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Quantum Deception: Honey-X Deception using Quantum Games

Efstratios Reppas, Ali Wadi, Brendan Gould, Kyriakos G. Vamvoudakis

TL;DR

This work extends Honey-X deception to quantum games by perturbing the payoff Hamiltonian $H$ with a bounded Hermitian $D$ to form $H' = H + D$. It shows that a victim who anticipates deception has the same equilibrium as a naive victim, enabling a single-level, bilinear semidefinite programming formulation to compute optimal deception and best-response strategies. The paper provides a theoretical derivation of quantum best responses, leverages minimax duality, and demonstrates the approach on quantum Penny Flip subgames, revealing richer deception patterns enabled by quantum interference. These results establish a computational and conceptual foundation for deception in quantum strategic interactions with potential cybersecurity implications.

Abstract

In this paper, we develop a framework for deception in quantum games, extending the Honey-X paradigm from classical zero-sum settings into the quantum domain. Building on a view of deception in classical games as manipulation of a player's perception of the payoff matrix, we formalize quantum deception as controlled perturbations of the payoff Hamiltonian subject to a deception budget. We show that when victims are aware of possible deception, their equilibrium strategies surprisingly coincide with those of naive victims who fully trust the deceptive Hamiltonian. This equivalence allows us to cast quantum deception as a bilevel optimization problem, which can be reformulated into a bilinear semidefinite program. To illustrate the framework, we present simulations on quantum versions of the Penny Flip game, demonstrating how quantum strategy spaces and non-classical payoffs can amplify the impact of deception relative to classical formulations.

Quantum Deception: Honey-X Deception using Quantum Games

TL;DR

This work extends Honey-X deception to quantum games by perturbing the payoff Hamiltonian with a bounded Hermitian to form . It shows that a victim who anticipates deception has the same equilibrium as a naive victim, enabling a single-level, bilinear semidefinite programming formulation to compute optimal deception and best-response strategies. The paper provides a theoretical derivation of quantum best responses, leverages minimax duality, and demonstrates the approach on quantum Penny Flip subgames, revealing richer deception patterns enabled by quantum interference. These results establish a computational and conceptual foundation for deception in quantum strategic interactions with potential cybersecurity implications.

Abstract

In this paper, we develop a framework for deception in quantum games, extending the Honey-X paradigm from classical zero-sum settings into the quantum domain. Building on a view of deception in classical games as manipulation of a player's perception of the payoff matrix, we formalize quantum deception as controlled perturbations of the payoff Hamiltonian subject to a deception budget. We show that when victims are aware of possible deception, their equilibrium strategies surprisingly coincide with those of naive victims who fully trust the deceptive Hamiltonian. This equivalence allows us to cast quantum deception as a bilevel optimization problem, which can be reformulated into a bilinear semidefinite program. To illustrate the framework, we present simulations on quantum versions of the Penny Flip game, demonstrating how quantum strategy spaces and non-classical payoffs can amplify the impact of deception relative to classical formulations.

Paper Structure

This paper contains 7 sections, 3 theorems, 20 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Quantum Games
  4. Honey-X Deception
  5. Resolving Quantum Deception
  6. Simulations
  7. Conclusion

Key Result

Lemma 1

For the quantum game with the Hermitian payoff operator $H \in \mathcal{H}_A \otimes \mathcal{H}_B$, player density operators $\rho_A \in \mathcal{P}_A$ and $\rho_B \in \mathcal{P}_B$, and payoff $u(\rho_A,\rho_B) = \operatorname{tr}\qty((\rho_A \otimes\rho_B)H)$, the best response is given by, if p

Figures (2)

  • Figure 1: The schematic of the quantum deception game. Rectangles denote numerical values, while parallelograms represent strategic decisions. Arrows illustrate causal relationships, indicating that the origin influences the destination.
  • Figure 2: Dependence of the deception cost $\Delta$ on (a) the realized payoff of the initial game $H$ from the perspective of the deceiver/minimizer and (b) the perceived payoff $u$ of the deceptive game $H'$ from the perspective of the victim/maximizer, for each of the three games: "pure", "diagonal", and "quantum" PFG. The payoff in (a) decreases (increases in absolute value) approximately linearly with increasing $\Delta$, saturating at the maximum possible absolute value of $100$ for large deception budgets in the first two games, and $200$ for the "quantum" PFG (the maximum possible absolute value would be $400$ with sufficient deception budget). The optimal perceived payoff $u$ in (b) grows linearly with $\Delta$ for the "quantum" PFG, but remains close to $0$ for the other games before exhibiting slight fluctuations at larger values.

Theorems & Definitions (8)

  • Remark 1
  • Remark 2
  • Remark 3
  • Lemma 1
  • Definition 1
  • Definition 2
  • Theorem 1
  • Theorem 2