This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.This paper proposes a quantum mechanical state equation for describing evolution of projects of financial investment, while the parameters of this equation well simulate the fundamental elements of financial market, including investment (input), assets loss (assets decrease), assets increase and income (output), the quantum mechanics operators involved in this equation also can reflect the dynamic process and characteristics of the project, so the equation can be taken as the evolution model of a kind of financial investment projects in the market. The entangled state representation is introduced to solve this equation and its solution is obtained in an infinite operator-sum form, which exhibits the link between the initial state and final state, i.e., the dynamic process of the financial investment project. As an example, we derive the evolution law of a pure investment project in financial market, which conforms with the evolution trend of the market. In solving the equation we also find a new state which we name it as the binomial-negative binomial entangled state. Throughout the discussions we make full use of Dirac's symbolic method and the technique of integration within an ordered product (IWOP) of operators.

Acta Physica SinicaJan 1, 20143 citations

Quantum Macroeconomics

Routledge eBooksOct 4, 20167 citations

A Quantum Model of Supply and Demand

David Orrell

Physica A Statistical Mechanics and its ApplicationsJan 1, 201932 citations

Optimal noninvasive measurement of full counting statistics by a single qubit

A. V. Lebedev, Gordey B. Lesovik, G. Blatter

The complete characterization of the charge transport in a mesoscopic device is provided by the full counting statistics (FCS) ${P}_{t}(m)$ , describing the amount of charge $Q=me$ transmitted during the time $t$ . Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function ${P}_{t}(m)$ or its moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ is rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\ensuremath{\chi}(\ensuremath{\lambda})$ and moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$, by a qubit with a set of different couplings ${\ensuremath{\lambda}}_{j}$, $j=1,\ensuremath{\cdots},k,\ensuremath{\cdots}k+p$, $k=\ensuremath{\lceil}n/2\ensuremath{\rceil}$, $p\ensuremath{\ge}0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths ${\ensuremath{\lambda}}_{j}$, and we find the optimal distribution for these couplings ${\ensuremath{\lambda}}_{j}$ as well as the optimal distribution ${N}_{j}$ of $N=\ensuremath{\sum}{N}_{j}$ measurements among the different couplings ${\ensuremath{\lambda}}_{j}$. We determine the precision scaling for the moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\ensuremath{\gg}1$ are included in the measurement scheme.The complete characterization of the charge transport in a mesoscopic device is provided by the full counting statistics (FCS) ${P}_{t}(m)$, describing the amount of charge $Q=me$ transmitted during the time $t$. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function ${P}_{t}(m)$ or its moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ is rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\ensuremath{\chi}(\ensuremath{\lambda})$ and moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$, by a qubit with a set of different couplings ${\ensuremath{\lambda}}_{j}$, $j=1,\ensuremath{\cdots},k,\ensuremath{\cdots}k+p$, $k=\ensuremath{\lceil}n/2\ensuremath{\rceil}$, $p\ensuremath{\ge}0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths ${\ensuremath{\lambda}}_{j}$, and we find the optimal distribution for these couplings ${\ensuremath{\lambda}}_{j}$ as well as the optimal distribution ${N}_{j}$ of $N=\ensuremath{\sum}{N}_{j}$ measurements among the different couplings ${\ensuremath{\lambda}}_{j}$. We determine the precision scaling for the moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ with the number $N$ of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\ensuremath{\gg}1$ are included in the measurement scheme.

arXiv:1603.03896Physical review. B./Physical review. BMar 24, 20166 citations

The complete characterization of the charge transport in a mesoscopic device is provided by the full counting statistics (FCS)

{P}_{t}(m)

, describing the amount of charge

Q=me

transmitted during the time

t

. Although numerous systems have been theoretically characterized by their FCS, the experimental measurement of the distribution function

{P}_{t}(m)

or its moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ is rare and often plagued by strong back-action. Here, we present a strategy for the measurement of the FCS, more specifically its characteristic function $\ensuremath{\chi}(\ensuremath{\lambda})$ and moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$, by a qubit with a set of different couplings ${\ensuremath{\lambda}}_{j}$, $j=1,\ensuremath{\cdots},k,\ensuremath{\cdots}k+p$, $k=\ensuremath{\lceil}n/2\ensuremath{\rceil}$, $p\ensuremath{\ge}0$, to the mesoscopic conductor. The scheme involves multiple readings of Ramsey sequences at the different coupling strengths ${\ensuremath{\lambda}}_{j}$, and we find the optimal distribution for these couplings ${\ensuremath{\lambda}}_{j}$ as well as the optimal distribution

{N}_{j}

of $N=\ensuremath{\sum}{N}_{j}$ measurements among the different couplings ${\ensuremath{\lambda}}_{j}$. We determine the precision scaling for the moments $\ensuremath{\langle}{Q}^{n}\ensuremath{\rangle}$ with the number

N

of invested resources and show that the standard quantum limit can be approached when many additional couplings $p\ensuremath{\gg}1$ are included in the measurement scheme.