# Simulating quantum correlations as a distributed sampling problem

## Abstract

It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, postselection or nonlocal boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a nonlocal box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.

- Authors:

- Laboratoire de Recherche en Informatique, UMR 8263, Universite Paris-Sud, 91405 Orsay (France)
- (Canada)

- Publication Date:

- OSTI Identifier:
- 20786277

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.062314; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; CORRELATIONS; DATA TRANSMISSION; DISTRIBUTION; ENERGY LEVELS; HIDDEN VARIABLES; QUANTUM COMPUTERS; QUANTUM ENTANGLEMENT; QUANTUM MECHANICS; QUBITS; RANDOMNESS; SAMPLING

### Citation Formats

```
Degorre, Julien, Laboratoire d'Informatique Theorique et Quantique, Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal, Laplante, Sophie, and Roland, Jeremie.
```*Simulating quantum correlations as a distributed sampling problem*. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.

```
Degorre, Julien, Laboratoire d'Informatique Theorique et Quantique, Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal, Laplante, Sophie, & Roland, Jeremie.
```*Simulating quantum correlations as a distributed sampling problem*. United States. doi:10.1103/PHYSREVA.72.0.

```
Degorre, Julien, Laboratoire d'Informatique Theorique et Quantique, Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal, Laplante, Sophie, and Roland, Jeremie. Thu .
"Simulating quantum correlations as a distributed sampling problem". United States.
doi:10.1103/PHYSREVA.72.0.
```

```
@article{osti_20786277,
```

title = {Simulating quantum correlations as a distributed sampling problem},

author = {Degorre, Julien and Laboratoire d'Informatique Theorique et Quantique, Departement d'Informatique et de Recherche Operationnelle, Universite de Montreal and Laplante, Sophie and Roland, Jeremie},

abstractNote = {It is known that quantum correlations exhibited by a maximally entangled qubit pair can be simulated with the help of shared randomness, supplemented with additional resources, such as communication, postselection or nonlocal boxes. For instance, in the case of projective measurements, it is possible to solve this problem with protocols using one bit of communication or making one use of a nonlocal box. We show that this problem reduces to a distributed sampling problem. We give a new method to obtain samples from a biased distribution, starting with shared random variables following a uniform distribution, and use it to build distributed sampling protocols. This approach allows us to derive, in a simpler and unified way, many existing protocols for projective measurements, and extend them to positive operator value measurements. Moreover, this approach naturally leads to a local hidden variable model for Werner states.},

doi = {10.1103/PHYSREVA.72.0},

journal = {Physical Review. A},

number = 6,

volume = 72,

place = {United States},

year = {Thu Dec 15 00:00:00 EST 2005},

month = {Thu Dec 15 00:00:00 EST 2005}

}