## Abstract

We show that partial transposition for pure and mixed two-particle states in a discrete N-dimensional Hilbert space is equivalent to a change in sign of a “momentum-like” variable of one of the particles in the Wigner function for the state. This generalizes a result obtained for continuous-variable systems to the discrete-variable system case. We show that, in principle, quantum mechanics allows measuring the expectation value of an observable in a partially transposed state, in spite of the fact that the latter may not be a physical state. We illustrate this result with the example of an “isotropic state”, which is dependent on a parameter r, and an operator whose variance becomes negative for the partially transposed state for certain values of r; for such rs, the original states are entangled.

Original language | English |
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Pages (from-to) | 177-188 |

Number of pages | 12 |

Journal | Quantum Studies: Mathematics and Foundations |

Volume | 5 |

Issue number | 2 |

DOIs | |

State | Published - 1 Jun 2018 |

## Keywords

- Entanglement
- Finite-dimensional Hilbert space
- Partial transposition

## ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics
- Mathematical Physics