A monogamy-of-entanglement game for subspace coset states

TL;DR

This paper proves a strong monogamy-of-entanglement property for subspace coset states, confirming a recent conjecture and enabling applications in quantum cryptography such as unclonable encryption and pseudorandom function copy-protection.

Contribution

It provides two proofs of the monogamy property, one following the original approach and another simplifying the analysis using BB'84 states, confirming a recent conjecture.

Findings

Established a strong monogamy-of-entanglement property for subspace coset states.

Presented two different proofs, one direct and one simplified using BB'84 states.

Confirmed the conjecture by Coladangelo et al. and enabled cryptographic applications.

Abstract

We establish a strong monogamy-of-entanglement property for subspace coset states, which are uniform superpositions of vectors in a linear subspace of $\mathbb{F}_2^n$ to which has been applied a quantum one-time pad. This property was conjectured recently by [Coladangelo, Liu, Liu, and Zhandry, Crypto'21] and shown to have applications to unclonable decryption and copy-protection of pseudorandom functions. We present two proofs, one which directly follows the method of the original paper and the other which uses an observation from [Vidick and Zhang, Eurocrypt'20] to reduce the analysis to a simpler monogamy game based on BB'84 states. Both proofs ultimately rely on the same proof technique, introduced in [Tomamichel, Fehr, Kaniewski and Wehner, New Journal of Physics '13].