Quantum history cannot be copied. (English) Zbl 1195.81013
Summary: We show that unitarity does not allow cloning of any two points in a ray. This has implication for cloning of the geometric phase information in a quantum state. In particular, the quantum history which is encoded in the geometric phase during cyclic evolution of a quantum system cannot be copied. We also prove that the generalized geometric phase information cannot be copied by a unitary operation. We argue that our result also holds in the consistent history formulation of quantum mechanics.
References:
| [1] | Wootters, W.; Zurek, W. H., Nature (London), 299, 802 (1982) · Zbl 1369.81022 |
| [2] | Dieks, D., Phys. Lett. A, 92, 271 (1982) |
| [3] | Yuen, H. P., Phys. Lett. A, 113, 405 (1986) |
| [4] | Buzek, V.; Hillery, M., Phys. Rev. A, 54, 1844 (1996) |
| [5] | Duan, L. M.; Guo, G. C., Phys. Rev. Lett., 80, 4999 (1998) |
| [6] | Pati, A. K., Phys. Rev. Lett., 83, 2849 (1999) · Zbl 0946.81016 |
| [7] | Pati, A. K.; Braunstein, S. L., Nature, 404, 164 (2000) |
| [8] | Berry, M. V., Proc. R. Soc. London, 392, 45 (1984) · Zbl 1113.81306 |
| [9] | Pancharatnam, S., Proc. Indian Acad. Sci. A, 44, 247 (1956) |
| [10] | Schiff, L. I., Quantum Mechanics (1968), McGraw-Hill: McGraw-Hill New York · Zbl 0068.40202 |
| [11] | Messiah, A., Quantum Mechanics (1962), North-Holland: North-Holland Amsterdam · Zbl 0102.42602 |
| [12] | Aharonov, Y.; Anandan, J., Phys. Rev. Lett., 58, 1539 (1987) |
| [13] | Samuel, J.; Bhandari, R., Phys. Rev. Lett., 60, 2339 (1988) |
| [14] | Mukunda, N.; Simon, R., Ann. Phys., 228, 205 (1993) · Zbl 0791.58121 |
| [15] | Pati, A. K., Phys. Rev. A, 52, 2576 (1995) |
| [16] | Pati, A. K., J. Phys. A, 28, 2087 (1995) · Zbl 0848.46048 |
| [17] | Pati, A. K., Phys. Lett. A, 159, 105 (1991) |
| [18] | Griffiths, R. B., J. Stat. Phys., 36, 219 (1984) · Zbl 0586.60097 |
| [19] | Omnes, R., J. Stat. Phys., 53, 893 (1988) · Zbl 0677.03042 |
| [20] | Gell-Mann, M.; Hartle, J. B., Phys. Rev. D, 47, 3345 (1993) |
| [21] | Anastopoulos, C.; Savvidou, N., Int. J. Theor. Phys., 41, 1572 (2002) |
| [22] | Isham, C. J., Int. J. Theor. Phys., 36, 785 (1997) · Zbl 0881.03039 |
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