The Uncertainty Principle in the Presence of Quantum Memory

TL;DR

This paper extends the uncertainty principle to account for entanglement with quantum memory, providing bounds on measurement uncertainties that depend on entanglement, with implications for entanglement detection and quantum cryptography.

Contribution

It introduces a strengthened uncertainty relation that incorporates quantum memory, linking measurement uncertainties to entanglement levels, advancing quantum information theory.

Findings

Derived a new lower bound on uncertainties with quantum memory

Applied the relation to entanglement witnessing

Demonstrated implications for quantum key distribution

Abstract

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device which is likely to soon be available, it is possible to predict the outcomes for both measurement choices precisely. In this work we strengthen the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.