zbMATH — the first resource for mathematics

Steering in spin tomographic probability representation. (English) Zbl 1400.81030
Summary: The steering property known for two-qubit state in terms of specific inequalities for the correlation function is translated for the state of qudit with the spin \(j = 3 / 2\). Since most steering detection inequalities are based on the correlation functions we introduce analogs of such functions for the single qudit systems. The tomographic probability representation for the qudit states is applied. The connection between the correlation function in the two-qubit system and the single qudit is presented in an integral form with an intertwining kernel calculated explicitly in tomographic probability terms.

81P40 Quantum coherence, entanglement, quantum correlations
82B10 Quantum equilibrium statistical mechanics (general)
Full Text: DOI
[1] Schrödinger, E., Discussion of probability relations between separated systems, Math. Proc. Cambridge Philos. Soc., 31, 04, 555-563 (1935) · JFM 61.1561.03
[2] Einstein, A.; Podolsky, Yu.; Rosen, N., Can quantum-mechanical description of physical reality be considered, Phys. Rev., 47, 777-780 (1935) · Zbl 0012.04201
[3] Klyachko, A. A.; Can, M. A.; Binicioglu, S.; Shumovsky, A. S., Simple test for hidden variables in spin-1 systems, Phys. Rev. Lett., 101, Article 020403 pp. (2008) · Zbl 1228.81068
[4] Chen, J. L.; Ye, X. J.; Wu, C. F.; Su, H. Y.; Cabello, A.; Kwek, L. C.; Oh, C. H., Proof of Einstein-Podolsky-Rosen steering, Sci. Rep., 88, 2143 (1983)
[5] Saunders, D. J.; Jones, S. J.; Wiseman, H. M.; Pryde, G. J., Experimental epr-steering using bell-local states, Nat. Phys., 6, 845-849 (2010)
[6] Jevtic, S.; Pusey, M.; Jennings, D.; Rudolph, T., Quantum steering ellipsoids, Phys. Rev. Lett., 113, Article 020402 pp. (2014)
[8] Wiseman, H. M.; Jones, S. J.; Doherty, A. C., Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox, Phys. Rev. Lett., 98, Article 140402 pp. (2007) · Zbl 1228.81078
[9] Man’ko, V. I.; Markovich, L. A., Steering and correlations for the single qudit state on the example of \(j = 3 / 2\), J. Russ. Laser Res., 36, 4, 343-349 (2015)
[10] Beghi, A.; Ferrante, A.; Pavon, M., How to steer a quantum system over a Schrodinger bridge, Quantum Inf. Process., 1, 3, 183-206 (2002)
[11] Zukowski, M.; Dutta, A.; Yin, Z., Geometric bell-like inequalities for steering, Phys. Rev. A, 91, Article 032107 pp. (2015)
[12] Schneeloch, J.; Broadbent, C. J.; Walborn, S.; Cavalcanti, E. G.; Howell, J., Einstein-Podolsky-Rosen steering inequalities from entropic uncertainty relations, Phys. Rev. A, 87, Article 062103 pp. (2013)
[13] Schneeloch, J.; Broadbenta, C. J.; Howella, J. C., Improving Einstein-Podolsky-Rosen steering inequalities with state information, Phys. Lett. A, 378, 10, 766-769 (2014) · Zbl 1323.81011
[14] Neumann, J.v., Zur theorie der gesellschaftsspiele, Math. Ann., 100, 1, 295-320 (1928) · JFM 54.0543.02
[15] Tsallis, C., Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479 (1988) · Zbl 1082.82501
[16] Umegaki, H., Conditional expectation in an operator algebra. IV. Entropy and information, Kodai Math. Sem. Rep., 14, 59-85 (1962) · Zbl 0199.19706
[17] Petz, D., Sufficient subalgebras and the relative entropy of states of a von Neumann algebra, Comm. Math. Phys., 105, 123-131 (1986) · Zbl 0597.46067
[18] Ohya, M.; Petz, D., Sufficient Subalgebras and the Relative Entropy of States of a Von Neumann Algebra (1986), Springer: Springer Berlin
[19] Rastegin, A. E., Fano type quantum inequalities in terms of \(q\)-entropies, Quantum Inf. Process., 11, 1895-1910 (2012) · Zbl 1263.81093
[21] Landau, L. D.; Lifshitz, E., Quantum Mechanics: Non-Relativistic Theory (1977), Butterworth-Heinemann · Zbl 0178.57901
[22] Manko, M. A.; Manko, V. I., Hidden quantum correlations in single qudit systems, J. Russ. Laser Res., 36, 4, 301-311 (2015)
[23] Ibort, A.; Man’ko, V. I.; Marmo, G.; Simoni, A.; Ventriglia, F., An introduction to the tomographic picture of quantum mechanics, Phys. Scr., 79, 6 (2010) · Zbl 1237.81043
[24] Kiktenko, E. O.; Fedorov, A. K.; Man’ko, O. V.; Man’ko, V. I., Multilevel superconducting circuits as two-qubit systems: Operations, state preparation, and entropic inequalities, Phys. Rev. A, 91, Article 042312 pp. (2015)
[25] Glushkova, A.; Glushkov, E.; Manko, V. I., On testing entropic inequalities for superconducting qudit, J. Russ. Laser Res., 36, 5, 448-457 (2015)
[26] Kesse, A. R.; Yakovleva, N. M., Schemes of implementation in NMR of quantum processors and Deutsch-Jozsa algorithm by using virtual spin representation, Phys. Rev. A, 66, Article 062322 pp. (2002)
[27] Shalibo, Y.; Resh, R.; Fogel, O.; Shwa, D.; Bialczak, R.; Martinis, J. M.; Katz, N., Quantum and classical chirps in an anharmonic oscillato, Phys. Rev. Lett., 110, Article 100404 pp. (2013)
[28] Filippov, S. N.; Manko, V. I., Quantumness tests and witnesses in the tomographic-probability representation, Phys. Scr., 79, Article 055007 pp. (2009) · Zbl 1170.81012
[29] Manko, O. V.; Manko, V. I.; Marmo, G.; Vitale, P., Star products, duality and double Lie algebras, Phys. Lett. A, 360, 522 (2007)
[30] Manko, O. V.; Manko, V. I., Spin state tomography, Zh. Eksp. Teor. Fiz., 112:3, 9, 796-804 (1997)
[31] Bell, J. S., On the Einstein Podolsky Rosen paradox, Physics, 1, 195-200 (1964)
[32] Clauser, J. F.; Horne, M. A.; Shimony, A.; Holt, R., Proposed experiment to test local hidden-variable theories, Phys. Rev. Lett., 23, 15, 880 (1969) · Zbl 1371.81014
[33] Aspect, A.; Roger, G.; Reynaud, S.; Dalibard, J.; Cohen-Tannoudji, C., Time correlations between the two sidebands of the resonance fluorescence triplet, Phys. Rev. Lett., 45, 617 (1980)
[34] Dodonov, V. V.; Klimov, A. B.; Nikonov, D. E., Quantum phenomena in nonstationary media, Phys. Rev. A, 47, 5, 4422 (1993)
[35] Dodonov, A. V.; Dodonov, E. V.; Dodonov, V. V., Photon generation from vacuum in nondegenerate cavities with regular and random periodic displacements of boundaries, Phys. Lett. A, 317, 378 (2003) · Zbl 1058.81764
[36] Fujii, T.; Matsuo, S.; Hatakenaka, N.; Kurihara, S.; Zeilinger, A., Quantum circuit analog of the dynamical casimir effect, Phys. Rev. B, 84, 17, Article 174521 pp. (2011)
[37] Shalibo, Y.; Rofe, Y.; Barth, I.; Friedland, L.; Bialczack, R.; Martinis, J. M.; Katz, N., Quantum and classical chirps in an anharmonic oscillator, Phys. Rev. Lett., 108, Article 037701 pp. (2012)
[38] Braumuller, J.; Cramer, J.; Schlor, S.; Rotzinger, H.; Radtke, L.; Lukashenko, A.; Yang, P.; Marthaler, M.; Guo, L.; Ustinov, A. V.; Weides, M., Multi-photon dressing of an anharmonic superconducting many-level quantum circuit, Phys. Rev. B, 91, Article 054523 pp. (2015)
[39] Lapkiewicz, R.; Li, P.; Schaff, C.; Langford, N. K.; Ramelow, S.; Wiesniak, M.; Zeilinger, A., Experimental non-classicality of an indivisible quantum system, Nature, 474, 490 (2011)
[40] Kiktenko, E. O.; Fedorov, A. K.; Strakhov, A. A.; Man’ko, V. I., Single qudit realization of the Deutsch algorithm using superconducting many-level quantum circuits, Phys. Lett. A, 379, 22, 1409-1413 (2015) · Zbl 1349.81071
[41] Man’ko, M. A.; Man’ko, V. I., Hidden correlations in indivisible qudits as a resource for quantum technologies on examples of superconducting circuits
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.