Stronger steerability criterion for more uncertain continuous variable systems

TL;DR

This paper introduces a new fine-grained uncertainty relation for continuous variable quantum systems, leading to a stronger steering criterion that can detect steerability in N00N states and improve quantum key distribution security bounds.

Contribution

The authors derive a novel fine-grained uncertainty relation for continuous variables and develop a stronger steering criterion that surpasses previous methods in detecting steerability.

Findings

Continuous variable systems exhibit greater uncertainty than discrete ones.

The new steering criterion detects steerability in N00N states previously undetectable.

An improved lower bound on secret key rate for quantum key distribution is established.

Abstract

We derive a fine-grained uncertainty relation for the measurement of two incompatible observables on a single quantum system of continuous variables, and show that continuous variable systems are more uncertain than discrete variable systems. Using the derived fine-grained uncertainty relation, we formulate stronger steering criterion that is able to reveal the steerability of N00N states that has hitherto not been possible using other criteria. We further obtain a monogamy relation for our steering inequality which leads to an, in principle, improved lower bound on the secret key rate of a one-sided device independent quantum key distribution protocol for continuous variables.