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Volumn 68, Issue 2, 2003, Pages 13-

Mutually exclusive aspects of information carried by physical systems: Complementarity between local and nonlocal information

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EID: 85037229734     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.68.022307     Document Type: Article
Times cited : (43)

References (59)
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    • P. Bush, M. Grabowski, and P.J. Lahti, Operational Quantum Physics (Springer, New York, 1995)
    • P. Bush, M. Grabowski, and P.J. Lahti, Operational Quantum Physics (Springer, New York, 1995).
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    • N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Vol. 121 (Interscience, New York, 1963)
    • N. Bohr, Essays 1958–1962 on Atomic Physics and Human Knowledge, Vol. 121 (Interscience, New York, 1963).
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    • R. Horodecki, in Proceedings of International Conference on Problems in Quantum Physics: Gdańsk’87, edited by L. Kostro, A. Posiewnik, J. Pykacz, and M. Zukowski (World Scientific, Singapore, 1988)
    • R. Horodecki, in Proceedings of International Conference on Problems in Quantum Physics: Gdańsk’87, edited by L. Kostro, A. Posiewnik, J. Pykacz, and M. Zukowski (World Scientific, Singapore, 1988).
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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)
    • 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).
  • 24
    • 85037184326 scopus 로고    scopus 로고
    • 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
    • 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.
  • 26
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    • M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer, New York, 1993)
    • 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)
    • T. M. Cover and J. A. Thomas, Elements of Information Theory (Wiley, New York, 1991).
  • 28
    • 85037230817 scopus 로고    scopus 로고
    • By classical system we mean a d-level system, the states of which are probability distributions over d items
    • By classical system we mean a d-level system, the states of which are probability distributions over d items.
  • 29
    • 18344396639 scopus 로고    scopus 로고
    • 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).
    • (1999) Phys. Rev. Lett. , vol.83 , pp. 3081
    • Bennett, H.1    Shor, P.W.2    Smolin, J.A.3    Thapliyal, A.V.4
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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)
    • 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).
  • 36
    • 85037248777 scopus 로고    scopus 로고
    • 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
    • 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.
  • 39
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    • R. Werner, e-print quant-ph/0003070.
    • Werner, R.1
  • 40
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    • For example, data hiding 57 might also be considered to be a form of quantum work
    • For example, data hiding 57 might also be considered to be a form of quantum work.
  • 41
    • 85037221925 scopus 로고    scopus 로고
    • 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.
  • 42
    • 85037204353 scopus 로고    scopus 로고
    • 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
    • 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.
  • 43
    • 85037235383 scopus 로고    scopus 로고
    • 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
    • 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.
  • 45
    • 85037209357 scopus 로고    scopus 로고
    • 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
    • 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.
  • 46
    • 85037225408 scopus 로고    scopus 로고
    • 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)]
    • 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)].
  • 55
    • 0002906681 scopus 로고
    • 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.
    • (1991) Nature (London) , vol.351 , pp. 111
    • Scully, M.O.1    Englert, B.-G.2    Walther, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.