Beyond the Quantum Switch: Quantum Circuits with Quantum Control of Causal Order

Zapraszamy w środę 03.03.2021 o godz. 14:00 na seminarium.

Seminarium ONLINE pod tytułem: "Beyond the Quantum Switch: Quantum Circuits with Quantum Control of Causal Order" poprowadzi Hippolyte Lazourenko-Dourdent  (Institut Néel / Université Grenoble Alpes)

Abstract: While the standard formulation of quantum theory relies on a fixed background causal structure, one can consider a more general framework - based on quantum theory - where the causal structure is indefinite (the "process matrix formalism"). Interestingly, the tools introduced to identify causal indefiniteness - causal non-separability and causal inequalities - have been developed by analogy with quantum entanglement and Bell inequalities. An explicit example of a physical process with indefinite causal structure is the so-called 'quantum switch'.

In this work, we take a bottom-up approach. We identify two new types of circuits that naturally generalise the fixed-order case which we fully characterise. We first introduce “quantum circuits with classical control of causal order ”, in which the order of operations is still well-defined, but not necessarily fixed in advance: it can in particular be established dynamically, in a classically-controlled manner, as the circuit is being used. We then consider “ quantum circuits with quantum control of causal order ”, in which the order of operations is controlled coherently. The latter encompasses all known examples of physically realisable processes with indefinite causal order, including the celebrated quantum switch. Interestingly, it also contains new examples arising from the combination of dynamical and coherent control of causal order, and we detail explicitly one such process. Nevertheless, we show that quantum circuits with quantum control of causal order can only generate “causal” correlations, compatible with a well-defined causal order. We furthermore extend our considerations to probabilistic circuits that produce also classical outcomes, and we demonstrate by an example how the characterisations derived in this work allow us to identify new advantages for quantum information processing tasks that could be demonstrated in practice.