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Physical Review A

Conditions for Simple Bounds on Elementary-Excitation Observables Given a Single Measured Observable

Duane P. Johnson, Allen Jay Kassman

Published Apr 1, 1972• 7 citations
Publisher

Abstract

Bounds are found for the values of an observable which are consistent with the measured value of a second observable and satisfy the conditions that ${f}_{0}(e)$, ${f}_{1}(e)$, and $Y(e)=\frac{{f}_{0}^{\ensuremath{'}}(e)}{{f}_{1}^{\ensuremath{'}}(e)}$ are well behaved and have nonzero slope on the open interval ${e}_{L} \mathrm{to} {e}_{U}$. ${f}_{0}(e)$ and ${f}_{1}(e)$ are, respectively, the contributions to the undetermined and determined observable from an elementary excitation state of energy $e$.

DOI
10.1103/physreva.5.1962

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Journal of Mathematical Physics•Apr 1, 1972•1 citation

Quantum Ergodicity and Thermalization in Interval Quantum Mechanics

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Bounds are found for the values of an observable which are consistent with the measured value of a second observable and satisfy the conditions that f0(e){f}_{0}(e)f0​(e), f1(e){f}_{1}(e)f1​(e), and Y(e)=f0\ensuremath′(e)f1\ensuremath′(e)Y(e)=\frac{{f}_{0}^{\ensuremath{'}}(e)}{{f}_{1}^{\ensuremath{'}}(e)}Y(e)=f1\ensuremath′​(e)f0\ensuremath′​(e)​ are well behaved and have nonzero slope on the open interval eLtoeU{e}_{L} \mathrm{to} {e}_{U}eL​toeU​. f0(e){f}_{0}(e)f0​(e) and f1(e){f}_{1}(e)f1​(e) are, respectively, the contributions to the undetermined and determined observable from an elementary excitation state of energy eee.
We propose a single observable to witness the nonzero quantum discord of an unknown quantum state provided that we have four copies of the state. The expectation value of this observable provides a necessary and sufficient condition for the nonzero quantum discord in $2\ifmmode\times\else\texttimes\fi{}N$ systems and a necessary condition in higher finite-dimensional bipartite systems. Furthermore, a nontrivial lower bound of the quantum discord can be obtained from this expectation value. The proposed observable can be experimentally measured in exactly the same way as the entanglement witness. Moreover, a quantum circuit is designed to determine the expectation value of our observable with four simultaneous local qubit measurements.
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