arXiv subjects

Faisal Shah Khan

Publications and source records attributed to Faisal Shah Khan.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Coordination without Conditioning under Restricted Information

We study which joint probability distributions can be implemented by distributed systems when agents have restricted information. Classical local operations cannot implement all distributions that are achievable with full conditioning on history. We show that shared quantum states can overcome this limitation even when using only separable states. In particular, separable states that are diagonal in a fixed basis allow certain joint distributions to be implemented through local measurements without requiring agents to condition on an inaccessible latent variable. These distributions cannot be implemented by classical local rules under the same information constraints. However, quantum implementations cannot reproduce fully adaptive dependence on past outcomes when those outcomes are observationally indistinguishable. Quantum state preparation therefore provides a partial operational substitute for perfect recall under restricted information.

quant-ph↗

arXiv2025

When Recall Fails, Discord Remembers: A Quantum Analogue of Kuhn's Theorem

A behavioral quantum strategy is shown to replicate the payoff of a classical mixed strategy in an extensive-form game with imperfect recall, using only local measurements on a separable quantum state with zero entanglement and nonzero discord. Classical behavioral strategies, constrained by imperfect recall, cannot achieve this coordination. The result suggests a quantum analogue to Kuhn's classical equivalence: discord enables behavioral-style strategies to functionally substitute for strategic memory and recover coordination lost in the classical setting. This highlights quantum discord as a minimal and robust resource for extending bounded rationality beyond classical limits.

quant-ph↗

arXiv2025

Quantum Advantage in Trading: A Game-Theoretic Approach

Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.

quant-ph↗

arXiv2022

Calculating Nash Equilibrium on Quantum Annealers

Adiabatic quantum computing is implemented on specialized hardware using the heuristics of the quantum annealing algorithm. This setup requires the addressed problems to be formatted as discrete quadratic functions without constraints and the variables to take binary values only. The problem of finding Nash equilibrium in two-player, non-cooperative games is a two-fold quadratic optimization problem with constraints. This problem was formatted as a single, constrained quadratic optimization in 1964 by Mangasarian and Stone. Here, we show that adding penalty terms to the quadratic function formulation of Nash equilibrium gives a quadratic unconstrained binary optimization (QUBO) formulation of this problem that can be executed on quantum annealers. Three examples are discussed to highlight the success of the formulation, and an overall, time-to-solution (hardware + software processing) speed up of seven to ten times is reported on quantum annealers developed by D-Wave System.

cs.GT↗

arXiv2021

Quantum Prisoner's Dilemma and High Frequency Trading on the Quantum Cloud

High-frequency trading (HFT) offers an excellent user case and a potential killer application of the commercially available, first generation quasi-quantum communication and computation technologies. To this end, we offer here a simple but complete game-theoretic model of HFT as the famous two player game, Prisoner's Dilemma. We explore the implementation of HFT as a game on the (quasi) quantum cloud using the Eisert, Wilkens, and Lewenstein quantum mediated communication protocol, and how this implementation can increase transaction speed and improve the lot of the players in HFT. Using cooperative game-theoretic reasoning, we also note that in the near future when the internet is properly quantum, players will be able to achieve Pareto-optimality in HFT as an instance of reinforced learning.

quant-ph↗

arXiv2020

Partitions of Correlated N-Qubit Systems

The production and manipulation of quantum correlation protocols will play a central role where the quantum nature of the correlation can be used as a resource to yield properties unachievable within a classical framework is a very active and important area of research. In this work, we provide a description of a measure of correlation strength between quantum systems, especially for multipartite quantum systems.

quant-ph↗

arXiv2020

Optimal Control of Traffic Signals using Quantum Annealing

Quadratic unconstrained binary optimization (QUBO) is the mathematical formalism for phrasing and solving a class of optimization problems that are combinatorial in nature. Due to their natural equivalence with the two dimensional Ising model for ferromagnetism in statistical mechanics, problems from the QUBO class can be solved on quantum annealing hardware. In this paper, we report a QUBO formatting of the problem of optimal control of time-dependent traffic signals on an artificial grid-structured road network so as to ease the flow of traffic, and the use of D-Wave Systems' quantum annealer to solve it. Since current-generation D-Wave annealers have a limited number of qubits and limited inter-qubit connectivity, we adopt a hybrid (classical/quantum) approach to this problem. As traffic flow is a continuous and evolving phenomenon, we address this time-dependent problem by adopting a workflow to generate and solve multiple problem instances periodically.

quant-ph↗

arXiv2019

Nash embedding: a road map to realizing quantum hardware

The non-Euclidean nature of the mathematical model of quantum circuits leaves open the question of their practical implementation in hardware platforms which necessarily reside in the Euclidean space $\mathbb{R}^3$. On the other hand, reversible circuits are elements of Euclidean spaces, making their physical realization in hardware platforms possible and practical. Here, the quantum circuit model for quantum computing is mapped into that of reversible computing in a mathematically robust fashion using Nash embedding so that every quantum computation can be realized as an equivalent reversible one.

physics.gen-ph↗

arXiv2019

Cavity-induced mirror-mirror entanglement in a single-atom Raman laser

We address an experimental scheme to analyze the optical bistability and the entanglement of two movable mirrors coupled to a two-mode laser inside a doubly resonant cavity. With this aim we investigate the master equations of the atom-cavity subsystem in conjunction with the quantum Langevin equations that describe the interaction of the mirror cavity. The parametric amplification-type coupling induced by the two-photon coherence on the optical bistability of the intracavity mean photon numbers is found and investigated. Under this condition, the optical intensities exhibit bistability for all large values of cavity laser detuning. We also provide numerical evidence for the generation of strong entanglement between the movable mirrors and show that it is robust against environmental thermalization.

quant-ph↗

arXiv2018

Quantum games: a review of the history, current state, and interpretation

We review both theoretical and experimental developments in the area of quantum games since the inception of the subject circa 1999. We will also offer a narrative on the controversy that surrounded the subject in its early days, and how this controversy has affected the development of the subject.

quant-ph↗

arXiv2018

Compiling Adiabatic Quantum Programs

We develop a non-cooperative game-theoretic model for the problem of graph minor-embedding to show that optimal compiling of adiabatic quantum programs in the sense of Nash equilibrium is possible.

cs.GT↗

arXiv2018

Nash embedding and equilibrium in pure quantum states

With respect to probabilistic mixtures of the strategies in non-cooperative games, quantum game theory provides guarantee of fixed-point stability, the so-called Nash equilibrium. This permits players to choose mixed quantum strategies that prepare mixed quantum states optimally under constraints. In this letter, we show that fixed-point stability of Nash equilibrium can also be guaranteed for pure quantum strategies via an application of the Nash embedding theorem, permitting players to prepare pure quantum states optimally under constraints.

quant-ph↗

arXiv2017

No fixed-point guarantee of Nash equilibrium in quantum games

The theory of quantum games permits players to choose strategies that prepare and measure quantum states. Whereas conventional game theory provides guarantees for fixed-point stability in non-cooperative games, so-called Nash equilibria, we find this guarantee is not provided for quantum games. In particular, we show the conditions for Glickberg's fixed-point theorem do not apply to pure quantum games when the payoff is a physical observable. We further show that Nash equilibrium can be guaranteed when the payoff is defined with respect to state preparation.

quant-ph↗

arXiv2015

Nash equilibrium quantum states and optimal quantum data classification

This letter reports a novel application of game theory to quantum informational processes which can be used to optimally classify data generated by these processes. To this end, the notion of simultaneously distinguishing a pure quantum state, generated by a quantum informational process, from its constituent observable states optimally - given the constraint of these observables being orthogonal to each other, is first introduced. This problem is solved via a non-cooperative game model and the affiliated solution concept of Nash equilibrium. The notion of Nash equilibrium quantum states is introduced and used to classify quantum data optimally.

quant-ph↗

arXiv2015

Preferences in Quantum Games

A quantum game can be viewed as a state preparation in which the final output state results from the competing preferences of the players over the set of possible output states that can be produced. It is therefore possible to view state preparation in general as being the output of some appropriately chosen (notional) quantum game. This reverse engineering approach in which we seek to construct a suitable notional game that produces some desired output state as its equilibrium state may lead to different methodologies and insights. With this goal in mind we examine the notion of preference in quantum games since if we are interested in the production of a particular equilibrium output state, it is the competing preferences of the players that determine this equilibrium state. We show that preferences on output states can be viewed in certain cases as being induced by measurement with an appropriate set of numerical weightings, or payoffs, attached to the results of that measurement. In particular we show that a distance-based preference measure on the output states is equivalent to a having a strictly-competitive set of payoffs on the results of some measurement.

quant-ph↗

arXiv2015

Dominant Strategies in Two Qubit Quantum Computations

Nash equilibrium is a solution concept in non-strictly competitive, non-cooperative game theory that finds applications in various scientific and engineering disciplines. A non-strictly competitive, non-cooperative game model is presented here for two qubit quantum computations that allows for the characterization of Nash equilibrium in these computations via the inner product of their state space. Nash equilibrium outcomes are optimal under given constraints and therefore offer a game-theoretic measure of constrained optimization of two qubit quantum computations.

quant-ph↗

arXiv2013

Mini-maximizing two qubit quantum computations

Two qubit quantum computations are viewed as two player, strictly competitive games and a game-theoretic measure of optimality of these computations is developed. To this end, the geometry of Hilbert space of quantum computations is used to establish the equivalence of game-theoretic solution concepts of Nash equilibrium and mini-max outcomes in games of this type, and quantum mechanisms are designed for realizing these mini-max outcomes.

quant-ph↗

arXiv2013

The Role of Correlation in Quantum and Classical Games

We use the example of playing a 2-player game with entangled quantum objects to investigate the effect of quantum correlation. We find that for simple game scenarios it is classical correlation that is the central feature and that these simple quantum games are not sensitive to the quantum part of the correlation. In these games played with quantum objects it is possible to transform a game such as Prisoner's Dilemma into the game of Chicken. We show that this behaviour, and the associated enhanced equilibrium payoff over playing the game with quantum objects in non-entangled states, is entirely due to the classical part of the correlation. Generalizing these games to the pure strategy 2-player quantum game where the players have finite strategy sets and a projective joint measurement is made on the output state produced by the players, we show that a given quantum game of this form can always be reproduced by a classical model, such as a communication channel. Where entanglement is a feature of the these 2-player quantum games the matrix of expected outcomes for the players can be reproduced by a classical channel with correlated noise.

quant-ph↗