A Diagrammatic Approach to Information Transmission in Generalised Switches

Abstract

The quantum switch is a higher-order operation that takes as an input two quantum processes and combines them in a coherent superposition of two alternative orders. Here we provide an approach to the quantum switch based on the methods of categorical quantum mechanics. Specifically, we represent the quantum switch as a sum of diagrams in the category of finite dimensional Hilbert spaces, or, equivalently, as a sum of diagrams built from Selinger's CPM construction. The sum-of-diagrams picture provides intuition for the activation of classical capacity of completely depolarising channels (CDPCs) and allows for generalisation to N-channel switches. We demonstrate the use of these partially diagrammatic methods by deriving a permutation condition for computing the output of any N-channel switch of CDPCs, we then use that condition to prove that amongst all possible terms, the interference terms associated to cyclic permutations of the N channels are the information-transmitting terms with maximum normalisation

In Proceedings QPL 2020, arXiv:2109.01534

References in corpus (5)

• Transforming quantum operations: quantum supermaps
• Quantum Metrology with Indefinite Causal Order
• Resource theories of communication
• Sending classical information via three noisy channels in superposition of causal orders
• Abstract structure of unitary oracles for quantum algorithms

Cited by in corpus (6)

• Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Quantum Supermaps are Characterized by Locality
• Addressable quantum gates
• Indefinite Time Directed Quantum Metrology
• Multifold behavior of the information transmission by the quantum 3-switch