In this work, we consider "decision" variants of a well-known monogamy-of-entanglement game by Tomamichel, Fehr, Kaniewski, and Wehner [New Journal of Physics '13]. In its original "search" variant, Alice prepares a (possibly entangled) state on registers ABC; register 𝖠, consisting of n qubits, is sent to a Referee, while 𝖡 and 𝖢 are sent to Bob and Charlie; the Referee then measures each qubit in the standard or Hadamard basis (chosen uniformly at random). The basis choices are sent to Bob and Charlie, whose goal is to simultaneously guess the Referee’s n-bit measurement outcome string x. Tomamichel et al. show that the optimal winning probability is cos^{2n}(π/8), following a perfect parallel repetition theorem. We consider the following "decision" variants of this game: - Variant 1, "XOR repetition": Bob and Charlie’s goal is to guess the XOR of all the bits of x. Ananth et al. [Asiacrypt '24] conjectured that the optimal advantage over random guessing decays exponentially in n. Surprisingly, we show that this conjecture is false, and, in fact, there is no decay at all: there exists a strategy that wins with probability cos²(π/8) ≈ 0.85 for any n. Moreover, this strategy does not involve any entanglement between Alice, Bob, and Charlie! - Variant 2, "Goldreich-Levin": The Referee additionally samples a uniformly random n-bit string r that is sent to Bob and Charlie along with the basis choices. Their goal is to guess the parity of r⋅ x. We show that the optimal advantage over random guessing decays exponentially in n for the restricted class of adversaries that do not share entanglement. A similar result was already shown by Champion et al. and Çakan et al.; we give a more direct proof. Showing that Variant 2 is "secure" (i.e., that the optimal winning probability is exponentially close to 1/2) against general adversaries would imply the existence of an information-theoretically "unclonable bit". We put forward a reasonably concrete conjecture that is equivalent to the general security of Variant 2.

We give a meta-complexity characterization of EFI pairs, which are considered the “minimal” primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy.

A central task in quantum information science is state certification: testing whether an unknown state is є1-close to a fixed target state, or є2-far. Recent work has shown that surprisingly simple measurement protocols – comprising only single-qubit measurements – suffice to certify arbitrary n-qubit states. However, these certification protocols are not robust: rather than allowing constant є1, they can only positively certify states within є1=O(1/n) trace distance of the target. In many experimental settings, the appropriate error tolerance is constant as the system size grows, so this lack of robustness renders existing tests inapplicable at scale, no matter how many times the test is repeated.

Bell non-locality is a fundamental feature of quantum mechanics whereby measurements performed on “spatially separated” quantum systems can exhibit correlations that cannot be understood as revealing predetermined values. This is a special case of the more general phenomenon of “quantum contextuality”, which says that such correlations can occur even when the measurements are not necessarily on separate quantum systems, but are merely “compatible” (i.e. commuting). Crucially, while any non-local game yields an experiment that demonstrates quantum advantage by leveraging the “spatial separation” of two or more devices (and in fact several such demonstrations have been conducted successfully in recent years), the same is not true for quantum contextuality: finding the contextuality analogue of such an experiment is arguably one of the central open questions in the foundations of quantum mechanics. In this work, we show that an arbitrary contextuality game can be compiled into an “operational test of contextuality” involving a single quantum device, by only making the assumption that the device is computationally bounded. Our work is inspired by the recent work of Kalai et al. (STOC '23) that converts any non-local game into a classical test of quantum advantage with a single device. The central idea in their work is to use cryptography to enforce spatial separation within subsystems of a single quantum device. Our work can be seen as using cryptography to enforce “temporal separation”, i.e. to restrict communication between sequential measurements. Beyond contextuality, we employ our ideas to design a “proof of quantumness” that, to the best of our knowledge, is arguably even simpler than the ones proposed in the literature so far.

Quantum copy protection, introduced by Aaronson, enables giving out a quantum program-description that cannot be meaningfully duplicated. Despite over a decade of study, copy protection is only known to be possible for a very limited class of programs. As our first contribution, we show how to achieve "best-possible" copy protection for all programs. We do this by introducing quantum state indistinguishability obfuscation (qsiO), a notion of obfuscation for quantum descriptions of classical programs. We show that applying qsiO to a program immediately achieves best-possible copy protection. Our second contribution is to show that, assuming injective one-way functions exist, qsiO is concrete copy protection for a large family of puncturable programs --- significantly expanding the class of copy-protectable programs. A key tool in our proof is a new variant of unclonable encryption (UE) that we call coupled unclonable encryption (cUE). While constructing UE in the standard model remains an important open problem, we are able to build cUE from one-way functions. If we additionally assume the existence of UE, then we can further expand the class of puncturable programs for which qsiO is copy protection. Finally, we construct qsiO relative to an efficient quantum oracle.

We give a comprehensive characterisation of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle:

(Sender-)Deniable encryption provides a very strong privacy guarantee: a sender who is coerced by an attacker into “opening” their ciphertext after-the-fact is able to generate “fake” local random choices that are consistent with any plaintext of their choice. The only known fully-efficient constructions of public-key deniable encryption rely on indistinguishability obfuscation (iO) (which currently can only be based on sub-exponential hardness assumptions).