Eric Culf

We show for the first time that uncloneable encryption exists with no computational assumptions, with security inverse-polynomial in the security parameter. We use properties of a monogamy-of-entanglement game associated with the Haar measure encryption to guarantee that any state that succeeds with high probability cannot be close to maximally-entangled between the referee and either of the players, whence we can apply the decoupling principle to show that either player becomes completely uncorrelated, and therefore cannot win significantly better than random guessing.

A non-local quantum computation (NLQC) replaces an interaction between two quantum systems with a single simultaneous round of communication and shared entanglement. We study two classes of NLQC, f-routing and f-BB84. These are well studied in the context of position-verification, where they are leading candidates for feasible and secure verification schemes. Both settings require an honest prover implement only O(1) quantum operations. We prove that a dishonest prover must use linear quantum resources to attack the same scheme. First, we give the first non-trivial lower bounds on entanglement in both settings, but are restricted to lower bounding protocols with perfect correctness. Our bound can be stated in terms of the quantum non-deterministic communication complexity of f. For the equality, non-equality, and greater-than functions we obtain linear lower bounds on entanglement for f-routing and f-BB84 in the perfect setting. In a second result, which applies in the robust setting, we give a new lower bound on the number of quantum gates and measurements needed to attack these verification schemes. We lower bound the gates plus measurements linearly in the simultaneous message passing cost of the function f. This leads to a linear bound against the inner product function. This gives a clear separation between the difficulty of implementing these tasks in the honest and dishonest settings, and does so in a noise robust and loss tolerant setting.

Problems based on the structure of graphs – for example finding cliques, independent sets, or colourings – are of fundamental importance in classical complexity. It is well motivated to consider similar problems about quantum graphs, which are an operator system generalisation of graphs. Defining well-formulated decision problems for quantum graphs faces several technical challenges, and consequently the connections between quantum graphs and complexity have been underexplored. In this work, we introduce and study the clique problem for quantum graphs. Our approach utilizes a well-known connection between quantum graphs and quantum channels. The inputs for our problems are presented as quantum channels induced by circuits, which implicitly determine a corresponding quantum graph. We also use this approach to reimagine the clique and independent set problems for classical graphs, by taking the inputs to be circuits of deterministic or noisy channels which implicitly determine confusability graphs. We show that, by varying the collection of channels in the language, these give rise to complete problems for the classes NP, MA, QMA, and QMA(2). In this way, we exhibit a classical complexity problem whose natural quantisation is QMA(2), rather than QMA, which is commonly assumed. To prove the results in the quantum case, we make use of methods inspired by self-testing. To illustrate the utility of our techniques, we include a new proof of the reduction of QMA(k) to QMA(2) via cliques for quantum graphs. We also study the complexity of a version of the independent set problem for quantum graphs, and provide preliminary evidence that it may be in general weaker in complexity, contrasting to the classical case where the clique and independent set problems are equivalent.

We develop an extension of a recently introduced subspace coset state monogamy-of-entanglement game [Coladangelo, Liu, Liu, and Zhandry; Crypto'21] to general group coset states, which are uniform superpositions over elements of a subgroup to which has been applied a group-theoretic generalization of the quantum one-time pad. We give a general bound on the winning probability of a monogamy game constructed from subgroup coset states that applies to a wide range of finite and infinite groups. To study the infinite-group case, we use and further develop a measure-theoretic formalism that allows us to express continuous-variable measurements as operator-valued generalizations of probability measures. We apply the monogamy game bound to various physically relevant groups, yielding realizations of the game in continuous-variable modes as well as in rotational states of a polyatomic molecule. We obtain explicit strong bounds in the case of specific group-space and subgroup combinations. As an application, we provide the first proof of one sided-device independent security of a squeezed-state continuous-variable quantum key distribution protocol against general coherent attacks.

Much of the strength of quantum cryptography may be attributed to the no-cloning property of quantum information. We construct three new cryptographic primitives whose security is based on uncloneability, and that have in common that their security can be established via a novel monogamy-of-entanglement (MoE) property: -- We define interactive uncloneable encryption, a version of the uncloneable encryption defined by Broadbent and Lord [TQC 2020] where the receiver must partake in an interaction with the sender in order to decrypt the ciphertext. We provide a one-round construction that is secure in the information-theoretic setting, in the sense that no other receiver may learn the message even if she eavesdrops on all the interactions. -- We provide a way to make a bit string commitment scheme uncloneable. The scheme is augmented with a check step chronologically in between the commit and open steps, where an honest sender verifies that the commitment may not be opened by an eavesdropper, even if the receiver is malicious. Our construction preserves the assumptions of the original commitment while requiring only a polynomial decrease in the length of the committed string. -- We construct a receiver-independent quantum key distribution (QKD) scheme, which strengthens the notion of one-sided device independent QKD of Tomamichel, Fehr, Kaniewski, and Wehner (TFKW) [NJP 2013] by also permitting the receiver's classical device to be untrusted. Explicitly, the sender remains fully trusted while only the receiver's communication is trusted. We provide a construction that achieves the same asymptotic error tolerance as the scheme of TFKW. To show security, we prove an extension of the MoE property of coset states introduced by Coladangelo, Liu, Liu, and Zhandry [Crypto 2021]. In our stronger version, the player Charlie also receives Bob's answer prior to making his guess, thus simulating a party who eavesdrops on an interaction. To make use of this property, we express it as a new type of entropic uncertainty relation which arises naturally from the structure of the underlying MoE game.