not yet have a complete fundamental physical theory of the world [191, 193] new perspectives on old theories such as quantum mechanics may be extremely ....

....and quantum information that require new ideas to be introduced to make quantum error correcting codes possible: ffl No cloning: One might try to implement the repetition code quantum mechanically by duplicating the quantum state three or more times. This is forbidden by the no cloning theorem [60, 196]. Even if cloning were possible, it would not be possible to measure and compare the three quantum states output from the channel. ffl Errors are continuous: A continuum of different errors may occur on a single qubit. Determining which error occurred in order to correct it would appear to ....

W. K. Wootters and W. H. Zurek. A single quantum cannot be cloned. Nature, 299:802--803, 1982.

....stored, there is no feed back channel from the receiver to the sender. Then, information must be encoded in such a manner that possible errors can be corrected, or that no errors occur. 4.1. Quantum Error Correcting Codes Unlike classical information, unknown quantum information cannot be copied [6]. Therefore, the simple idea of a say triple repetition code does not work. Nevertheless, it is possible to encode quantum information in a subspace of a higher dimensional space such that error correction is possible. Following the first example of a quantum error correcting code (QECC) of ....

W. K. Wootters and W. H. Zurek, "A single quantum cannot be cloned", Nature, vol. 299, no. 5886, pp. 802--803, 28. Oct. 1982.

....complexity on classical strings. However, quantum Kolmogorov complexity should not be expected to always behave the way classical Kolmogorov complexity does. The reader may want to bear in mind quantum phenomena such as the no cloning theorem, whose consequences we will discuss later in the paper. [23] 2.1 Critical issues A first attempt at defining quantum Kolmogorov complexity of a qubit string X is to consider the length of the shortest quantum program that produces X as its output. There are many questions that arise from this definition . Bits or qubits The first question to consider ....

William K. Wootters and Wojceich H. Zurek, "A single quantum cannot be cloned", Nature, Volume 229, pp. 802--803 (1982)

....ball in door 1 or door 2. It might guess right, and open the correct door, and then it can make a good copy. But if it guesses wrong and opens the wrong door, it will damage the information that I stored in the box, and it won t be able to copy it faithfully. Quantum information cannot be copied[3]. This is disconcerting. Sometimes it is very useful to be able to copy information. On the other hand, sometimes it might be a good feature if information cannot be copied. For example, were we to carry quantum dollar bills, we would not have to worry about counterfeiters. Well, I don t know ....

W. K. Wootters and W. H. Zurek, "A single quantum cannot be cloned," Nature 299, 802, 1982; D. Dieks, "Communication by electron-paramagnetic-resonance devices, Physics Letters A 92, 271, 1982.

....all operations performed on the data must be reversible and must not entangle the state with any temporary variables. Furthermore, it is essential that the original state must be entirely obliterated in producing the encoded state, because quantum states cannot be cloned, see, Wootters and Zurek [12] and Dieks [13] Cleve and DiVincenzo [14] have proposed a block coding algorithm, which is, in fact, a generalization of the classical enumerative coding of Cover [15] and Schalkwijk [16] Recently, Braunstein et al. 17] have studied quantum extensions of Huffman coding. The statistics ....

....but in reality, are specially constructed to be quantum. Three characteristics make our algorithms quantum mechanical. First, they are reversible; this is required as previously explained. Second, they completely erase their inputs; this is a necessity because quantum states cannot be cloned [12, 13], and thus there is no sense to a sender sending a faithfully encoded quantum state elsewhere without erasing her own knowledge of that state in the process. Third, our algorithms produce no information other than the encoded (or decoded) state, which would allow differentiation between ....

W. K. Wootters and W. H. Zurek, "A single quantum cannot be cloned," Nature, vol. 299, pp. 802--3, 1982.

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Wooters, W.K., and W.H. Zurek, A single quantum cannot be cloned," Nature, 299 (1982), pp982-983. email: Lomonaco@UMBC.EDU

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W. Wootters and W. Zurek. A single quantum cannot be cloned. Nature 299, 802--803 (1982).

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W.K. Wootters and W.H. Zurek. A single quantum cannot be cloned. Nature, 299:802--803, 1982.

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W.K. Wootters and W.H. Zurek. A single quantum cannot be cloned. Nature, vol. 299, pp. 802-803, 1982.

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Wootters, W. and Zurek., W. (1982) A single quantum cannot be cloned. Nature 299, 802--803.

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Wootters W K and Zurek W H 1982 A single quantum cannot be cloned, Nature 299, 802

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W.K. Wootters, W.H. Zurek: "A single quantum cannot be cloned", Nature 299 (1982) 802--803

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W.K. Wootters, W.H. Zurek, A single quantum cannot be cloned, Nature 299, (1982), p. 802.

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W. K. Wooters and W. H. Zurek, "A single quantum cannot be cloned," Nature, vol. 299, pp. 802--803, 1982.

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Wootters W K and Zurek W H 1982 A single quantum cannot be cloned, Nature 299, 802

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