Partial Transposition in a Finite-Dimensional Hilbert Space: Physical Interpretation, Measurement of Observables and Entanglement
arXiv:1705.09613
Abstract
We show that partial transposition for pure and mixed two-particle states in a discrete -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 , and an operator whose variance becomes negative for the partially transposed state for certain values of ; for such , the original states are entangled.
Submitted to: "Quantum Studies: Mathematics and Foundations". arXiv admin note: substantial text overlap with arXiv:1601.04481