Quantum sampling and entropic uncertainty

Keegan Yao, Walter O. Krawec, Jiadong Zhu

It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. Along the way, we prove several interesting results in the asymptotic case for our entropic uncertainty relations. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems, and the approaches we use here may be applicable to an even wider range of scenarios.

R. Blankenbecler, M. Hossein Partovi

Keegan Yao, Walter O. Krawec, Jiadong Zhu

It has been shown recently that the framework of quantum sampling, as introduced by Bouman and Fehr, can lead to new entropic uncertainty relations highly applicable to finite-key cryptographic analyses. Here we revisit these so-called sampling-based entropic uncertainty relations, deriving newer, more powerful, relations and applying them to source-independent quantum random number generators and high-dimensional quantum key distribution protocols. Along the way, we prove several interesting results in the asymptotic case for our entropic uncertainty relations. These sampling-based approaches to entropic uncertainty, and their application to quantum cryptography, hold great potential for deriving proofs of security for quantum cryptographic systems, and the approaches we use here may be applicable to an even wider range of scenarios.

David Puertas‐Centeno

H. S. Karthik, A. R. Usha Devi, J. Prabhu Tej +1 more

Vladimír Bužek, Christoph H. Keitel, P. L. Knight

We present an entropic description of quantum-mechanical states based on an operational approach to a phase-space measurement. We give a simple phase-space interpretation of sampling entropies in terms of which we derive very general entropic uncertainty relations reflecting the degree of the phase-space uncertainty of the quantum-mechanical state in the given measurement (i.e., for a given ``quantum-ruler'' state). We relate the sampling entropy to the von Neumann and Shannon entropy and show that the Wehrl entropy represents a particular example of a sampling entropy when the quantum ruler is represented by coherent states.