Optimal quantum networks and one-shot entropies

2016/06/30 by Giulio Chiribella, Daniel Ebler · 4 citations
Computer Science · Mathematics · Physics and Astronomy · #Physics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Shot (pellet) #Statistical physics #Theoretical physics #cs.IT #cs.NI #math-ph #math.IT #math.MP #quant-ph

paper · pdf · doi:10.1088/1367-2630/18/9/093053

published as New Journal of Physics 18, 093053 (2016) · 37 + 15 pages, 6 figures, accepted for publication in New Journal of Physics

arxiv created 2016/09/06 · openalex publication_date 2016/09/29 · arxiv updated 2018/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We develop a semidefinite programming method for the optimization of quantum networks, including both causal networks and networks with indefinite causal structure. Our method applies to a broad class of performance measures, defined operationally in terms of interative tests set up by a verifier. We show that the optimal performance is equal to a max relative entropy, which quantifies the informativeness of the test. Building on this result, we extend the notion of conditional min-entropy from quantum states to quantum causal networks. The optimization method is illustrated in a number of applications, including the inversion, charge conjugation, and controlization of an unknown unitary dynamics. In the non-causal setting, we show a proof-of-principle application to the maximization of the winning probability in a non-causal quantum game.

Citations

• Advances in quantum teleportation
• Reformulating and Reconstructing Quantum Theory
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• Quantum Circuit Architecture
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• Probabilistic theories with purification
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• Causal and localizable quantum operations
• Optimal realization of the transposition maps
• Quantifying Entanglement

Cited by

• Symmetries of quantum evolutions
• Time-reversal of rank-one quantum strategy functions
• Quantum Metrology for Non-Markovian Processes
• Units of rotational information