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arXiv:1504.00233 · SpringerBriefs in mathematical physics

Quantum Information Processing with Finite Resources

Marco Tomamichel

Published Oct 8, 2015• 326 citations
arXivHTMLPDF
DOI
10.1007/978-3-319-21891-5

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Many quantum information processing tasks require the consumption of various types of informational resource. Entanglement is a well-studied example of this type of resource; frameness is another. Both types of resource may be quantified through the use of realvalued functions known as monotones, a collection of which can fully characterize the resourcefulness of a state. A complete characterization of the entanglement or frameness of even a finite-dimensional quantum state might require an infinite collection of monotones, despite finiteness of the descriptions of the states in question. We propose a new framework of relative monotones. A relative monotone quantifies the resourcefulness of a quantum state relative to another quantum state. We give an example of the efficacy of relative monotones by characterizing a simple type of frameness with a single relative monotone. This type of frameness is unlikely to yield to analysis with 'absolute' monotones.
Abstract The processing of quantum information always has a cost in terms of physical resources such as energy or time. Determining the resource requirements is not only an indispensable step in the design of practical devices—the resources need to be actually provided—but may also yield fundamental constraints on the class of processes that are physically possible. Here we study how much energy is required to implement a desired unitary gate on a quantum system with a non-trivial energy spectrum. We derive a general lower bound on the energy requirement, extending the main result of Chiribella et al (2021 Phys. Rev. X 11 021014) from finite dimensional systems to systems with unbounded Hamiltonians. Such an extension has immediate applications in quantum information processing with optical systems, and allows us to provide bounds on the energy requirement of continuous variable quantum gates, such as displacement and squeezing gates.