I recently found out about shadowgraphy and was wondering if a technique like this could be used to:

• Visually show entanglement
• Suffice as a measure (e.g. continous partial trace)
• Most useful applications

Resources

There is an analogue to shadowgraphy which shows up in quantum information, which is the phase-space representation of quantum states via the Wigner function.

The Wigner function W(q,p) is a phase-space representation of quantum states of a single particle, which gives the quantum mechanical probability distributions for position measurements, momentum measurements, and in general for any quadrature observable (i.e. linear combinations of position and momentum). For a general introduction, check this link:

https://en.wikipedia.org/wiki/Wigner_quasiprobability_distribution

These marginal distributions can be interpreted as a shadow of the quantum state along a direction specified by which quadrature is measured. Interestingly, there are quantum states for which the Wigner function may be negative in some phase-space regions! This is an indication of non-classicality, as the multiple "shadows" fail to make sense together: each shadow is a sensible probability distribution, but the "object" that casts the shadows is a phase-space distribution without direct interpretation in terms of probabilities (as it can be negative in some regions).

At least for some definitions of discrete Wigner functions (useful for describing states in finite-dimensional Hilbert spaces), this negativity has been linked to contextuality and advantage in quantum computation, as pointed out for example in these papers:

https://arxiv.org/abs/1201.1256

https://arxiv.org/abs/0710.5549