Source-linked AI summary
Noncommuting mixed states cannot be broadcast
H. Barnum, C. M. Caves, C. A. Fuchs, R. Jozsa, B. Schumacher
TL;DR
The paper asks whether unknown mixed quantum states can be broadcast onto two systems, extending the pure-state no-cloning question. It proves that broadcasting is possible only for commuting states, while noncommuting states cannot be broadcast.
Problem
The paper asks whether physical processes can broadcast an unknown quantum state onto separate systems, since the no-cloning theorem alone does not address mixed states.
Source: p. 2Method
The authors model the most general quantum process using an auxiliary system, a standard auxiliary state, and unitary evolution, then analyze fidelity and commutation.
Source: p. 3Results
Broadcasting is possible if and only if the states commute; noncommuting mixed states therefore cannot be broadcast.
Source: pp. 3, 10Takeaways & Limitations
The theorem generalizes and extends the pure-state no-cloning theorem to mixed quantum states.
Source: p. 2The analysis constrains broadcasting to physical processes modeled within quantum theory, and sufficient conditions for process realizability are not known.
Source: pp. 3, 10
Abstract
from arXiv · showhide
We show that, given a general mixed state for a quantum system, there are no physical means for {\it broadcasting\/} that state onto two separate quantum systems, even when the state need only be reproduced marginally on the separate systems. This result generalizes and extends the standard no-cloning theorem for pure states.