# Information processing in generalized probabilistic theories

## Abstract

I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the nonunique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary nonsignaling correlations, including the superquantum correlations that have become known in the literature as nonlocal machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory tomore »

- Authors:

- Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, Ontario N2L 2Y5 (Canada)

- Publication Date:

- OSTI Identifier:
- 20982250

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032304; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPARATIVE EVALUATIONS; INFORMATION THEORY; MIXED STATE; PROBABILISTIC ESTIMATION; QUANTUM COMPUTERS; QUANTUM CRYPTOGRAPHY; QUANTUM MECHANICS; QUANTUM TELEPORTATION

### Citation Formats

```
Barrett, Jonathan.
```*Information processing in generalized probabilistic theories*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032304.

```
Barrett, Jonathan.
```*Information processing in generalized probabilistic theories*. United States. doi:10.1103/PHYSREVA.75.032304.

```
Barrett, Jonathan. Thu .
"Information processing in generalized probabilistic theories". United States.
doi:10.1103/PHYSREVA.75.032304.
```

```
@article{osti_20982250,
```

title = {Information processing in generalized probabilistic theories},

author = {Barrett, Jonathan},

abstractNote = {I introduce a framework in which a variety of probabilistic theories can be defined, including classical and quantum theories, and many others. From two simple assumptions, a tensor product rule for combining separate systems can be derived. Certain features, usually thought of as specifically quantum, turn out to be generic in this framework, meaning that they are present in all except classical theories. These include the nonunique decomposition of a mixed state into pure states, a theorem involving disturbance of a system on measurement (suggesting that the possibility of secure key distribution is generic), and a no-cloning theorem. Two particular theories are then investigated in detail, for the sake of comparison with the classical and quantum cases. One of these includes states that can give rise to arbitrary nonsignaling correlations, including the superquantum correlations that have become known in the literature as nonlocal machines or Popescu-Rohrlich boxes. By investigating these correlations in the context of a theory with well-defined dynamics, I hope to make further progress with a question raised by Popescu and Rohrlich, which is why does quantum theory not allow these strongly nonlocal correlations? The existence of such correlations forces much of the dynamics in this theory to be, in a certain sense, classical, with consequences for teleportation, cryptography, and computation. I also investigate another theory in which all states are local. Finally, I raise the question of what further axiom(s) could be added to the framework in order to identify quantum theory uniquely, and hypothesize that quantum theory is optimal for computation.},

doi = {10.1103/PHYSREVA.75.032304},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}