### Abstract

We analyze robustness of correlations of the N-qubit GHZ and Dicke states against white noise admixture. For sufficiently large N, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of (N - 3) pure qubits is the most robust against white noise admixture among any N-qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin's theorem.

Original language | English |
---|---|

Article number | 465301 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 48 |

Issue number | 46 |

DOIs | |

Publication status | Published - Oct 26 2015 |

### Fingerprint

### Keywords

- entanglement
- violation of local realism
- white noise

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modelling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

*Journal of Physics A: Mathematical and Theoretical*,

*48*(46), [465301]. https://doi.org/10.1088/1751-8113/48/46/465301

**Highly noise resistant multiqubit quantum correlations.** / Laskowski, Wiesław; Vértesi, T.; Wies̈niak, Marcin.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 48, no. 46, 465301. https://doi.org/10.1088/1751-8113/48/46/465301

}

TY - JOUR

T1 - Highly noise resistant multiqubit quantum correlations

AU - Laskowski, Wiesław

AU - Vértesi, T.

AU - Wies̈niak, Marcin

PY - 2015/10/26

Y1 - 2015/10/26

N2 - We analyze robustness of correlations of the N-qubit GHZ and Dicke states against white noise admixture. For sufficiently large N, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of (N - 3) pure qubits is the most robust against white noise admixture among any N-qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin's theorem.

AB - We analyze robustness of correlations of the N-qubit GHZ and Dicke states against white noise admixture. For sufficiently large N, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of (N - 3) pure qubits is the most robust against white noise admixture among any N-qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin's theorem.

KW - entanglement

KW - violation of local realism

KW - white noise

UR - http://www.scopus.com/inward/record.url?scp=85053361574&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85053361574&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/48/46/465301

DO - 10.1088/1751-8113/48/46/465301

M3 - Article

VL - 48

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 46

M1 - 465301

ER -