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The Quantum State Continuity Problem and Temporal Enforcement Against Fork Attacks

Samet Ünsal

TL;DR

This work formalizes the Quantum State Continuity Problem (QSCP), a security objective that links a system’s current execution to a unique past, independent of identity authentication. It introduces the Quantum State Continuity Witness (QSCW), a minimal, stateful quantum primitive that enforces temporal linkage through round-by-round challenges and cumulative audits, achieving fork resistance. A security game and a toy, GHZ-based instantiation demonstrate that stateless approaches fail to prevent fork attacks, while temporal enforcement yields exponential suppression of fork success as the audit window grows (approximately $2^{-W}$). The results suggest execution continuity as a distinct dimension of security and offer a practical, quantum-aware building block for enforcing continuity in real systems, robust to noise and parameter variations. These insights pave the path for integrating temporal continuity into quantum-aware security architectures and motivate further experimental and protocol-level developments.

Abstract

We introduce the Quantum State Continuity Problem (QSCP), a security objective orthogonal to identity authentication that captures whether a systems current execution is a legitimate continuation of a unique past execution. We show that classical and stateless quantum authentication mechanisms fail to enforce continuity and remain vulnerable to fork attacks. To address this gap, we propose the Quantum State Continuity Witness (QSCW), a minimal quantum-assisted primitive that enforces temporal linkage of execution through stateful quantum evolution and cumulative auditing. Using a GHZ-based toy instantiation and extensive simulation, we demonstrate that temporal enforcement suppresses fork attacks with exponential decay in success probability, while remaining robust to noise and system parameters. Our results highlight execution continuity as a distinct and underexplored dimension of system security.

The Quantum State Continuity Problem and Temporal Enforcement Against Fork Attacks

TL;DR

This work formalizes the Quantum State Continuity Problem (QSCP), a security objective that links a system’s current execution to a unique past, independent of identity authentication. It introduces the Quantum State Continuity Witness (QSCW), a minimal, stateful quantum primitive that enforces temporal linkage through round-by-round challenges and cumulative audits, achieving fork resistance. A security game and a toy, GHZ-based instantiation demonstrate that stateless approaches fail to prevent fork attacks, while temporal enforcement yields exponential suppression of fork success as the audit window grows (approximately ). The results suggest execution continuity as a distinct dimension of security and offer a practical, quantum-aware building block for enforcing continuity in real systems, robust to noise and parameter variations. These insights pave the path for integrating temporal continuity into quantum-aware security architectures and motivate further experimental and protocol-level developments.

Abstract

We introduce the Quantum State Continuity Problem (QSCP), a security objective orthogonal to identity authentication that captures whether a systems current execution is a legitimate continuation of a unique past execution. We show that classical and stateless quantum authentication mechanisms fail to enforce continuity and remain vulnerable to fork attacks. To address this gap, we propose the Quantum State Continuity Witness (QSCW), a minimal quantum-assisted primitive that enforces temporal linkage of execution through stateful quantum evolution and cumulative auditing. Using a GHZ-based toy instantiation and extensive simulation, we demonstrate that temporal enforcement suppresses fork attacks with exponential decay in success probability, while remaining robust to noise and system parameters. Our results highlight execution continuity as a distinct and underexplored dimension of system security.
Paper Structure (58 sections, 1 equation, 9 figures, 4 algorithms)

This paper contains 58 sections, 1 equation, 9 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Contributions
  3. Paper Organization
  4. Background and Preliminaries
  5. Identity Authentication vs. Execution Continuity
  6. Fork Attacks in Modern Systems
  7. Quantum Properties Relevant to Continuity
  8. Limitations of Stateless Quantum Authentication
  9. Towards Temporal Enforcement
  10. System and Threat Model
  11. System Model
  12. Temporal Model
  13. Adversarial Capabilities
  14. Adversary Models
  15. Success Conditions
  16. ...and 43 more sections

Figures (9)

  • Figure 1: Temporal fork success rate under a limited-$k$ attacker model. As attacker capability $k$ increases, fork success rises but remains bounded, indicating partial resistance even against adaptive replay strategies.
  • Figure 2: Temporal acceptance and fork sensitivity as a function of the number of qubits $n$. Temporal acceptance remains high, while stateless fork success stays near zero, highlighting robustness independent of system size.
  • Figure 3: Temporal audit robustness with respect to the number of measurement shots. Acceptance remains stable while fork success stays negligible, indicating resilience to finite sampling effects.
  • Figure 4: Tradeoff between temporal acceptance and fork suppression as a function of the audit threshold $\tau_x$. Temporal protocols maintain strong fork resistance across a wide threshold range.
  • Figure 5:
  • ...and 4 more figures