2011/12/16 by Alessandro Bisio, Giacomo Mauro D’Ariano, Giacomo Mauro D'Ariano +3
Computer Science · Mathematics · Physics and Astronomy · #Computer science #Covariant transformation #Dimension (graph theory) #Mathematics #Physics #Protocol (science) #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum cloning #Quantum computer #Quantum error correction #Quantum mechanics #Quantum memory #Quantum network #Qubit #Transformation (genetics) #Unitary state #Unitary transformation #Value (mathematics) #quant-ph
paper · pdf · doi:10.1103/physreva.85.032333
published as Phys. Rev. A 85, 032333 (2012) · 9 pages
arxiv created 2011/12/16 · openalex publication_date 2012/03/30 · arxiv updated 2012/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the problem of minimizing the ancillary systems required to realize an arbitrary strategy of a quantum protocol, with the assistance of classical memory. For this purpose we introduce the notion of memory cost of a strategy to measure the resources required in terms of ancillary dimension. We provide a condition for the cost to be equal to a given value, and we use this result to evaluate the cost in some special cases. As an example, we show that any covariant protocol for the cloning of a unitary transformation requires at most one ancillary qubit. We also prove that the memory cost has to be determined globally and cannot be calculated by optimizing the resources independently at each step of the strategy.