Quantum inputs in the prepare-and-measure scenario and stochastic teleportation

Abstract

We investigate prepare-and-measure scenarios in which a sender and a receiver use entanglement to send quantum information over a channel with limited capacity. We formalise this framework, identify its basic properties and provide numerical tools for optimising quantum protocols for generic communication tasks. The seminal protocol for sending quantum information over a classical channel is teleportation. We study a natural stochastic generalisation in which the sender holds $N$ qubits from which the receiver can recover one on demand. We show that with two bits of communication alone, this task can be solved exactly for all $N$, if the sender and receiver have access to stronger-than-quantum nonlocality. We then consider entanglement-based protocols and show that these can be constructed systematically by leveraging connections to several well-known quantum information primitives, such as teleportation, cloning machines and random access coding. In particular, we show that by using genuine multi-particle entangled measurements, one can construct a universal stochastic teleportation machine, i.e.~a device whose teleportation fidelity is independent of the quantum input.

References in corpus (15)

• Dimension witnesses and quantum state discrimination
• Quantum Random Access Codes using Single $d$-level Systems
• Semidefinite Programming in Quantum Information Science
• Semidefinite programming relaxations for quantum correlations
• Entanglement-assisted quantum communication with simple measurements
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Entanglement in prepare-and-measure scenarios: many questions, a few answers
• Scalable entanglement certification via quantum communication
• Quantum stochastic communication via high-dimensional entanglement
• Correspondence between entangled states and entangled bases under local transformations
• Interplays between classical and quantum entanglement-assisted communication scenarios
• Simple and general bounds on quantum random access codes
• Absolute dimensionality of quantum ensembles
• Compression of Entanglement Improves Quantum Communication
• Two instances of random access code in the quantum regime