• Publications
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The uncertainty principle in the presence of quantum memory
The Heisenberg uncertainty principle bounds the uncertainties about the outcomes of two incompatible measurements on a quantum particle. This bound, however, changes if a memory device is involved
Entropic uncertainty relations and their applications
This review surveys entropic uncertainty relations that capture Heisenberg’s idea that the results of incompatible measurements are impossible to predict, covering both finite- and infinite-dimensional measurements.
Advances in Quantum Cryptography
This review begins by reviewing protocols of quantum key distribution based on discrete variable systems, and considers aspects of device independence, satellite challenges, and high rate protocols based on continuous variable systems.
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory
A new proof of the Quantum Reverse Shannon Theorem is provided, which has been proved by Bennett, Devetak, Harrow, Shor, and Winter and is based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.
One-Shot Decoupling
If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under
Smooth Entropy Bounds on One-Shot Quantum State Redistribution
A strong converse for quantum state redistribution is obtained, which even holds when allowing for feedback, and an alternative proof of optimality of these rates for quantumstate redistribution in the i.i.d. asymptotic limit is obtained.
Converse Bounds for Private Communication Over Quantum Channels
This paper establishes several converse bounds on the private transmission capabilities of a quantum channel by using the notion of a private state along with a “privacy test” to establish a general meta-converse bound for private communication, which has a number of applications.
Single-shot Quantum State Merging
  • M. Berta
  • Computer Science
  • 22 December 2009
It is shown that the minimal amount of quantum communication needed to achieve this single-shot state merging is given by minus the smooth conditional min-entropy of Alice conditioned on the environment, which gives an operational meaning to the smooth conditionality of Alice.
Rényi Divergences as Weighted Non-commutative Vector-Valued $$L_p$$Lp-Spaces
A Riesz–Thorin theorem for Araki-Masuda’s weighted non-commutative vector-valued Lp-spaces is derived and an Araki–Lieb–Thirring inequality for states on von Neumann algebras is derived.
Multivariate Trace Inequalities
Several trace inequalities that extend the Golden–Thompson and the Araki–Lieb–Thirring inequality to arbitrarily many matrices are proved, and the first explicit remainder terms that are tight in the commutative case are found.