# Nonlinearity without superluminality

## Abstract

Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowskimore »

- Authors:

- Centre for Quantum Computation, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 OWA (United Kingdom) and Hewlett-Packard Laboratories, Filton Road, Stoke Gifford, Bristol BS34 8QZ (United Kingdom)

- Publication Date:

- OSTI Identifier:
- 20718299

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 72; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevA.72.012108; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; CAUSALITY; EQUATIONS OF MOTION; HIDDEN VARIABLES; NONLINEAR PROBLEMS; QUANTUM ENTANGLEMENT; RELATIVITY THEORY; SCHROEDINGER EQUATION

### Citation Formats

```
Kent, Adrian.
```*Nonlinearity without superluminality*. United States: N. p., 2005.
Web. doi:10.1103/PhysRevA.72.012108.

```
Kent, Adrian.
```*Nonlinearity without superluminality*. United States. doi:10.1103/PhysRevA.72.012108.

```
Kent, Adrian. Fri .
"Nonlinearity without superluminality". United States. doi:10.1103/PhysRevA.72.012108.
```

```
@article{osti_20718299,
```

title = {Nonlinearity without superluminality},

author = {Kent, Adrian},

abstractNote = {Quantum theory is compatible with special relativity. In particular, though measurements on entangled systems are correlated in a way that cannot be reproduced by local hidden variables, they cannot be used for superluminal signaling. As Czachor, Gisin, and Polchinski pointed out, this is not generally true of general nonlinear modifications of the Schroedinger equation. Excluding superluminal signaling has thus been taken to rule out most nonlinear versions of quantum theory. The no-superluminal-signaling constraint has also been used for alternative derivations of the optimal fidelities attainable for imperfect quantum cloning and other operations. These results apply to theories satisfying the rule that their predictions for widely separated and slowly moving entangled systems can be approximated by nonrelativistic equations of motion with respect to a preferred time coordinate. This paper describes a natural way in which this rule might fail to hold. In particular, it is shown that quantum readout devices which display the values of localized pure states need not allow superluminal signaling, provided that the devices display the values of the states of entangled subsystems as defined in a nonstandard, although natural, way. It follows that any locally defined nonlinear evolution of pure states can be made consistent with Minkowski causality.},

doi = {10.1103/PhysRevA.72.012108},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 72,

place = {United States},

year = {2005},

month = {7}

}