Extremal quantum cloning machines

Abstract

We investigate the problem of cloning a set of states that is invariant under the action of an irreducible group representation. We then characterize the cloners that are "extremal" in the convex set of group covariant cloning machines, among which one can restrict the search for optimal cloners. For a set of states that is invariant under the discrete Weyl-Heisenberg group, we show that all extremal cloners can be unitarily realized using the so-called "double-Bell states", whence providing a general proof of the popular ansatz used in the literature for finding optimal cloners in a variety of settings. Our result can also be generalized to continuous-variable optimal cloning in infinite dimensions, where the covariance group is the customary Weyl-Heisenberg group of displacements.

revised version accepted for publication

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Cited by in corpus (8)

• Quantum Cloning Machines and the Applications
• Symmetries in Quantum Key Distribution and the Connection between Optimal Attacks and Optimal Cloning
• Quantum and Classical Data Transmission through Completely Depolarising Channels in a Superposition of Cyclic Orders
• Quantum replication at the Heisenberg limit
• Optimal cloning of qubits given by arbitrary axisymmetric distribution on Bloch sphere
• Agents, subsystems, and the conservation of information
• Fundamental quantum limits for practical devices
• State-dependent linear-optical qubit amplifier