Activated zero-error classical communication over quantum channels assisted with quantum no-signalling correlations

Preprint English OPEN
Duan, Runyao ; Wang, Xin (2015)
  • Subject: Computer Science - Information Theory | Quantum Physics
    arxiv: Computer Science::Information Theory

We study the activated quantum no-signalling-assisted zero-error classical capacity by first allowing the assistance from some noiseless forward communication channel and later paying back the cost of the helper. This activated communication model considers the additional forward noiseless channel as a catalyst for communication. First, we show that the one-shot activated capacity can be formulated as a semidefinite program and we derive a number of striking properties of this capacity. We further present a sufficient condition under which a noisy channel can be activated. Second, we show that one-bit noiseless classical communication is able to fully activate any classical-quantum channel to achieve its asymptotic capacity, or the semidefinite (or fractional) packing number. Third, we prove that the asymptotic activated capacity cannot exceed the original asymptotic capacity of any quantum channel. We also show that the asymptotic no-signalling-assisted zero-error capacity does not equal to the semidefinite packing number for quantum channels, which differs from the case of classical-quantum channels.
  • References (3)

    † Electronic address: xin.wang-8@student.uts.edu.au [1] C. E. Shannon, IRE Trans. Inf. Theory 2, 3 (1956). [2] L. Lova´sz, IEEE Trans. Inf. Theory 25, 1 (1979). [3] T. S. Cubitt, D. Leung, W. Matthews, A. Winter, Phys. Rev. Lett. 104, 230503 (2010). [4] D. Leung, L. Mancˇinska, W. Matthews, M. Ozols, A. Roy, Commun. Math. Phys. 311 (2012). [5] R. Duan, arXiv:0906.2526 [6] R. Duan, Y. Shi, Phys. Rev. Lett. 101, 020501 (2008). [7] T. S. Cubitt, J. Chen, A. W. Harrow, IEEE Trans. Inf. Theory 57, 12 (2011). [8] T. S. Cubitt, G. Smith, IEEE Trans. Inf. Theory 58, 3 (2012). [9] S. Beigi, Phys. Rev. A 82, 010303 (2010). [10] R. Duan, S. Severini, A. Winter, IEEE Trans. Inf. Theory 59, 2 (2013). [11] D. Beckman, D. Gottesman, M. A. Nielsen, J. Preskill, Phys. Rev. A 64, 052309 (2001). [12] T. Eggeling, D. Schlingemann, R. F. Werner, Europhys. Lett. 57, 6 (2002). [13] M. Piani, M. Horodecki, P. Horodecki, R. Horodecki, Phys. Rev. A 74, 012305 (2006). [14] O. Oreshkov, F. Costa, Cˇ . Brukner, Nature Comm. 3, 10 (2012). [15] T. S. Cubitt, D. Leung, W. Matthews, A. Winter, IEEE Trans. Inf. Theory 57, 8 (2011). [16] L. Vandenberghe, S. Boyd, SIAM Rev. 38, 1 (1996). [17] R. Duan, A. Winter, arXiv:1409.3426 [18] R. Duan, S. Severini, A. Winter, arXiv:1502.02987 [19] H. Barnum, M. A. Nielsen, and B. Schumacher, Phys. Rev. A 57, 4153 (1998). [20] M. Grant and S. Boyd. CVX: Matlab software for disciplined convex programming, version 2.1.

    http://cvxr.com/cvx (2014). [21] Nathaniel Johnston, Alessandro Cosentino, and Vincent Russo, QETLAB: A MATLAB toolbox for

    quantum entanglement, http://qetlab.com (2015). [22] A. Ac´ın, R. Duan, A. B. Sainz, and A. Winter, arXiv:1505.01265 [23] A. Winter and D. Yang, arXiv:1505.00907

  • Metrics
    No metrics available
Share - Bookmark