Optimal Cloning and Singlet Monogamy

Abstract

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins (known as monogamy), and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that the optimal Completely Positive map can be implemented as a teleportation operation into a standard, reference, state. The case of arbitrary 1 to N asymmetric cloning of d-dimensional spins can then be solved exactly, yielding the concept of `singlet monogamy'. The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.

4 pages, 1 figure. v2: conjecture upgraded to proof and generalized to arbitrary local hilbert space dimensions. v3: published version

References in corpus (15)

• Distributed Entanglement
• Quantum Copying: Beyond the No-Cloning Theorem
• General Monogamy Inequality for Bipartite Qubit Entanglement
• Optimal Quantum Cloning Machines
• Quantum cloning
• Optimal Universal and State-Dependent Quantum Cloning
• Optimal Cloning of Pure States
• Entanglement-assisted local manipulation of pure quantum states
• Optimal universal quantum cloning and state estimation
• Optimal Cloning of Pure States, Judging Single Clones
• Asymmetric quantum cloning machines in any dimension
• Multipartite Asymmetric Quantum Cloning
• Regional versus Global Entanglement in Resonating-Valence-Bond states
• Extremal equation for optimal completely-positive maps
• Separability in Asymmetric Phase-Covariant Cloning

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• Monogamy of quantum correlations reveals frustration in a quantum Ising spin system: Experimental demonstration
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
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• Local Realism of Macroscopic Correlations
• Maximally dense coding capable quantum states
• Enhancement of Quantum Correlation Length in Quenched Disordered Spin Chains
• Unified Universal Quantum Cloning Machine and Fidelities
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• Complementarity between Tripartite Quantum Correlation and Bipartite Bell Inequality Violation in Three Qubit States
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• Beating no-go theorems by engineering defects in quantum spin models
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• Generalised monogamy relation of convex-roof extended negativity in multi-level systems
• Asymmetric quantum multicast network coding: asymmetric optimal cloning over quantum networks
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• Better bounds on optimal measurement and entanglement recovery, with applications to uncertainty and monogamy relations
• Co-Processors for Quantum Devices
• On state vs. channel quantum extension problems: exact results for UxUxU symmetry
• A geometrical description of the universal $1\to 2$ asymmetric quantum cloning region
• The Asymmetric Quantum Cloning Region
• Universal Asymmetric Quantum Cloning Revisited
• Several Trade off Features of Quantum Steering in Distributed Scenario
• Two instances of random access code in the quantum regime