Transforming quantum operations: quantum supermaps

Abstract

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.

6 pages, 1 figure, published version

References in corpus (12)

• Programmable quantum gate arrays
• Quantum Channels with Memory
• Coding Theorems for Quantum Channels
• Semicausal operations are semilocalizable
• Choi's Proof and Quantum Process Tomography
• A universal programmable quantum state discriminator that is optimal for unambiguously distinguishing between unknown states
• Imprinting a complete information about a quantum channel on its output state
• Quantum multimeters: A programmable state discriminator
• Maximization of capacity and p-norms for some product channels
• Efficient universal programmable quantum measurements
• Approximate programmable quantum processors
• Realization of POVMs using measurement-assisted programmable quantum processors

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