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Moment matrices are a powerful way of turning difficult questions in quantum information into tractable optimisation problems, but building them correctly can be surprisingly complicated: many entries are actually the same because the underlying quantum operators obey mathematical relations such as commutation, orthogonality, and idempotency.

MoMPy is an open-source Python package that automates this bookkeeping. You declare the operators and their relations, choose the products you want to include, and MoMPy constructs the corresponding moment matrix, automatically identifying equivalent terms and producing the variables needed for a semidefinite-programming relaxation. Read here a tutorial introducing the package. You can find all codes here.

When two objects interact, some of their physical properties can become correlated, establishing an invisible connection between them. If one of these properties is measured in one object, the corresponding property in the other becomes instantaneously affected, even if they are at opposite ends of the universe. This mysterious connection, commonly known as entanglement, is a fascinating phenomenon discovered over a century ago and still defying our notions of reality. Entanglement is also an extremely useful resource in quantum information, and can appear in various forms. Certain states (known as “bound entangled states”) exhibit a form of entanglement which is restricted, i.e., cannot be strengthened operating individually in both objects. Bound entangled states have for long been deemed useless in communication tasks. Here we show that this is no longer true, proving a significant communication advantage when bound entangled states are employed.

Read more here about how bound entanglement can be useful to boost communication, and here about how this usefulness can become an unbounded advantage.

Random numbers are essential for modern security, but trusting a random-number generator is harder than it sounds: how do we know its outputs are genuinely unpredictable, rather than secretly known to an hypothetical adversary? One powerful answer comes from quantum physics, where measurement outcomes can be certified as random even when the devices’ inner workings are only partly known.

Here we ask whether quantum devices can certify more randomness than any comparable “classical” device. Here, classical does not simply mean old-fashioned; it means noncontextual, when measurement outcomes may be explainable by revealing pre-existing values. The comparison is more subtle than a simple “quantum always wins”. If the hypothetical adversary is restricted to the same noncontextual classical rules, then classical-looking models can sometimes certify as much, or even more, randomness . But when the adversary is allowed the full power of quantum physics, quantum devices recover the advantage, although noncontextual statistics can still generate genuine randomness.