Describing the non-classical properties of a complex many-body system (such as entanglement or coherence) is an important part of quantum technologies.

An ideal tool for this task would work well with large systems, be easily computable and easily measurable. Unfortunately, such a tool for every situation does not yet exist.

With this goal in mind a team of researchers from Spain and Poland began work on a special type of quantum state used in quantum computing – graph states.

These states can be visualised as graphs or networks where each vertex represents a qubit, and each edge represents an interaction between pairs of qubits.

The team studied four different shapes of graph states using new mathematical tools they developed. They found that one of these in particular, the Turán graph, could be very useful in quantum metrology.

Their method is (relatively) straightforward and does not require many assumptions. This means that it could be applied to any shape of graph beyond the four studied here.

The results will be useful in various quantum technologies wherever precise knowledge of many-body quantum correlations is necessary.