A Holevo-Type Bound for a Hilbert Schmidt Distance Measure

We prove a new version of the Holevo bound employing the Hilbert-Schmidt norm instead of the Kullback-Leibler divergence. Suppose Alice is sending classical information to Bob by using a quantum channel while Bob is performing some projective measurements. We bound the classical mutual information in terms of the Hilbert-Schmidt norm by its quantum Hilbert-Schmidt counterpart. This constitutes a Holevo-type upper bound on the classical information transmission rate via a quantum channel. The resulting inequality is rather natural and intuitive relating classical and quantum expressions using the same measure.

Weak measurements and quantum-to-classical transitions in free electron-photon interactions

How does the quantum-to-classical transition of measurement occur?This question is vital for both foundations and applications of quantum mechanics.Here,we develop a new measurement-based framework for characterizing the classical and quantum free electron-photon interactions and then experimentally test it.We first analyze the transition from projective to weak measurement in generic light-matter interactions and show that any classical electron-laserbeam interaction can be represented as an outcome of weak measurement.In particular,the appearance of classical point-particle acceleration is an example of an amplified weak value resulting from weak measurement.A universal factor,exp(-Γ^(2)=2),quantifies the measurement regimes and their transition from quantum to classical,whereΓcorresponds to the ratio between the electron wavepacket size and the optical wavelength.This measurement-based formulation is experimentally verified in both limits of photon-induced near-field electron microscopy and the classical acceleration regime using a DLA.Our results shed new light on the transition from quantum to classical electrodynamics,enabling us to employ the essence of the wave-particle duality of both light and electrons in quantum measurement for exploring and applying many quantum and classical light-matter interactions.

Ano malous weak values via a single phot on detection

Is it possible that a measurement of a spin component of a spin-1/2 particle yields the value 100?In 1988 Aharonov,Albert and Vaidman argued that upon pre-and postselection of particular spin states,weakening the coupling of a standard measurement procedure ensures this paradoxical result1.This theoretical prediction,called weak value,was realised in numerous experiments2-9,but its meaning remains very controversialsince its"anomalous"nature,i.e.z the possibility to exceed the eigenvalue spectrum,as well as its"quantumness"are debated20-22.We address these questions by presenting the first experiment measuring anomalous weak values with just a single click,without the need for statistical averaging.The measurement uncertainty is significantly smaller than the gap between the measured weak value and the nearest eigenvalue.Beyond clarifying the meaning of weak values,demonstrating their non-statistical,single-particle nature,this result represents a breakthrough in understanding the foundations of quantum measurement,showing unprecedented measurement capability for further applications of weak values to quantum photonics.