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Provable DI-QRNG protocols based on self-testing methodologies in preparation and measure scenario

Asmita Samanta, Arpita Maitra, Goutam Paul

TL;DR

This work advances device-independent quantum random number generation in prepare-and-measure settings by linking CHSH-based self-testing to Tavakoli et al.'s protocol and introducing a novel self-testing approach derived from a multi-party pseudo-telepathy game. It presents two DI-QRNG protocols, P and Q, with rigorous no-signalling-based device-independence proofs and entropy-based randomness guarantees, including a new measurement scheme that yields true randomness from specific qubit bases. The equivalence results unify different self-testing viewpoints (CHSH, Tavakoli, and G) into a single framework, while the PT-derived protocol offers a distinct route to DI-QRNG using only preparation and measurement without entanglement. Practical implications include potential commercial DI-QRNG implementations based on P&M setups, complemented by a comparative analysis against existing SQRNG and MQRNG schemes. The work thus broadens the toolkit for secure, device-independent randomness generation with explicit security guarantees.

Abstract

We present two Device Independent Quantum Random Number Generator (DI-QRNG) protocols using two self-testing methodologies in Preparation \& Measure (P\&M) scenario. These two methodologies are the variants of two well-known non-local games, namely, CHSH and pseudo-telepathy games, in P\&M framework. We exploit them as distinguishers in black-box settings to differentiate the classical and the quantum paradigms and hence to certify the Device Independence. The first self-test was proposed by Tavakoli et al. (Phys. Rev. A, 2018). We show that this is actually a P\&M variant of the CHSH game. Then based on this self-test, we design our first DI-QRNG protocol. We also propose a new self-testing methodology, which is the first of its kind that is reducible from pseudo-telepathy game in P\&M framework. Based on this new self-test, we design our second DI-QRNG protocol.

Provable DI-QRNG protocols based on self-testing methodologies in preparation and measure scenario

TL;DR

This work advances device-independent quantum random number generation in prepare-and-measure settings by linking CHSH-based self-testing to Tavakoli et al.'s protocol and introducing a novel self-testing approach derived from a multi-party pseudo-telepathy game. It presents two DI-QRNG protocols, P and Q, with rigorous no-signalling-based device-independence proofs and entropy-based randomness guarantees, including a new measurement scheme that yields true randomness from specific qubit bases. The equivalence results unify different self-testing viewpoints (CHSH, Tavakoli, and G) into a single framework, while the PT-derived protocol offers a distinct route to DI-QRNG using only preparation and measurement without entanglement. Practical implications include potential commercial DI-QRNG implementations based on P&M setups, complemented by a comparative analysis against existing SQRNG and MQRNG schemes. The work thus broadens the toolkit for secure, device-independent randomness generation with explicit security guarantees.

Abstract

We present two Device Independent Quantum Random Number Generator (DI-QRNG) protocols using two self-testing methodologies in Preparation \& Measure (P\&M) scenario. These two methodologies are the variants of two well-known non-local games, namely, CHSH and pseudo-telepathy games, in P\&M framework. We exploit them as distinguishers in black-box settings to differentiate the classical and the quantum paradigms and hence to certify the Device Independence. The first self-test was proposed by Tavakoli et al. (Phys. Rev. A, 2018). We show that this is actually a P\&M variant of the CHSH game. Then based on this self-test, we design our first DI-QRNG protocol. We also propose a new self-testing methodology, which is the first of its kind that is reducible from pseudo-telepathy game in P\&M framework. Based on this new self-test, we design our second DI-QRNG protocol.
Paper Structure (24 sections, 14 theorems, 23 equations, 1 figure, 12 tables)

This paper contains 24 sections, 14 theorems, 23 equations, 1 figure, 12 tables.

Table of Contents

  1. introduction
  2. Preliminaries
  3. CHSH Game
  4. Classical Strategy
  5. Quantum Strategy
  6. Multi-Party Pseudo-Telepathy Game
  7. Revisiting the protocol by Tavakoli et al. tavakoli
  8. Equivalence of CHSH game to the Self-Testing Protocol by Tavakoli et al. tavakoli
  9. Defining CHSH1 from CHSH Game
  10. An entangled version $\mathcal{G}$ of the self-testing protocol by Tavakoli et al. tavakoli
  11. The Equivalence Proof
  12. Our Device Independent QRNG protocol $\mathcal{P}$ deduced from the protocol by Tavakoli et al. tavakoli
  13. Security Proofs of the QRNG Protocol $\mathcal{P}$
  14. Proof of Device Independence of our protocol $\mathcal{P}$
  15. Proof of Randomness of our protocol $\mathcal{P}$
  16. ...and 9 more sections

Key Result

Theorem 1

The game $\mathcal{G}$ with the winning condition $x_0 = a$ and $x_y =b$ is the entangled version of the self-testing proposed by Tavakoli et al. tavakoli.

Figures (1)

  • Figure 1: Schematic Diagram of the Self-testing Methodology tavakoli

Theorems & Definitions (28)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • Remark 1
  • Lemma 1
  • proof
  • Theorem 3
  • proof
  • ...and 18 more