Spin chains and channels with memory. (English) Zbl 1228.81107
Summary: In most studies of quantum channels, it is assumed that the errors in each use of the channel are independent. However, recent investigations of the effect of memory or correlations in error have led to speculation that nonanalytic behavior may occur in the capacity. Motivated by these observations, we connect the study of channels with correlated error to the study of many-body systems. This enables us to use many-body theory to solve some interesting models of correlated error. These models can display nonanalyticities analogous to quantum phase transitions.
MSC:
| 81P45 | Quantum information, communication, networks (quantum-theoretic aspects) |
| 81P68 | Quantum computation |
| 82B20 | Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics |
| 94A40 | Channel models (including quantum) in information and communication theory |
References:
| [1] | M.A. Nielsen, in: Quantum Information and Computation (2000) |
| [2] | DOI: 10.1109/TIT.2004.839515 · Zbl 1293.94063 · doi:10.1109/TIT.2004.839515 |
| [3] | DOI: 10.1103/PhysRevLett.92.257901 · doi:10.1103/PhysRevLett.92.257901 |
| [4] | DOI: 10.1103/PhysRevA.69.012306 · doi:10.1103/PhysRevA.69.012306 |
| [5] | DOI: 10.1088/0305-4470/38/50/008 · Zbl 1092.81006 · doi:10.1088/0305-4470/38/50/008 |
| [6] | DOI: 10.1103/PhysRevA.65.050301 · doi:10.1103/PhysRevA.65.050301 |
| [7] | DOI: 10.1103/PhysRevA.69.010303 · doi:10.1103/PhysRevA.69.010303 |
| [8] | DOI: 10.1103/PhysRevA.76.012310 · doi:10.1103/PhysRevA.76.012310 |
| [9] | DOI: 10.1103/PhysRevA.74.032332 · doi:10.1103/PhysRevA.74.032332 |
| [10] | DOI: 10.1103/PhysRevA.74.032320 · doi:10.1103/PhysRevA.74.032320 |
| [11] | DOI: 10.1103/PhysRevA.72.062323 · doi:10.1103/PhysRevA.72.062323 |
| [12] | M. Gregoratti, J. Mod. Opt. 50 pp 915– (2003) ISSN: http://id.crossref.org/issn/0950-0340 |
| [13] | DOI: 10.1103/PhysRevA.54.3824 · Zbl 1371.81041 · doi:10.1103/PhysRevA.54.3824 |
| [14] | DOI: 10.1109/18.959270 · Zbl 0998.81012 · doi:10.1109/18.959270 |
| [15] | DOI: 10.1103/PhysRevLett.95.090501 · doi:10.1103/PhysRevLett.95.090501 |
| [16] | D. Welsh, in: Codes and Cryptography (1993) |
| [17] | DOI: 10.1063/1.1495537 · Zbl 1060.94047 · doi:10.1063/1.1495537 |
| [18] | DOI: 10.1007/BF02099178 · Zbl 0755.46039 · doi:10.1007/BF02099178 |
| [19] | DOI: 10.1103/PhysRevLett.97.110403 · doi:10.1103/PhysRevLett.97.110403 |
| [20] | S. Sachdev, in: Quantum Phase Transitions (1999) · Zbl 1233.82003 |
| [21] | DOI: 10.1126/science.1091806 · doi:10.1126/science.1091806 |
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