The classical communication capacities of quantum Pauli channels with memory (correlation) are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel correlation identification. We treat the complete class of Pauli channels with correlation and determine the maximum quantum Fisher information achievable both with pure separable channel probe states and with maximally entangled bipartite probe states. A comparison of these Fisher informations reveals four distinct classes of Pauli channels and shows that only those channels that exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit this effect, the threshold at which it occurs has a simple analytic expression.

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References

S. Mancini, Journal of Physics: Conference Series 36, 121 (2006), DOI: 10.1088/1742-6596/36/1/019. Web of Science, Google Scholar
D. Kretschmann and R. F. Werner, Phys. Rev. A 72, 062323 (2005), DOI: 10.1103/PhysRevA.72.062323. Web of Science, Google Scholar
G. Bowen and S. Mancini, Phys. Rev. A 69, 012306 (2004), DOI: 10.1103/PhysRevA.69.012306. Web of Science, Google Scholar
D. Daems, Phys. Rev. A 76, 012310 (2007), DOI: 10.1103/PhysRevA.76.012310. Web of Science, Google Scholar
C. Macchiavello and G. M. Palma, Phys. Rev. A 65, 050301(R) (2002), DOI: 10.1103/PhysRevA.65.050301. Web of Science, Google Scholar
A. Fujiwara, Phys. Rev. A 63, 042304 (2001), DOI: 10.1103/PhysRevA.63.042304. Web of Science, Google Scholar
M. Sasaki, M. Ban and S. M. Barnett, Phys. Rev. A 66, 022308 (2002), DOI: 10.1103/PhysRevA.66.022308. Web of Science, Google Scholar
A. Fujiwara and H. Imai, Journal of Physics A: Matheamtical and General 36, 8093 (2003), DOI: 10.1088/0305-4470/36/29/314. Google Scholar
Z. Jiet al., IEEE Transactions on Information Theory 54(11), 5172 (2008), DOI: 10.1109/TIT.2008.929940. Web of Science, Google Scholar
J. H. Shapiro and S. R. Shepard, Phys. Rev. A 43(7), 3795 (1991), DOI: 10.1103/PhysRevA.43.3795. Web of Science, Google Scholar
M. A. Neilsen and I. L. Chuang , Quantum Computation and Information ( Cambridge University Press , Cambridge, UK , 2000 ) . Google Scholar
F. Carusoet al., Phys. Rev. A 77, 052323 (2008), DOI: 10.1103/PhysRevA.77.052323. Web of Science, Google Scholar
E. J. Donkor , A. R. Pirich and H. E. Brandt (eds.) , Quantum Information and Computation VII 7342 ( Orlando, Florida , 2009 ) . Google Scholar
C. Helstrom, Phys. Lett. A 25(2), 101 (1967), DOI: 10.1016/0375-9601(67)90366-0. Web of Science, Google Scholar
M. G. A. Paris, Int. J. Quant. Inf. 7(), 125 (2009), DOI: 10.1142/S0219749909004839. Link, Web of Science, Google Scholar
M. B. Ruskai, Rev. Math. Phys. 15(6), 643 (2003), DOI: 10.1142/S0129055X03001710. Link, Web of Science, Google Scholar
T. C. Bschorr, D. G. Fischer and M. Freyburger, Phys. Lett. A 292, 15 (2001), DOI: 10.1016/S0375-9601(01)00781-2. Web of Science, Google Scholar
A. Fujiwara, Phys. Rev. A 70, 012317 (2004), DOI: 10.1103/PhysRevA.70.012317. Web of Science, Google Scholar