2011/08/31 by Hamed Saberi
Computer Science · Mathematics · Physics and Astronomy · #Algebra over a field #Algorithm #Computer science #Fidelity #Formalism (music) #Hilbert space #Impossibility #Mathematics #Operator (biology) #Physics #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum entanglement #Quantum many-body systems #Quantum mechanics #Qubit #Unitary operator #Unitary state #cond-mat.mes-hall #cond-mat.str-el #quant-ph
paper · pdf · doi:10.1103/physreva.84.032323
published as Phys. Rev. A 84, 032323 (2011) · Slightly improved version as published in Phys. Rev. A
openalex publication_date 2011/09/16 · arxiv created 2012/01/06 · arxiv updated 2015/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the recently proposed ``no-go'' theorem of Lamata et al. [Phys. Rev. Lett. 101, 180506 (2008)] on the impossibility of sequential implementation of global unitary operations with the aid of an itinerant ancillary system and view the claim within the language of Kraus representation. By virtue of an extremely useful tool for analyzing entanglement properties of quantum operations, namely, operator-Schmidt decomposition, we provide alternative proof to the no-go theorem and also study the role of initial correlations between the qubits and ancilla in sequential preparation of unitary entanglers. Despite the negative response from the no-go theorem, we demonstrate explicitly how the matrix-product operator (MPO) formalism provides a flexible structure to develop protocols for sequential implementation of such entanglers with an optimal fidelity. The proposed numerical technique, which we call variational matrix-product operator (VMPO), offers a computationally efficient tool for characterizing the ``globalness'' and entangling capabilities of nonlocal unitary operations.