Multifold behavior of the information transmission by the quantum 3-switch

Abstract

We uncover new behaviors of the transmission of information by three quantum channels in superposition of causal orders subject to some level of noise. We find that the transmission can exhibit three different behaviors as the level of noise is varied. This multifold behavior can be explained by the different equivalence classes of quantum switch matrices related to specific combinations of causal orders. We classify these matrices using their characteristic polynomials and matrix invariants, and we calculate analytical expressions for the Holevo information in three representative cases. Our results are a step forward to understand and harness quantum control of causal orders with different levels of noise. We also study the Holevo information as function of a continuous order parameter and analyse transitions at integer values.

References in corpus (25)

• Quantum computations without definite causal structure
• Experimental Superposition of Orders of Quantum Gates
• Experimental Verification of an Indefinite Causal Order
• Enhanced communication with the assistance of indefinite causal order
• Perfect discrimination of no-signalling channels via quantum superposition of causal structures
• Indefinite Causal Order in a Quantum Switch
• Exponential Communication Complexity Advantage from Quantum Superposition of the Direction of Communication
• Quantum Metrology with Indefinite Causal Order
• Experimental transmission of quantum information using a superposition of causal orders
• Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity
• Quantum Refrigeration with Indefinite Causal Order
• Indefinite causal order enables perfect quantum communication with zero capacity channels
• Quantum Shannon theory with superpositions of trajectories
• Quantum Switch for the Quantum Internet: Noiseless Communications through Noisy Channels
• Experimental Quantum Communication Enhancement by Superposing Trajectories
• Communication through coherent control of quantum channels
• Communicating via ignorance: Increasing communication capacity via superposition of order
• Computational advantage from quantum superposition of multiple temporal orders of photonic gates
• Communication Enhancement Through Quantum Coherent Control of $N$ Channels in an Indefinite Causal-order Scenario
• Sending classical information via three noisy channels in superposition of causal orders
• Channel capacity enhancement with indefinite causal order
• Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
• Classical Communications with Indefinite Causal Order for $N$ completely depolarizing channels
• Classical communication through quantum causal structures
• A Diagrammatic Approach to Information Transmission in Generalised Switches

Cited by in corpus (2)

• Practical computational advantage from the quantum switch on a generalized family of promise problems
• Parameter estimation via indefinite causal structures