## Abstract

Two types of randomness are associated with a mixed quantum state: the uncertainty in the probability coefficients of the constituent pure states and the uncertainty in the value of each observable captured by the Born’s rule probabilities. Entropy is a quantification of randomness, and we propose a spin-entropy for the observables of spin pure states based on the phase space of a spin as described by the geometric quantization method, and we also expand it to mixed quantum states. This proposed entropy overcomes the limitations of previously-proposed entropies such as von Neumann entropy which only quantifies the randomness of specifying the quantum state. As an example of a limitation, previously-proposed entropies are higher for Bell entangled spin states than for disentangled spin states, even though the spin observables are less constrained for a disentangled pair of spins than for an entangled pair. The proposed spin-entropy accurately quantifies the randomness of a quantum state, it never reaches zero value, and it is lower for entangled states than for disentangled states.

Original language | English (US) |
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Article number | 1292 |

Journal | Entropy |

Volume | 24 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2022 |

## Keywords

- entangled states
- geometric quantization
- spin entropy

## ASJC Scopus subject areas

- Information Systems
- Mathematical Physics
- Physics and Astronomy (miscellaneous)
- Electrical and Electronic Engineering