L.P. Hughston, R. Jozsa, and W.K. Wootters. A complete classification of quantum ensembles having a given density operator. Phys. Lett. A, 183:14, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....vim, zip, pep, punch, pizzazz Generally there need be hardly any relation between the two sets of states: only that when the states are weighted by their probabilities, they mix together to form the initial density operator for system B alone. For a precise statement of this freedom, see Ref. [36]. What relation is there between the state ( quantum state ) described by a function # and a real deterministic situation (that we call the real state ) Does the quantum state characterize completely (1) or only incompletely (2) a real state One cannot respond unambiguously to this ....

L. P. Hughston, R. Jozsa, and W. K. Wootters, "A Complete Classification of Quantum Ensembles Having a Given Density Matrix," Phys. Lett. A 183, 14--18 (1993).

....very notion of separate systems 6 Generally there need be hardly any relation between the two sets of states: only that when the states are weighted by their probabilities, they mix together to form the initial density operator for system B alone. For a precise statement of this freedom, see Ref. [21]. 7 The rigid connection of all nature, on the other hand, is exactly what the Bohmians and Everettistas do embrace, even glorify. So, I suspect these words will fall on deaf ears with them. But similarly would they fall on deaf ears with the believer who says that God wills each and every event ....

L. P. Hughston, R. Jozsa, and W. K. Wootters, "A Complete Classification of Quantum Ensembles Having a Given Density Matrix," Phys. Lett. A 183, 14--18 (1993).

....jfi z i such that ae AB = P nz z=1 p z P ff z Omega P fi z , where P ff z denotes the one dimensional projector onto the subspace spanned by jff z i. Let us first assume that n z dim HE . Then there exists a basis fjzig of HE such that Psi = P z p p z jff z ; fi z ; zi holds [23] 12] [19]. If n z dim HE , then Eve can add an auxiliary system H aux to hers (usually called an ancilla) and we have Psi Omega jfl 0 i = P z p p z jff z ; fi z ; fl z i, where jfl 0 i 2 H aux is the state of Eve s auxiliary system, and fjfl z ig is a basis of HE Omega H aux . We define the ....

L. P. Hughston, R. Jozsa, and W. K. Wootters, A complete classification of quantum ensembles having a given density matrix, Phys. Lett. A, Vol. 183, pp. 14--18, 1993.

....system in various bases; these give rise to probabilities for measurement results, and states for the system of interest relative to those measurement results; the resulting ensemble corresponds to the reduced density operator. Indeed, it follows from results of Hughston, Jozsa and Wooters [31] that any ensemble (set of probabilities) of pure states which gives rise to a given density operator, may be realized in this fashion. Either interpretation helps us formulate notions of superpositions of mixed states: the elements of two ensembles may be superposed pairwise to give a new ....

L. P. Hughston, R. Jozsa, and W. K. Wootters, "A complete classification of quantum ensembles having a given density matrix," Phys. Lett. A, vol. 183, pp. 14, 1993.

....variations consists in having the photons travel in the reverse direction compared with the original BCJL protocol. This is natural for many cryptographic applications. Nevertheless, all these variations fail as well for different reasons related to subtle points in quantum information theory [5, 6] that only began to be understood at the time the BCJL paper was written. A proof that none of these variations work will be the subject of a forthcoming paper: the current paper focuses on the correct attack against the original BCJL protocol. Lo and Chau ask the question: Is quantum bit ....

....what happens when Alice executes a measurement on the system A. It is enough to consider the cases where the incremented system is in a pure state. Let M be a complete measurement executed by Alice on the system A and = M) be the classical outcome of this measurement. It is explained in [5] that, after that Alice has obtained the classical outcome , the final state of the incremented system is a product j i M;A Omega j i M;B where jci M;A and jci M;B are respectively pure states of A and the n photons. In what follows, we suppress M in some notations. As far as Alice is ....

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L. P. Hughston, R. Jozsa, and W. K. Wootters, "A complete classification of quantum ensembles having a given density matrix", Physics Letters A, vol. 183, pp. 14 -- 18, 1993.

....as b = 1. This is precisely what we have always known she can do to cheat the BB84 coin flipping protocol: postpone this choice until unveiling of her bit. Mayers attack is based on a theorem of Lane P. Hughston, Richard Jozsa and Willam K. Wootters about the classification of quantum ensembles [47]. In a nutshell, this theorem states that when two quantum systems have a similar description it is always possible to postpone the decision of whether a state comes from the first or the second system. A simple application of this theorem is the original 1984 attack against the BB84 coin flipping ....

Hughston, L. P., R. Jozsa and W. K. Wootters, "A complete classification of quantum ensembles having a given density matrix", Physics Letters A, Vol. 183, 1993, pp. 14 -- 18.

....postpone this choice to the moment of unveiling her bit. The same cheat will work here as we now explain. 4 The general attack of Mayers The attack to this protocol due to Mayers [20] is based on a recent theorem of Hughston, Jozsa, and Wootters about classification of quantum ensembles [15] that we now review. Theorem 4.1 Let 1 ; 2 ; m and 1 ; 2 ; n be two sets of possible quantum states with associated probabilities described by an identical density matrix ae. It is possible to construct a composite system ff Omega fi such that fi alone has density matrix ae ....

L.P. Hughston, R. Jozsa and W.K. Wootters, "A complete classification of quantum ensembles having a given density matrix", Physics Letters A, vol. 183, 1993, pp. 14 -- 18.

....fi fi = fi fi fi fi fi 1 2 Gamma 1 X b=0 P (B = b) P Gamma X b = b Delta fi fi fi fi fi 2 Gammaffn : This constraint says that no matter which measurement Bob uses to decide between B = 0 and B = 1, the probability of error is exponentially close to 1=2. It has been shown in [14, 22], building on the work of [20, 23] that this implies the existence of two purifications j 0 i and j 1 i for ae B 0 and ae B 1 respectively such that h 0 j 1 i 2 (1 Gamma 2 Theta 2 Gammaffn ) We have that j 0 i and j 1 i are almost the same state. In order to cheat, Alice ....

Hughston, L. P., R. Jozsa, and W. K. Wootters, "A complete classification of quantum ensembles having a given density matrix", Physics Letters A, vol. 183, pp. 14 -- 18, 1993.

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L.P. Hughston, R. Jozsa, and W.K. Wootters. A complete classification of quantum ensembles having a given density operator. Phys. Lett. A, 183:14, 1993.

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