Virtual quantum broadcasting

Abstract

The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show that, although quantum broadcasting cannot be achieved by any physical process, it can be achieved by a virtual process, described by a Hermitian-preserving trace-preserving map. This virtual process is canonical: it is the only map that broadcasts all quantum states, is covariant under unitary evolution, is invariant under permutations of the copies, and reduces to the classical broadcasting map when subjected to decoherence. We show that the optimal physical approximation to the canonical broadcasting map is the optimal universal quantum cloning, and we also show that virtual broadcasting can be achieved by a virtual measure-and-prepare protocol, where a virtual measurement is performed, and, depending on the outcomes, two copies of a virtual quantum state are generated. Finally, we use canonical virtual broadcasting to prove a uniqueness result for quantum states over time.

arXiv comment5 pages + appendices

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Cited by in corpus (13)

• Properties and Applications of the Kirkwood-Dirac Distribution
• Uniqueness of quantum state over time function
• Certifying Quantum Temporal Correlation via Randomized Measurements: Theory and Experiment
• Optimal unilocal virtual quantum broadcasting
• Quantum dynamics as a pseudo-density matrix
• Multipartite quantum states over time from two fundamental assumptions
• Experimental Virtual Quantum Broadcasting
• Shadow Simulation of Quantum Processes
• No Practical Quantum Broadcasting: Even Virtually
• Virtual Quantum Markov Chains
• Bipartite quantum states admitting a causal explanation
• Virtual phase-covariant quantum broadcasting for qubits
• Virtual Cloning of Quantum States