### Abstract

We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems.

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

Pages (from-to) | 4810-4820 |

Number of pages | 11 |

Journal | Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 370 |

Issue number | 1976 |

DOIs | |

Publication status | Published - 2012 Oct 13 |

### Fingerprint

### Keywords

- Large-number limit
- Purity
- Quantumness witness

### ASJC Scopus subject areas

- Mathematics(all)
- Physics and Astronomy(all)
- Engineering(all)

### Cite this

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*370*(1976), 4810-4820. https://doi.org/10.1098/rsta.2011.0353

**Classical to quantum in large-number limit.** / Modi, Kavan; Fazio, Rosario; Pascazio, Saverio; Vedral, Vlatko; Yuasa, Kazuya.

Research output: Contribution to journal › Article

*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, vol. 370, no. 1976, pp. 4810-4820. https://doi.org/10.1098/rsta.2011.0353

}

TY - JOUR

T1 - Classical to quantum in large-number limit

AU - Modi, Kavan

AU - Fazio, Rosario

AU - Pascazio, Saverio

AU - Vedral, Vlatko

AU - Yuasa, Kazuya

PY - 2012/10/13

Y1 - 2012/10/13

N2 - We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems.

AB - We construct a quantumness witness following the work of Alicki & van Ryn (AvR). We reformulate the AvR test by defining it for quantum states rather than for observables. This allows us to identify the necessary quantities and resources to detect quantumness for any given system. The first quantity turns out to be the purity of the system. When applying the witness to a system with even moderate mixedness, the protocol is unable to reveal any quantumness. We then show that having many copies of the system leads the witness to reveal quantumness. This seems contrary to the Bohr correspondence, which asserts that, in the large-number limit, quantum systems become classical, whereas the witness shows quantumness when several non-quantum systems, as determined by the witness, are considered together. However, the resources required to detect the quantumness increase dramatically with the number of systems. We apply the quantumness witness for systems that are highly mixed but in the large-number limit that resembles nuclear magnetic resonance (NMR) systems. We make several conclusions about detecting quantumness in NMR-like systems.

KW - Large-number limit

KW - Purity

KW - Quantumness witness

UR - http://www.scopus.com/inward/record.url?scp=84866388602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866388602&partnerID=8YFLogxK

U2 - 10.1098/rsta.2011.0353

DO - 10.1098/rsta.2011.0353

M3 - Article

VL - 370

SP - 4810

EP - 4820

JO - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

JF - Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

SN - 0962-8428

IS - 1976

ER -