Seyoon Ragavan - Cloning Games, Black Holes, and Cryptography скачать в хорошем качестве

Seyoon Ragavan - Cloning Games, Black Holes, and Cryptography

Abstract: We revisit the notion of unclonable encryption introduced by Broadbent and Lord (TQC 2020), where a classical message comprising n bits is encrypted into a quantum ciphertext state comprising n qubits. Informally, an adversary should not be able to distribute this ciphertext state between two isolated parties such that both parties can decrypt if the secret key is later revealed to them. Our main contributions are twofold: 1. We propose the first candidate unclonable encryption scheme which is plausibly multi-copy secure: if the adversary receives t identical ciphertext states, they cannot enable t+1 isolated parties to simultaneously decrypt. Previous candidates, based on BB84 states and coset states, are multi-copy insecure for some t = poly(n). Additionally, we provide evidence towards this scheme’s multi-copy security by proving security whenever t is less than n/log n and each of the t+1 parties is permitted one oracle query to the decryption function. In fact, we show that for any constant t, the maximum adversarial winning probability (under the same restrictions) is O(2^{-n}), which is optimal up to constant factors; previous candidates only achieve bounds of O(2^{-0.228n}). This improvement turns out to be crucial for our application to black hole physics, which we describe next. 2. We apply our results to show that, in the idealized model of a black hole which features Haar (pseudo-)random scrambling dynamics, information from infalling qubits can be recovered from either the black hole’s interior state or the external Hawking radiation – but never from both places at the same time. Our construction uses binary phase states, which were previously used in the context of constructing pseudorandom quantum states (Ji, Liu, and Song, CRYPTO 2018). We analyze these states using the new notion of binary subtypes, together with novel bounds on the operator norms of block-wise tensor products of matrices. Joint work with Alexander Poremba (MIT) and Vinod Vaikuntanathan (MIT).