Quantum‐Memory‐Assisted Entropic Uncertainty Relations

Abstract

Uncertainty relations take a crucial and fundamental part in the frame of quantum theory, and are bringing on many marvelous applications in the emerging field of quantum information sciences. Especially, as entropy is imposed into the uncertainty principle, entropy-based uncertainty relations lead to a number of applications including quantum key distribution, entanglement witness, quantum steering, quantum metrology, and quantum teleportation. Herein, the history of the development of the uncertainty relations is discussed, especially focusing on the recent progress with regard to quantum-memory-assisted entropic uncertainty relations and dynamical characteristics of the measured uncertainty in some explicit physical systems. The aims are to help deepen the understanding of entropic uncertainty relations and prompt further explorations for versatile applications of the relations on achieving practical quantum tasks.

Entropic uncertainty relation in neutrino oscillations

“…However, so far, there have been no observations on entropic uncertainty relations in neutrino systems. Entropic uncertainty relation gives rise to many potential applications in the course of quantum information processing [36], including entanglement witness, quantum randomness, quantum metrology, quantum steering, quantum key distribution, and so on. Exploring the entropic uncertainty relations of neutrino systems may be open an exciting window to utilize neutrinos in the domain of quantum information science.…”

In Praise of Quantum Uncertainty

“…It should be noted that, here, we chose what we believe to be the simplest notion of uncertainty in quantum mechanics and more general theories, i.e., a bound on the product of variances, but other inequalities exist involving the sum of the variances [ 2 , 3 , 4 ] or the entropy (entropic uncertainty relations) [ 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 ].…”

An Optimal Measurement Strategy to Beat the Quantum Uncertainty in Correlated System

“…To compare with the existing result on the entropic uncertainty relation in the presence of quantum memory, relation (3), we transform the CMUR (8) into the entropic form. In practice this is quite straightforward by applying an arbitrary Schur's concave function to ⃗ p(x|x ′ ) ≺ ⃗ s (x) and ⃗ p(y|y ′ ) ≺ ⃗ s (y) .…”

“…The term S(A|B) on the right-hand side of Equation 3is supposed to signify the influence of entanglement on the uncertainty relation, but actually it has no business with the local measurement uncertainties, namely, H(X) or H(Y). In the literature, though a lot of effort has been made, [8,9] Equation 3is still subject to the absence of optimal lower bound in entropic uncertainty relation. [10] Contrary to the variance and entropy, a vectorized measure of uncertainty was introduced in ref.…”