### Abstract

The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it corresponds to making measurements diagonal in a corresponding Schmidt basis. More generally, it is shown that the maximum correlation may be characterized in terms of a correlation basis for the joint density operator, which defines the corresponding (nondegenerate) optimal measurements. The maximum coincidence rate for spin measurements on two-qubit systems is determined to be (1+s)/2, where s is the spectral norm of the spin correlation matrix, and upper bounds are obtained for n-valued measurements on general bipartite systems. It is shown that the maximum coincidence rate is never greater than the computable cross norm measure of entanglement, and a much tighter upper bound is conjectured. Connections with optimal state discrimination and entanglement bounds are briefly discussed.

Original language | English |
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Number of pages | 11 |

Journal | Physical Review A |

Volume | 74 |

Issue number | 6 |

DOIs | |

Publication status | Published - 18 Dec 2006 |

### Keywords

- bipartite quantum system
- qubit
- quantum physics
- quantum

## Cite this

Hall, M. J. W., Andersson, E., & Brougham, T. (2006). Maximum observable correlation for a bipartite quantum system.

*Physical Review A*,*74*(6). https://doi.org/10.1103/PhysRevA.74.062308