Theoretical framework for quantum networks
By Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti. 2009
525 citations recorded by the source corpus.
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such as, e.g., cloning, discrimination, estimation, and tomography. Our framework is based on the concepts of quantum comb---which describes all transformations achievable by a given quantum network---and link product---the operation of connecting two quantum networks. Quantum networks are treated both from a constructive point of view---based on connections of elementary circuits---and from an axiomatic one---based on a hierarchy of admissible quantum maps. In the axiomatic context a fundamental property is shown, which we call universality of quantum memory channels: any admissible transformation of quantum networks can be realized by a suitable sequence of memory channels. The open problem whether this property fails for some nonquantum theory, e.g., for no-signaling boxes, is posed.
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/19bce49b95345dc58608b514656451d0a92d7680
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In Artificial Intelligence
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- Guillaume Verdon
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In Atomic and Molecular Physics, and Optics
- Neill Lambert
- Lukasz Cincio
- M. Cerezo
- Patrick J. Coles
- Clive Emary
- Guillaume Verdon
- Lucien Hardy
- Hsin-Yuan Huang
Citations in the corpus
- Reformulating and Reconstructing Quantum Theory (2011, methodology): “We will now translate the equations of CDP into the notation of the present paper.”
- Leggett–Garg inequalities (2013, background): “Central to this is the Choi–Jamiołkowski isomorphism [99, 100] between the space of bipartite systems ρAB ∈ HA ⊗ HB and the set of evolutions from HA to HB .”
- Challenges and opportunities in quantum machine learning (2022, background): “Here, the states contain information obtained from some physical process such as quantum sensing [15], quantum metrology [16], quantum networks [17], quantum control [18], or even quantum analog-digital transduction [19].”