Optimal Quantum Cloning Machines

Abstract

We present Quantum Cloning Machines (QCM) that transform N identical qubits into $M>N$ identical copies and we prove that the fidelity (quality) of these copies is optimal. The connection between cloning and measurement is discussed in detail. When the number of clones M tends towards infinity, the fidelity of each clone tends towards the optimal fidelity that can be obtained by a measurement on the input qubits. More generally, the QCM are universal devices to translate quantum information into classical information.

4 pages, Latex, 1 postscript figure, (very) minor modifications

References in corpus (3)

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• Broadcasting of entanglement via local copying
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Cited by in corpus (338)

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• Quantum copying: A network
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• Mixed state sensitivity of several quantum information benchmarks
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• Experimental Quantum Cloning with Prior Partial Information
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• Quantum information distributors: Quantum network for symmetric and asymmetric cloning in arbitrary dimension and continuous limit
• Quantum cloning with an optical fiber amplifier
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• Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation
• Optimal N-to-M Cloning of Quantum Coherent States
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• Quantum State Separation, Unambiguous Discrimination and Exact Cloning
• Experimental optimal cloning of four-dimensional quantum states of photons
• Asymptotic quantum cloning is state estimation
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• Economical Phase-Covariant Cloning of Qudits
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• Robust Preparation of GHZ and W States of Three Distant Atoms
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• Trade-off capacities of the quantum Hadamard channels
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• Quantum Kolmogorov Complexity Based on Classical Descriptions
• Reexamination of optimal quantum state estimation of pure states
• Quantum superposition of multiple clones and the novel cloning machine
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• Optimal probabilistic storage and retrieval of unitary channels
• Universal Quantum Cloning in Cavity QED
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• The No-Broadcasting Theorem and its Classical Counterpart
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• Realization of the 1->3 optimal phase-covariant quantum cloning machine
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• Realization of Universal Optimal Quantum Machines by Projective Operators and Stochastic Maps
• Lower bound on the relative error of mixed-state cloning and related operations
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• Quantum Cloning and Distributed Measurements
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• Public and private resource trade-offs for a quantum channel
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• Optimal Broadcasting of Mixed States
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• Mixed Qubit Cannot Be Universally Broadcast
• Cloning of symmetric d-level photonic states in physical systems
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• Cloning of observables
• State estimation on correlated copies
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• Optimal 1->M universal quantum cloning via spin networks
• Asymmetric broadcasting of quantum correlations
• Upper Bounds for the Number of Quantum Clones under Decoherence
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• Perfect quantum-state synchronization
• Trade-off coding for universal qudit cloners motivated by the Unruh effect
• Extremal asymmetric universal cloning machines
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• Broadcasting of quantum correlations in qubit-qudit systems
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• Superbroadcasting of conjugate quantum variables
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• The measurement postulates of quantum mechanics are not redundant
• Broadcasting of correlations via orthogonal & non-orthogonal state dependent cloners
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• Quantum Cloning of Binary Coherent States - Optimal Transformations and Practical Limits
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• The Asymmetric Quantum Cloning Region
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• Universal Asymmetric Quantum Cloning Revisited
• On optimal cloning and incompatibility
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• Probabilistic implementation of universal Hadamard and Unitary gates
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• Quantum Chernoff bound as a measure of efficiency of quantum cloning for mixed states
• Topological obstructions to quantum computation with unitary oracles
• Information flow at the quantum-classical boundary
• Photonic quantum simulator for unbiased phase covariant cloning
• A Physical Perspective on Classical Cloning
• Representation matching for delegated quantum computing
• No-compressing of quantum phase information
• A simple formulation of no-cloning and no-hiding that admits efficient and robust verification
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• Optimal cloning of single photon polarization by coherent feedback of beam splitter losses
• Nonclassical resource for continuous variable telecloning with non-Gaussian advantage
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• Conical Designs and Categorical Jordan Algebraic Post-Quantum Theories
• Nondigital implementation of the arithmetic of real numbers by means of quantum computer media
• Application of the no-signaling principle to obtain quantum cloners for any allowed value of fidelity
• Secure and Robust Transmission and Verification of Unknown Quantum States in Minkowski Space
• Quantum-information Division and an Optimal Uncorrelated Channel
• Accidental cloning of a single-photon qubit in two-channel continuous-variable quantum teleportation
• Cloning of Qubits of a Quantum Computer
• Quantum comparison machines with one-sided error
• Certification of a functionality in a quantum network stage
• Quantum Process Randomness
• Is global asymptotic cloning state estimation?
• Three Party Quantum Networks Created by Quantum Cloning
• Two-qubit universal and state-dependent quantum cloning machine and quantum correlation broadcasting
• Process-optimized phase covariant quantum cloning
• Is It Possible To Clone Using An Arbitrary Blank State?
• Probabilistic quantum cloning of N quantum states
• Quantum communication and the creation of maximally entangled pairs of atoms over a noisy channel
• Characterizing nonclassical correlations of tensorizing states in a bilocal scenario
• On states of quantum theory
• Superbroadcasting of harmonic oscillators mixed states
• Broadcasting of non-locality
• Genuine fidelity gaps associated with a sequential decomposition of genuinely entangling isometry and unitary operations
• Characterizing quantum ensemble using geometric measure of quantum coherence
• Efficient classical simulation of the Gisin-Massar quantum cloning machine
• Optimal Quantum Subtracting Machine
• Compression of quantum shallow-circuit states
• Quantum deletion is possible via a partial randomization procedure
• Minimum Number of Copies in the Measurement of Multi-Photon Entanglement
• Thermodynamic Constraints on Information Transmission in Quantum Ensembles
• Multicast quantum network coding as optimal symmetric universal cloning over a quantum network
• Comparing quantum incompatibility of device sets from an operational perspective
• Virtual Cloning of Quantum States
• Single Qubit Multi-Party Transmission Using Universal Symmetric Quantum Cloning
• Key Disclosing in Multiphotons with Quantum Cloning
• Study on Entanglement and its Utility in Information Processing
• Entanglement is indispensable for masking arbitrary set of quantum states
• A Unified Quantum NOT Gate
• The roles of quantum correlations in quantum cloning
• Using Cloning to Solve NP Complete Problems
• Three-Party Entanglement in Tripartite Teleportation Scheme through Noisy Channels
• Test of Common Sense in Quantum Copying Process
• Broadcasting of NPT Entanglement in Two Qutrit Systems
• Quantum cloning with continuous variables