Kelly Betting with Quantum Payoff: a continuous variable approach
The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested cap...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2021-09-01
|
| Series: | Quantum |
| Online Access: | https://quantum-journal.org/papers/q-2021-09-21-545/pdf/ |
| _version_ | 1819063722213113856 |
|---|---|
| author | Salvatore Tirone Maddalena Ghio Giulia Livieri Vittorio Giovannetti Stefano Marmi |
| author_facet | Salvatore Tirone Maddalena Ghio Giulia Livieri Vittorio Giovannetti Stefano Marmi |
| author_sort | Salvatore Tirone |
| collection | DOAJ |
| description | The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude. |
| first_indexed | 2024-12-21T15:19:11Z |
| format | Article |
| id | doaj.art-b8ad88fd4da249118f52c95a56697226 |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-21T15:19:11Z |
| publishDate | 2021-09-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-b8ad88fd4da249118f52c95a566972262022-12-21T18:59:06ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2021-09-01554510.22331/q-2021-09-21-54510.22331/q-2021-09-21-545Kelly Betting with Quantum Payoff: a continuous variable approachSalvatore TironeMaddalena GhioGiulia LivieriVittorio GiovannettiStefano MarmiThe main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum memory element. In our scheme, we assume that the invested capital is explicitly associated with the quantum analog of the free-energy (i.e. ergotropy functional by Allahverdyan, Balian, and Nieuwenhuizen) of a single mode of the electromagnetic radiation which, depending on the outcome of the betting, experiences attenuation or amplification processes which model losses and winning events. The resulting stochastic evolution of the quantum memory resembles the dynamics of random lasing which we characterize within the theoretical setting of Bosonic Gaussian channels. As in the classical Kelly Criterion for optimal betting, we define the asymptotic doubling rate of the model and identify the optimal gambling strategy for fixed odds and probabilities of winning. The performance of the model are hence studied as a function of the input capital state under the assumption that the latter belongs to the set of Gaussian density matrices (i.e. displaced, squeezed thermal Gibbs states) revealing that the best option for the gambler is to devote all their initial resources into coherent state amplitude.https://quantum-journal.org/papers/q-2021-09-21-545/pdf/ |
| spellingShingle | Salvatore Tirone Maddalena Ghio Giulia Livieri Vittorio Giovannetti Stefano Marmi Kelly Betting with Quantum Payoff: a continuous variable approach Quantum |
| title | Kelly Betting with Quantum Payoff: a continuous variable approach |
| title_full | Kelly Betting with Quantum Payoff: a continuous variable approach |
| title_fullStr | Kelly Betting with Quantum Payoff: a continuous variable approach |
| title_full_unstemmed | Kelly Betting with Quantum Payoff: a continuous variable approach |
| title_short | Kelly Betting with Quantum Payoff: a continuous variable approach |
| title_sort | kelly betting with quantum payoff a continuous variable approach |
| url | https://quantum-journal.org/papers/q-2021-09-21-545/pdf/ |
| work_keys_str_mv | AT salvatoretirone kellybettingwithquantumpayoffacontinuousvariableapproach AT maddalenaghio kellybettingwithquantumpayoffacontinuousvariableapproach AT giulialivieri kellybettingwithquantumpayoffacontinuousvariableapproach AT vittoriogiovannetti kellybettingwithquantumpayoffacontinuousvariableapproach AT stefanomarmi kellybettingwithquantumpayoffacontinuousvariableapproach |