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New additivity properties in quantum resource theories

Optimization problems involving quantum relative entropies are ubiquitous in quantum information theory. Some prominent examples include the optimization of the fidelity function or the Umegaki relative entropy over a set of states satisfying some specific constraints. In our work, we … Continue reading

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Asymptotic and catalytic matrix majorization

Statistical experiments are a basis of much of classical statistics and its applications such as hypothesis testing: every hypothesis corresponds to a probability distribution over possible observations, and therefore a statistical experiment is simply a family of probability distributions on … Continue reading

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Fundamental limits on quantum cloning from the no-signalling principle

The no-cloning theorem states that within the framework of quantum mechanics, there does not exist any universal procedure that can replicate an unknown quantum state reliably. This fundamental principle was initially formalized in 1982 and later extended in various directions. … Continue reading

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Privacy and correctness trade-offs for information-theoretically secure quantum homomorphic encryption

Homomorphic encryption, which allows a server to compute on encrypted data of a client without first decrypting it, is like a “Swiss army knife” of classical cryptography. Namely, by treating homomorphic encryption as a cryptographic primitive, a broad range of … Continue reading

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Fundamental Limits on Correlated Catalytic State Transformations

Quantum state transformation is a fundamental problem in quantum resource theories. Resource theories offer a general framework to quantify the usefulness of quantum states and their inconvertibility under free operations. A resource theory is defined by a subset of quantum … Continue reading

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Multi-armed quantum bandits

The multi-armed bandit problem is a simple model of decision-making with uncertainty that lies in the class of classical reinforcement learning problems. Given a set of arms, a learner interacts sequentially with these arms sampling a reward at each round … Continue reading

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Quantum advantage with noisy shallow circuits

As larger and larger prototypes of quantum computers are being developed, one of the most exciting challenges in the theory of quantum computing is to find computational problems that can be solved by an noisy intermediate-scale noisy quantum devices, but … Continue reading

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