Process-optimized phase covariant quantum cloning

Abstract

After the appearance of the no-cloning theorem, approximate quantum cloning machines (QCMs) have become one of the most well-studied subject in quantum information theory. Among several measures to quantify the performance of a QCM, single-qudit fidelity and global fidelity have been most widely used. In this paper we compute the optimal global fidelity for phase-covariant cloning machines via semi-definite programming optimization, thereby completing a remaining gap in the previous results on QCMs. We also consider optimal simulations of the cloning and transpose cloning map, both by a direct optimization and by a composition of component-wise optimal QCMs. For the cloning map the composition method is sub-optimal whereas for the transpose cloning map the method is asymptotically optimal.

References in corpus (26)

• Quantum Copying: Beyond the No-Cloning Theorem
• Reference frames, superselection rules, and quantum information
• Optimal Quantum Cloning Machines
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Entanglement Measures under Symmetry
• Phase covariant quantum cloning
• Spin flips and quantum information for anti-parallel spins
• Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks
• Separability properties of tripartite states with UxUxU-symmetry
• Phase-covariant quantum cloning of qudits
• Optimal phase covariant cloning for qubits and qutrits
• Optimal Non-Universally Covariant Cloning
• Economical Phase-Covariant Cloning of Qudits
• Optimizing Completely Positive Maps using Semidefinite Programming
• Optimal probabilistic cloning and purification of quantum states
• Optimal Eavesdropping in Quantum Cryptography. I
• Quantum Cloning Machines of a d-level System
• Cloning a Qutrit
• On the Phase Covariant Quantum Cloning
• Optimal Eavesdropping in Quantum Cryptography. II. Quantum Circuit
• Optimal realization of the transposition maps
• Economical realization of phase covariant devices in arbitrary dimensions
• Separability properties of tripartite states with UxUxU-symmetry
• Process optimized quantum cloners via semidefinite programming