Information-theoretic limitations on approximate quantum cloning and broadcasting

Abstract

We prove new quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of $n$ qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control on the performance of generalized UQCMs on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a-priori information in the context of cloning. For example, we can control the performance of an antisymmetric analogue of the UQCM in recovering from the loss of $n-k$ fermionic particles.

13 pages; new results on approximate cloning between general subspaces, e.g., cloning of fermions

References in corpus (8)

• No-local-broadcasting theorem for quantum correlations
• A generalized no-broadcasting theorem
• Quantum Dynamics as an analog of Conditional Probability
• Multivariate Trace Inequalities
• The No-Broadcasting Theorem and its Classical Counterpart
• Optimal compression for identically prepared qubit states
• Universal and phase covariant superbroadcasting for mixed qubit states
• Transferring elements of a density matrix

Cited by in corpus (10)

• The Evolution of Quantum Secure Direct Communication: On the Road to the Qinternet
• A no-broadcasting theorem for quantum asymmetry and coherence and a trade-off relation for approximate broadcasting
• Entanglement Wedge Reconstruction using the Petz Map
• Approximate reversal of quantum Gaussian dynamics
• Approximate quantum Markov chains
• Asymmetric broadcasting of quantum correlations
• One-particle entanglement for one dimensional spinless fermions after an interaction quantum quench
• Entropic relations for indistinguishable quantum particles
• Quantum eigenstate broadcasting assisted by a coherent link
• Broadcasting of NPT Entanglement in Two Qutrit Systems