Optimal probabilistic cloning and purification of quantum states

Abstract

We investigate the probabilistic cloning and purification of quantum states. The performance of these probabilistic operations is quantified by the average fidelity between the ideal and actual output states. We provide a simple formula for the maximal achievable average fidelity and we explictly show how to construct a probabilistic operation that achieves this fidelity. We illustrate our method on several examples such as the phase covariant cloning of qubits, cloning of coherent states, and purification of qubits transmitted via depolarizing channel and amplitude damping channel. Our examples reveal that the probabilistic cloner may yield higher fidelity than the best deterministic cloner even when the states that should be cloned are linearly dependent and are drawn from a continuous set.

9 pages, 2 figures

References in corpus (8)

• Optimal teleportation with a mixed state of two qubits
• Coherent pulse implementations of quantum cryptography protocols resistant to photon number splitting attacks
• Optimal phase covariant cloning for qubits and qutrits
• Local Hidden Variable Theories for Quantum States
• Cloning a real d-dimensional quantum state on the edge of the no-signaling condition
• Cloning the entanglement of a pair of quantum bits
• Optimal realization of the transposition maps
• Checking $2\times M$ separability via semidefinite programming

Cited by in corpus (42)

• A high-fidelity noiseless amplifier for quantum light states
• Optimal quantum cloning of orbital angular momentum photon qubits via Hong-Ou-Mandel coalescence
• Quantum-Limited Amplification via Reservoir Engineering
• Quantum Cloning Machines and the Applications
• Quantum limits on probabilistic amplifiers
• Experimental realization of a minimal disturbance quantum measurement
• Key Generation: Foundations and a New Quantum Approach
• Surpassing the no-cloning limit with a heralded hybrid linear amplifier for coherent states
• NMR Experimental Demonstration of Probabilistic Quantum Cloning
• Quantum replication at the Heisenberg limit
• Optimal design and quantum benchmarks for coherent state amplifiers
• Optimal architecture for a non-deterministic noiseless linear amplifier
• Complete characterization of qubit masking
• Optimal quantum operations at zero energy cost
• Coherent-state discrimination via non-heralded probabilistic amplification
• Universal super-replication of unitary gates
• Optical implementation of the encoding of two qubits to a single qutrit
• Optimal quantum repeaters for qubits and qudits
• Optimal probabilistic estimation of quantum states
• Certifying quantumness: Benchmarks for the optimal processing of generalized coherent and squeezed states
• Quantum enhancement of signal-to-noise ratio with a heralded linear amplifier
• Impossibility of masking a set of quantum states of nonzero measure
• Implementation of optimal phase-covariant cloning machines
• Beating noise with abstention in state estimation
• Trace distance from the viewpoint of quantum operation techniques
• Novel cloning machine with supplementary information
• Quantum amplification and purification of noisy coherent states
• Quantum multipartite maskers vs quantum error-correcting codes
• Models of reduced-noise, probabilistic linear amplifiers
• Optimal partial estimation of quantum states from several copies
• Streaming quantum state purification
• Orthogonalization of partly unknown quantum states
• Probabilistic Metrology Attains Macroscopic Cloning of Quantum Clocks
• Probabilistically Perfect Cloning of Two Pure States: A Geometric Approach
• Quantum superreplication of states and gates
• Fundamental limits on quantum cloning from the no-signalling principle
• Masking quantum information encoded in pure and mixed states
• Process-optimized phase covariant quantum cloning
• The classical capacity for the quantum Markov channel of continuous variables
• Decoding Protocols for Classical Communication on Quantum Channels
• Masking quantum information into a tripartite syste
• Power and limitations of distributed quantum state purification