Happy to have provided my first contribution to @PRX_Quantum ! https://twitter.com/PRX_Quantum/status/1319386057847283715

Alright, let me tell you a little story about this result. In my opinion it has some cool consequences that you might find interesting. 1/n

At @mqo_lkb, we do continuous variable quantum optics, which means that we measure the phase and amplitude of the electric field of light (the quadratures to be exact). Mathematically, these quantities behave in exactly the same way as position and momentum in mechanics 2/n

When we measure the amplitude quadrature (let's call it X), we will always get some normal histogram of outcomes. When we measure the phase quadrature (P), yet another histogram appears. So far, everything seems normal, right? 3/n

Now let us see what happens when we try to combine these measurements. What is the chance of measuring a certain value for X and P at the same time? Well, if we want to respect quantum physics, we can obtain the answer trought the Wigner Function. 4/n
https://en.m.wikipedia.org/wiki/Wigner_quasiprobability_distribution

The Wigner function is a funky little function that behaves as a joint probability distribution for X and P: it reproduces the correct histograms for measurements. But you may have heard that jointly measuring X and P is not possible in quantum physics. What's the catch? 5/n

Well, the Wigner function is not actually a probability distribution. It can reach negative values for certain quantum states. This "Wigner negativity" is where the quantum magic lies. For example you need this negativity as fuel for a continuous variable quantum computer. 6/n

Why is this negativity so important? A simple way of understanding this is that fully positive Wigner functions *are* probability distributions. This means that they can be used as a hidden variable model! Want to do funky quantum stuff with X and P? Better have negativity! 7/n

Alright, what's our work about? Well it's about how to create quantum states with Wigner negativity. Very often, people do this by starting out from Gaussian states: states whose Wigner function is... a Gaussian, and thus positive. 8/n

You should produce a big Gaussian state, over several degrees of freedom which are entangled (so we'll have X1 and X2, P1 and P2). You will measure part of the entangled, and use the measurement result to project the rest of the system in a new state with Wigner negativity. 9/n

Sounds pretty simple, no? Well, we developed theory to describe exactly what that new state's Wigner function will look like, regardless of the measurement you perform. Given some entanglement, can you always find a measurement that gives you a Wigner negativity? 10/n

The answer is no! We prove that your Gaussian state needs more than just entanglement, it needs EPR steering . This means that Wigner negativity is hard to get.

Enough for now. Later today I'll continue by explaining you why this is important. 11/n

https://en.m.wikipedia.org/wiki/Quantum_steering