What the complex joint probabilities observed in weak measurements can tell us about quantum physics

TL;DR

This paper explores how complex joint probabilities derived from weak measurements reveal fundamental, state-independent relations between non-commuting quantum properties, offering insights into the universal laws of quantum physics.

Contribution

It demonstrates that complex conditional probabilities from weak measurements encode fundamental, state-independent relations between non-commuting observables in quantum mechanics.

Findings

Complex joint probabilities can predict outcomes of different measurements.

Weak measurements reveal state-independent relations.

These probabilities represent fundamental quantum laws.

Abstract

Quantum mechanics does not permit joint measurements of non-commuting observables. However, it is possible to measure the weak value of a projection operator, followed by the precise measurement of a different property. The results can be interpreted as complex joint probabilities of the two non-commuting measurement outcomes. Significantly, it is possible to predict the outcome of completely different measurements by combining the joint probabilities of the initial state with complex conditional probabilities relating the new measurement to the possible combinations of measurement outcomes used in the characterization of the quantum state. We can therefore conclude that the complex conditional probabilities observed in weak measurements describe fundamental state-independent relations between non-commuting properties that represent the most fundamental form of universal laws in quantum physics.