This post answers some questions that typically come up when discussing the quantum approach to economics and finance. For a list of broad objections (and responses) to the use of quantum probability outside of physics, see the post Ten reasons to (not) be quantum.

**Why use quantum probability instead of classical probability?**

The main difference between classical and quantum probability is that the former is based on yes or no, 0 or 1 logic, while the latter allows for superposition states (so yes *and *no, 0 *and *1). This allows us to handle properties including interference and entanglement which characterize human interactions as much as they do the subatomic world. Another advantage of quantum probability is that it provides a useful framework for modelling probabilities that evolve dynamically (an example is the oscillator model of stock markets). Note also that quantum probability simulates a state using a complex-valued wave function, and much of its power comes from what has been called “the magic of complex numbers“.

H**ow do quantum phenomena such as interference or entanglement occur in markets?**

The field of quantum cognition models the decision-making process using the quantum formalism exactly because it can handle phenomena such as interference between incompatible beliefs, or entanglement between subjective context and objective calculations. Finance also has a more direct form of entanglement through things like debt contracts or the use of money.

**Is this the same type of interference and entanglement as is seen in physical systems?**

The point is that the same kind of model can be used for each. For example we can model a debt contract, including the potential decision to default, using an entanglement circuit on a quantum computer. The debtor’s decision is entangled with their subjective context; the creditor’s money is entangled with the debtor. Note that the entanglement involves information rather than macroscopic objects.

**What are the practical applications of quantum economics?**

Quantum economics offers an alternative to traditional economics that it is based on a different form of probability, and can be applied to a broad range of economic problems including decision making (quantum cognition), stock market analysis, option pricing, and the basics of supply and demand. More generally, it provides a mathematical framework for modelling properties such as subjectivity, interconnectedness, and power relationships which are downplayed or ignored in traditional economics.

**Can the theory be used to make predictions?**

The theory has been used to make a range of predictions (really postdictions, since the answer is known) including for cognitive effects of the sort studied in behavioural economics such as the order effect, the rate of strategic default on mortgages, the volume of options sold as a function of strike price, and the square-root law of market impact. One novel prediction was a relationship between price change and volatility that has important consequences for option pricing, since it violates a key assumption of the Black-Scholes formula.

**Why is it appropriate to model social systems using concepts like force, mass and energy?**

An advantage of quantum probability is that it provides a way to handle dynamical systems by quantizing forces. The entropic forces used in quantum economics are generated by propensity curves which specify the probability of an event such as a transaction. They are therefore just another way to describe a probability distribution, but they also serve as an intermediate step to create a quantum model. This in turn leads to natural definitions for concepts such as energy and mass, for example mass represents a resistance to change. Note that it is traditional in economics to talk about forces of supply and demand, but they are assumed to simply cancel out at equilibrium, so there is no need to describe something like mass.

**Quantum systems are discrete, while observed systems are usually better described as continuous. For example a quantum harmonic oscillator has discrete energy levels, so how can we use that to model something like the price of a stock?**

In the quantum model an oscillator represents a potential transaction. The energy level corresponds to the number of transactions over a time step, which is necessarily discrete (in a typical application the oscillator spends most of the time in the ground state, with transactions occurring every few steps). Indeed a defining feature of the economy is that it involves discrete transactions including money transfers.

**What is the financial version of Planck’s constant?**

In physics Planck’s constant is treated as an invariant quantity of nature, in quantum economics it is a parameter which decides the scaling for quantities such as mass.

**Are quantum models more complicated than classical models?**

The models used in traditional finance and economics are often very complicated because they need lots of bells and whistles in order to capture the complexities of the system. Quantum models do involve wave functions with an imaginary component, but the result can be simpler because they provide a more natural fit in the first place. For example in the oscillator model, the ground state is a wave function which rotates around the real axis and acts as a counter for transactions, which is only possible because it has an imaginary component. The only extra parameter is the oscillator frequency, which is needed in any case to describe the frequency of transactions.

**Do you need a degree in quantum mechanics in order to work in this field?**

No, most of the mathematics is basic linear algebra or calculus. In fact, while physicists tend to be the go-to experts for tricky technical problems, a training in physics sometimes seems to be a blocker – for example physicists often struggle with the idea of social or financial entanglement because they want to relate it to the behaviour of subatomic particles, instead of just looking at the math.

**What is the difference between quantum economics as described here, and other quantum**

**approaches?**

Quantum economics starts with the idea that money has complex dualistic properties which are best handled using a quantum approach. It draws on ideas from quantum cognition and quantum finance, which developed independently. One approach to quantum finance is to see it just as a mathematical tool for solving hard problems from traditional quantitative finance (such as derivative valuation), without any attempt to incorporate effects such as interference or entanglement (for a critique see here). Another is the “quantum-like” approach which transposes models from physics, without necessarily trying to justify them from basic principles. Finally there is the two-state approach which focuses on price, and models stock markets in terms of a price operator with two states representing the bid and the offer. In this view, there is no concept of force or mass (instead mass is subsumed in the definition of the financial Planck’s constant). Quantum economics differs from the first in that it is concerned with quantum phenomena such as interference and entanglement; from the second (slightly) in that it derives models as far as possible from first principles rather than importing then from quantum physics; and from the third in that concepts such as force and mass are viewed as useful components of the model (however two-state models can be derived from it). Quantum economics is therefore broadly compatible with these other approaches, but treats mental and financial phenomena as quantum in their own right.

**Does quantum economics assume a direct link with quantum mechanics, for example through quantum processes in the brain?**

No, and even if consciousness turns out to rely on quantum processes we couldn’t infer from it that the economy should be modelled using wave equations. Similarly, the fact that quantum models are useful for modelling human cognition does not imply that the brain is quantum. In quantum economics, we take social properties such as interference and entanglement at face value rather than arguing that they are inherited from subatomic particles. The test of quantum probability in economics is not whether its use can be justified by physics; it is whether, if it had no known application in physics, we would still want to use it to model social systems.

**Where can I receive training in quantum economics?**

Quantum economics and finance has been chosen as a thesis topic by a number of students in higher education. Memorial University in Newfoundland has set up a Centre for Quantum Social and Cognitive Science whose remit includes quantum economics. People who wish to get into the area can check out a number of online resources including the papers here or for a general introduction this video series.

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