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The Role of piracy in quantum proofs

Anne Broadbent, Alex B. Grilo, Supartha Podder, Jamie Sikora

TL;DR

The study of anti-piracy proof systems is initiated, which are proof systems that inherently prevent piracy attacks and such a proof system for an oracle problem is demonstrated and a candidate anti-piracy proof system for NP is described.

Abstract

A well-known feature of quantum information is that it cannot, in general, be cloned. Recently, a number of quantum-enabled information-processing tasks have demonstrated various forms of uncloneability; among these forms, piracy is an adversarial model that gives maximal power to the adversary, in controlling both a cloning-type attack, as well as the evaluation/verification stage. Here, we initiate the study of anti-piracy proof systems, which are proof systems that inherently prevent piracy attacks. We define anti-piracy proof systems, demonstrate such a proof system for an oracle problem, and also describe a candidate anti-piracy proof system for NP. We also study quantum proof systems that are cloneable and settle the famous QMA vs. QMA(2) debate in this setting. Lastly, we discuss how one can approach the QMA vs. QCMA question, by studying its cloneable variants.

The Role of piracy in quantum proofs

TL;DR

The study of anti-piracy proof systems is initiated, which are proof systems that inherently prevent piracy attacks and such a proof system for an oracle problem is demonstrated and a candidate anti-piracy proof system for NP is described.

Abstract

A well-known feature of quantum information is that it cannot, in general, be cloned. Recently, a number of quantum-enabled information-processing tasks have demonstrated various forms of uncloneability; among these forms, piracy is an adversarial model that gives maximal power to the adversary, in controlling both a cloning-type attack, as well as the evaluation/verification stage. Here, we initiate the study of anti-piracy proof systems, which are proof systems that inherently prevent piracy attacks. We define anti-piracy proof systems, demonstrate such a proof system for an oracle problem, and also describe a candidate anti-piracy proof system for NP. We also study quantum proof systems that are cloneable and settle the famous QMA vs. QMA(2) debate in this setting. Lastly, we discuss how one can approach the QMA vs. QCMA question, by studying its cloneable variants.
Paper Structure (29 sections, 11 theorems, 27 equations, 3 figures)

This paper contains 29 sections, 11 theorems, 27 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Anti-piracy proof systems
  3. Challenges in defining uncloneable proof systems
  4. First attempt at a definition for uncloneable proof systems.
  5. "Cloning a functionality".
  6. "Differing verifications and pirate-verifier collusions".
  7. Our definition: anti-piracy proof systems
  8. Further remarks.
  9. Schemes that achieve the definition
  10. Related work
  11. Uncloneable proofs.
  12. Copy-Protecting information.
  13. Copy-protecting software.
  14. Uncloneable advice.
  15. Cloneable proof systems and their implications
  16. ...and 14 more sections

Key Result

Lemma 2.7

For any $A,B$ satisfying the properties in def:uncloneable_language, let $V^*$ be defined as in fig:honest-verification, and $P^*$ be the such that on input $x = 0^n$, outputs $\lvert\mspace{.5mu} A_n \mspace{.5mu}\rangle$. Then $(V^*, P^*)$ is a non-interactive proof system for $L_{A,B}$.

Figures (3)

  • Figure 1: The $\textsf{QMA}\xspace$ landscape with respect to cloneable proof systems. (Left) Immediate/known containments. (Right) Containments following our work.
  • Figure 2: Admissible verification $V^*$ for $L_{A,B}$
  • Figure 3: Candidate anti-piracy proof system for $\textsf{NP}\xspace$.

Theorems & Definitions (31)

  • Definition 2.1: Admissible verifier and non-interactive proof system
  • Definition 2.2
  • Definition 2.3: Anti-piracy proof for generator $G$
  • Definition 2.4: Anti-piracy proof for promise problem $A$
  • Remark 2.5
  • Definition 2.6
  • Lemma 2.7
  • proof
  • Lemma 2.8
  • proof
  • ...and 21 more