Aby Philip

Device-independent (DI) cryptography represents the highest level of security, enabling cryp- tographic primitives to be executed safely on uncharacterized devices. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite-size security proofs for protocols based on the CHSH game, which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on Rényi entropies, providing a simple method to obtain tighter finite-size key rates.

The notions of privacy tests and k-extendible states have both been instrumental in quantum information theory, particularly in understanding the limits of secure communication. In this paper, we determine the maximum probability with which an arbitrary k-extendible state can pass a privacy test, and we prove that it is equal to the maximum fidelity between an arbitrary k-extendible state and the standard maximally entangled state. Our findings, coupled with the resource theory of k-unextendibility, lead to an efficiently computable upper bound on the one-shot, one-way distillable key of a bipartite state, and we prove that it is equal to the best-known efficiently computable upper bound on the one-shot, one-way distillable entanglement. We also establish efficiently computable upper bounds on the one-shot, forward-assisted private capacity of channels. Extending our formalism to the independent and identically distributed setting, we obtain single-letter efficiently computable bounds on the n-shot, one-way distillable key of a state and the n-shot, forward-assisted private capacity of a channel. For some key examples of interest, our bounds are significantly tighter than other known efficiently computable bounds.

Simulating open quantum systems is essential for modeling realistic dynamics beyond closed-system Hamiltonian evolution. Such dynamics are described by the Lindblad master equation for Markovian systems and arise in fields ranging from condensed matter and quantum chemistry to quantum optics and noise analysis in quantum devices. Existing algorithms typically rely on sparse-access or linear-combination-of-unitaries input models. We propose an alternative framework, Wave Matrix Lindbladization, inspired by density matrix exponentiation for sample-based Hamiltonian simulation. In this model, Hamiltonians and Lindblad operators are encoded directly into program states, enabling sample-based Lindbladian simulation. We present algorithms for this task, analyze their sample and gate complexities, and demonstrate both efficiency and optimality. We also show that our algorithms achieve better sample complexity than any tomographic strategy for Lindbladian simulation. This further suggests a form of quantum copy-protection, where program states allow Lindbladian simulation without revealing the operators they encode.

Device-independent (DI) cryptography represents the highest level of security, enabling cryptographic primitives to be executed safely on untrusted hardware. Moreover, with successful proof-of-concept demonstrations in randomness expansion, randomness amplification, and quantum key distribution, the field is steadily advancing toward commercial viability. Critical to this continued progression is the development of tighter finite-size security proofs. In this work, we provide a simple method to obtain tighter finite size security proofs for protocols based on the CHSH game which is the nonlocality test used in all of the proof-of-concept experiments. We achieve this by analytically solving key-rate optimization problems based on Rényi entropies, providing a simple method to obtain tighter finite-size key rates.