Quantum technologies often imagine distant users – Alice and Bob – sharing entangled particles and trying to learn something about them. In principle, the most powerful measurements are global: Alice and Bob act as if their systems were in the same lab. In reality, they are usually limited to local operations and classical communication (LOCC). This means that each makes measurements locally and sends classical messages back and forth. A long standing debate is how much classical communication is actually required to perform a given quantum task.
In a recent article, Arthur Dutra and colleagues, tackled this question by analysing quantum measurements that use just one round of classical communication. Rather than treating LOCC as an all or nothing option, the team asked more precise questions. Who should measure first? How many classical bits are needed? Does Bob really need to adapt his measurement based on Alice’s message?
Their key contribution is a new mathematical framework that turns these questions into efficiently solvable optimisation problems. Using a hierarchy of semidefinite programmes (a standard tool in quantum information theory) the authors placed tight upper bounds on what one round LOCC measurements can achieve, even when the size and direction of the classical message are fixed.
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