## Superdensity operators for spacetime quantum mechanics

## 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. Here, we also suggest experimental protocols for measuring spacetime entropies.

- Authors:

- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics
- Microsoft Research, Santa Barbara, CA (United States); Univ. of California, Santa Barbara, CA (United States). Kavli Inst. of Theoretical Physics
- Stanford Univ., Stanford, CA (United States). Stanford Inst. for Theoretical Physics; Inst. for Advanced Study, Princeton, NJ (United States)
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics; Stockholm Univ., Stockholm (Sweden). The Oskar Klein Centre for Cosmoparticle Physics; Shanghai Jiao Tong Univ., Shanghai (China). T. D. Lee Inst. and Wilczek Quantum Center; Arizona State Univ., Tempe, AZ (United States). Dept. of Physics and Origins Project

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology, Cambridge (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1499044

- Grant/Contract Number:
- SC0012567

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of High Energy Physics (Online)

- Additional Journal Information:
- Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2018; Journal Issue: 9; Journal ID: ISSN 1029-8479

- Publisher:
- Springer Berlin

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Space-Time Symmetries; Lattice Quantum Field Theory

### Citation Formats

```
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, and Wilczek, Frank. Superdensity operators for spacetime quantum mechanics. United States: N. p., 2018.
Web. doi:10.1007/jhep09(2018)093.
```

```
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, & Wilczek, Frank. Superdensity operators for spacetime quantum mechanics. United States. doi:10.1007/jhep09(2018)093.
```

```
Cotler, Jordan, Jian, Chao -Ming, Qi, Xiao -Liang, and Wilczek, Frank. Mon .
"Superdensity operators for spacetime quantum mechanics". United States. doi:10.1007/jhep09(2018)093. https://www.osti.gov/servlets/purl/1499044.
```

```
@article{osti_1499044,
```

title = {Superdensity operators for spacetime quantum mechanics},

author = {Cotler, Jordan and Jian, Chao -Ming and Qi, Xiao -Liang and Wilczek, Frank},

abstractNote = {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. Here, we also suggest experimental protocols for measuring spacetime entropies.},

doi = {10.1007/jhep09(2018)093},

journal = {Journal of High Energy Physics (Online)},

number = 9,

volume = 2018,

place = {United States},

year = {2018},

month = {9}

}