Optimal asymptotic cloning machines

Abstract

We pose the question whether the asymptotic equivalence between quantum cloning and quantum state estimation, valid at the single-clone level, still holds when all clones are examined globally. We conjecture that the answer is affirmative and present a large amount of evidence supporting our conjecture, developing techniques to derive optimal asymptotic cloners and proving their equivalence with estimation in virtually all scenarios considered in the literature. Our analysis covers the case of arbitrary finite sets of states, arbitrary families of coherent states, arbitrary phase- and multiphase-covariant sets of states, and two-qubit maximally entangled states. In all these examples we observe that the optimal asymptotic fidelity enjoys a universality property, as its scaling does not depend on the specific details of the set of input states, but only on the number of parameters needed to specify them.

27 + 9 pages, corrected one observation about cloning of maximally entangled states

References in corpus (38)

• Optimal Quantum Cloning Machines
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• The resource theory of quantum reference frames: manipulations and monotones
• Fundamentals of Quantum Information Theory
• Phase covariant quantum cloning
• Optimal universal quantum cloning and state estimation
• Universal cloning of continuous quantum variables
• The theory of manipulations of pure state asymmetry: basic tools and equivalence classes of states under symmetric operations
• Quantum benchmark for storage and transmission of coherent states
• Two qubit copying machine for economical quantum eavesdropping
• Quantum cloning machines for equatorial qubits
• Schroedinger Cat: Entanglement test in a Micro-Macroscopic system
• Bell Measurements and Observables
• Optimal phase covariant cloning for qubits and qutrits
• Optimal N-to-M Cloning of Quantum Coherent States
• Optimal estimation of group transformations using entanglement
• The WAY theorem and the quantum resource theory of asymmetry
• Asymptotic quantum cloning is state estimation
• Economical Phase-Covariant Cloning of Qudits
• Phase estimation for thermal Gaussian states
• Covariant quantum measurements which maximize the likelihood
• Economical quantum cloning in any dimension
• Quantum Benchmark for Teleportation and Storage of Squeezed States
• Quantum replication at the Heisenberg limit
• Quantum information becomes classical when distributed to many users
• Optimal design and quantum benchmarks for coherent state amplifiers
• Investigating macroscopic quantum superpositions and the quantum-to-classical transition by optical parametric amplification
• Alignment of reference frames and an operational interpretation for the G-asymmetry
• Quantum benchmarks for pure single-mode Gaussian states
• Phase-Covariant Quantum Benchmarks
• Fidelity criterion for quantum-domain transmission and storage of coherent states beyond unit-gain constraint
• On quantum estimation, quantum cloning and finite quantum de Finetti theorems
• Maximum likelihood estimation for a group of physical transformations
• Applications of the group SU(1,1) for quantum computation and tomography
• Fundamental quantum limits for practical devices
• Phase-asymmetry resource interconversion via estimation

Cited by in corpus (8)

• Optimal quantum operations at zero energy cost
• Universal super-replication of unitary gates
• Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states
• Probabilistically Perfect Cloning of Two Pure States: A Geometric Approach
• Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks
• Quantum superreplication of states and gates
• No-signaling bounds for quantum cloning and metrology
• Quantum Measurement Complexity