Negativity as a resource for memory reduction in stochastic process modeling
| Autor: | Onggadinata, Kelvin, Tanggara, Andrew, Gu, Mile, Kaszlikowski, Dagomir |
|---|---|
| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In stochastic modeling, the excess entropy -- the mutual information shared between a processes past and future -- represents the fundamental lower bound of the memory needed to simulate its dynamics. However, this bound cannot be saturated by either classical machines or their enhanced quantum counterparts. Simulating a process fundamentally requires us to store more information in the present than than what is shared between past and future. Here we consider a hypothetical generalization of hidden Markov models beyond classical and quantum models -- n-machines -- that allow for negative quasi-probabilities. We show that under the collision entropy measure of information, the minimal memory of such models can equalize the excess entropy. Our results hint negativity as a necessary resource for memory-advantaged stochastic simulation -- mirroring similar interpretations in various other quantum information tasks. Comment: 22 pages, 13 figures |
| Databáze: | arXiv |
| Externí odkaz: |
|