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On Variational Expressions for Quantum Relative Entropies
Mario Berta, Omar Fawzi, Marco Tomamichel
Distance measures between quantum states like the trace distance and the fidelity can naturally be defined by optimizing a classical distance measure over all measurement statistic…
Entropic Uncertainty Relations and their Applications
Patrick J. Coles, Mario Berta, Marco Tomamichel +1
Heisenberg's uncertainty principle forms a fundamental element of quantum mechanics. Uncertainty relations in terms of entropies were initially proposed to deal with conceptual sho…
Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
David Sutter, Marco Tomamichel, Aram W. Harrow
The quantum relative entropy between two states satisfies a monotonicity property meaning that applying the same quantum channel to both states can never increase their relative en…
A largely self-contained and complete security proof for quantum key distribution
Marco Tomamichel, Anthony Leverrier
In this work we present a security analysis for quantum key distribution, establishing a rigorous tradeoff between various protocol and security parameters for a class of entanglem…
Quantum Coding with Finite Resources
Marco Tomamichel, Mario Berta, Joseph M. Renes
The quantum capacity of a memoryless channel is often used as a single figure of merit to characterize its ability to transmit quantum information coherently. The capacity determin…
Quantum Information Processing with Finite Resources -- Mathematical Foundations
Marco Tomamichel
One of the predominant challenges when engineering future quantum information processors is that large quantum systems are notoriously hard to maintain and control accurately. It i…