Quantum Portfolios of Observables and the Risk Neutral Valuation Model

TL;DR

This paper extends quantum portfolio analysis to continuous variables, deriving a risk-neutral valuation model for quantum observables using stochastic equations and Fokker-Planck formalism, with applications to quantum algorithms encoded on harmonic oscillators.

Contribution

It introduces a continuous variables framework for quantum portfolios and develops a risk-neutral valuation model analogous to Black-Scholes for quantum observables.

Findings

Derived a Fokker-Planck equation for quantum portfolios.

Established a risk-neutral valuation model for quantum observables.

Analyzed polarization of quantum bit portfolios.

Abstract

Quantum Portfolios of quantum algorithms encoded on qbits have recently been reported. In this paper a discussion of the continuous variables version of quantum portfolios is presented. A risk neutral valuation model for options dependent on the measured values of the observables, analogous to the traditional Black-Scholes valuation model, is obtained from the underlying stochastic equations. The quantum algorithms are here encoded on simple harmonic oscillator (SHO) states, and a Fokker-Planck equation for the Glauber P-representation is obtained as a starting point for the analysis. A discussion of the observation of the polarization of a portfolio of qbits is also obtained and the resultant Fokker-Planck equation is used to obtain the risk neutral valuation of the qbit polarization portfolio.