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N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Vol. 121 (Interscience, New York, 1963).
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R. Horodecki, in Proceeding of International Conference on Problems in Quantum Physics: Gdańsk’89, edited by J. Mizerski, A. Posiewnik, J. Pykacz, and M. Zukowski (World Scientific, Singapore, 1990).
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24
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85037184326
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Although we will only discuss bipartite states, the analysis presented here applies equally well for multipartite states. We also work with states made up of qubits but one could just as well consider more general states
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Although we will only discuss bipartite states, the analysis presented here applies equally well for multipartite states. We also work with states made up of qubits but one could just as well consider more general states.
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26
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M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer, New York, 1993).
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T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
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85037230817
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By classical system we mean a d-level system, the states of which are probability distributions over d items
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By classical system we mean a d-level system, the states of which are probability distributions over d items.
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29
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18344396639
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More generally, it was shown that the mutual information (Formula presented) describes the capacity of noisy channel assisted by entangled states. See H. Bennett, P.W. Shor, J.A. Smolin, and A.V. Thapliyal, Phys. Rev. Lett. 83, 3081 (1999).
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85037253124
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J. von Neumann, Mathematische Grundlagen der Quantenmachanik (Springer, Berlin, 1932), translated into English and reprinted in Quantum Theory and Measurement, edited by J. A. Wheeler and W. Zurek (Princeton University Press, Princeton, 1983).
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36
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85037248777
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We can think of the classical channel as a dephasing channel which transforms state (Formula presented) into a state (Formula presented) where (Formula presented) are orthogonal projection operators which are chosen by Alice and Bob
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We can think of the classical channel as a dephasing channel which transforms state (Formula presented) into a state (Formula presented) where (Formula presented) are orthogonal projection operators which are chosen by Alice and Bob.
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38
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0000795422
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C.H. Bennett, D.P. DiVincenzo, C.A. Fuchs, T. Mor, E. Rains, P.W. Shor, J. Smolin, and W.K. Wootters, Phys. Rev. A 59, 1070 (1999).
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Bennett, C.H.1
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39
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85037180575
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R. Werner, e-print quant-ph/0003070.
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Werner, R.1
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40
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85037179935
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For example, data hiding 57 might also be considered to be a form of quantum work
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For example, data hiding 57 might also be considered to be a form of quantum work.
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41
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85037221925
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The rest, (Formula presented) is still the quantum part of correlations, yet it perhaps should not be called “nonclassical.” Consider, for example, a separable state for which (Formula presented) Such states can be created by LOCC, hence it is unclear how to understand its nonlocality. In Ref. 38 it was understood as follows: “One can do better, if the particles are together.” However, since only LOCC is allowed this may be interpreted that we do not have classical correlations of classical local properties. Yet, we can still imagine that we have classical correlations between local quantum properties. The latter cannot be real, hence one cannot handle them by LOCC, yet nonlocality is not involved
-
The rest, (Formula presented) is still the quantum part of correlations, yet it perhaps should not be called “nonclassical.” Consider, for example, a separable state for which (Formula presented) Such states can be created by LOCC, hence it is unclear how to understand its nonlocality. In Ref. 38 it was understood as follows: “One can do better, if the particles are together.” However, since only LOCC is allowed this may be interpreted that we do not have classical correlations of classical local properties. Yet, we can still imagine that we have classical correlations between local quantum properties. The latter cannot be real, hence one cannot handle them by LOCC, yet nonlocality is not involved.
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42
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85037204353
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A CNOT, or controlled not gate, flips the state of a target qubit if the control qubit is in the (Formula presented) state, and does nothing otherwise
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A CNOT, or controlled not gate, flips the state of a target qubit if the control qubit is in the (Formula presented) state, and does nothing otherwise.
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43
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85037235383
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To ensure that we are actually extracting information from the state and not the measuring device, one needs to reset the measuring device after the entire procedure
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To ensure that we are actually extracting information from the state and not the measuring device, one needs to reset the measuring device after the entire procedure.
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44
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4243216277
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C.H. Bennett, D.P. DiVincenzo, J. Smolin, and W.K. Wootters, Phys. Rev. A 54, 3824 (1996).
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45
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85037209357
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After this paper had been submitted, we were able to show 22, subject to a reasonable assumption, that (Formula presented) is in fact the Shannon entropy in a particular basis
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After this paper had been submitted, we were able to show 22, subject to a reasonable assumption, that (Formula presented) is in fact the Shannon entropy in a particular basis.
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46
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85037225408
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This operational approach has been advocated by W. Unruh (private communication), and is also contained in the work of Janes and Gibbs [E.T. Janes, in Maximum Entropy and Bayesian Methods, edited by C.R. Smith, G.J. Erickson, and P.O. Neudorfer (Kluwer Academic Publishers, Dordrecht, Holland, 1992)]
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This operational approach has been advocated by W. Unruh (private communication), and is also contained in the work of Janes and Gibbs [E.T. Janes, in Maximum Entropy and Bayesian Methods, edited by C.R. Smith, G.J. Erickson, and P.O. Neudorfer (Kluwer Academic Publishers, Dordrecht, Holland, 1992)].
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Consider, for example, the recent two-slit experiment [M.O. Scully, B.-G. Englert, and H. Walther, Nature (London) 351, 111 (1991)] involving rubidium atoms where the “wave-particle” complementarity is due to entanglement of atoms with micromasser cavities. One could view this as giving a more fundamental role to complementarity versus the uncertainty principle.
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Nature (London)[See, in this context, S. Durr, T. Nonn, and G. Rempe, 395, 33 (1998); see also Ref. 58].
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