Superdensity operators for spacetime quantum mechanics

Journal of High Energy Physics, Sep 2018

Abstract We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac’s transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a super-density operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. We also suggest experimental protocols for measuring spacetime entropies.

A PDF file should load here. If you do not see its contents the file may be temporarily unavailable at the journal website or you do not have a PDF plug-in installed and enabled in your browser.

Alternatively, you can download the file locally and open with any standalone PDF reader:

https://link.springer.com/content/pdf/10.1007%2FJHEP09%282018%29093.pdf

Superdensity operators for spacetime quantum mechanics

Journal of High Energy Physics September 2018, 2018:93 | Cite as Superdensity operators for spacetime quantum mechanics AuthorsAuthors and affiliations Jordan CotlerChao-Ming JianXiao-Liang QiFrank Wilczek Open Access Regular Article - Theoretical Physics First Online: 17 September 2018 Received: 14 July 2018 Accepted: 24 August 2018 9 Downloads Abstract We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac’s transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime quantum channels. For example, we show that the von Neumann entropy of a super-density operator is related to a quantum generalization of the Kolmogorov-Sinai entropy, and compute this for a many-body system. We also suggest experimental protocols for measuring spacetime entropies. Keywords Space-Time Symmetries Lattice Quantum Field Theory  ArXiv ePrint: 1711.03119 Download to read the full article text Notes Open Access This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited. References [1] V.I. Arnold, Mathematical methods of classical mechanics, Springer, Germany (1989).CrossRefGoogle Scholar [2] R. Haag, Local quantum physics: fields, particles, algebras, Springer, Germany (2012).zbMATHGoogle Scholar [3] R.B. Griffiths, Consistent histories and the interpretation of quantum mechanics, J. Statist. Phys. 36 (1984) 219 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [4] R.B. Griffiths, Consistent interpretation of quantum mechanics using quantum trajectories, Phys. Rev. Lett. 70 (1993) 2201 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [5] R.B. Griffiths, Consistent quantum theory, Cambridge University Press, Cambridge U.K. (2002).zbMATHGoogle Scholar [6] H.F. Dowker and J.J. Halliwell, The quantum mechanics of history: the decoherence functional in quantum mechanics, Phys. Rev. D 46 (1992) 1580 [INSPIRE].ADSMathSciNetGoogle Scholar [7] R. Omnès, Interpretation of quantum mechanics, Phys. Lett. A 125 (1987) 169.ADSMathSciNetCrossRefGoogle Scholar [8] R. Omnès, The interpretation of quantum mechanics, Princeton University Press, Princeton U.S.A. (1994).zbMATHGoogle Scholar [9] M. Gell-Mann and J.B. Hartle. Quantum mechanics in the light of quantum cosmology, in Complexity, entropy and the physics of information, W. Zurek ed., Addison-Wesley, U.S.A. (1990).Google Scholar [10] M. Gell-Mann and J.B. Hartle, Alternative decohering histories in quantum mechanics in the proceedings of the 25th International Conference on High Energy Physics (ICHEP90), August 2–8, Singapore (1990).Google Scholar [11] J.B. Hartle, The quantum mechanics of cosmology, in Quantum cosmology and baby universes, S. Coleman et al. eds., World Scientific, Singapore (1991).Google Scholar [12] C.J. Isham, Quantum logic and the histories approach to quantum theory, J. Math. Phys. 35 (1994) 2157 [gr-qc/9308006] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [13] C.J. Isham and N. Linden, Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory, J. Math. Phys. 35 (1994) 5452 [gr-qc/9405029] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [14] C.J. Isham and N. Linden, Continuous histories and the history group in generalized quantum theory, J. Math. Phys. 36 (1995) 5392 [gr-qc/9503063] [INSPIRE]. [15] C.J. Isham, Topos theory and consistent histories: the internal logic of the set of all consistent sets, Int. J. Theor. Phys. 36 (1997) 785 [gr-qc/9607069] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar [16] J. Cotler and F. Wilczek, Entangled histories, Phys. Scripta T 168 (2016) 014004 [arXiv:1502.02480] [INSPIRE].ADSCrossRefGoogle Scholar [17] J. Cotler and F. Wilczek, Bell tests for histories, arXiv:1503.06458. [18] J. Cotler et al., Experimental test of entangled histories, Ann. Phys. 387 (2017) 334 [arXiv:1601.02943] [INSPIRE].ADSCrossRefGoogle Scholar [19] J. Cotler and F. Wilczek, Emporal observables and entangled histories, arXiv:1702.05838. [20] Y. Aharonov, P.G. Bergmann and J.L. Lebowitz. Time symmetry in the quantum process of measurement, Phys. Rev. B 134 (1964) 1410.ADSMathSciNetCrossRefGoogle Scholar [21] Y. Aharonov and L. Vaidman, Complete description of a quantum system at a given time, J. Phys. A 24 (1991) 2315.ADSMathSciNetGoogle Scholar [22] Y. Aharonov et al., Multiple-time states and multipl (...truncated)


This is a preview of a remote PDF: https://link.springer.com/content/pdf/10.1007%2FJHEP09%282018%29093.pdf

Jordan Cotler, Chao-Ming Jian, Xiao-Liang Qi, Frank Wilczek. Superdensity operators for spacetime quantum mechanics, Journal of High Energy Physics, 2018, pp. 93, Volume 2018, Issue 9, DOI: 10.1007/JHEP09(2018)093