### Abstract

We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.

Original language | English |
---|---|

Article number | 083017 |

Journal | New Journal of Physics |

Volume | 11 |

DOIs | |

Publication status | Published - 13 Aug 2009 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*New Journal of Physics*,

*11*, [083017]. https://doi.org/10.1088/1367-2630/11/8/083017

**The information about the state of a qubit gained by a weakly coupled detector.** / Ashhab, Sahel; You, J. Q.; Nori, Franco.

Research output: Contribution to journal › Article

*New Journal of Physics*, vol. 11, 083017. https://doi.org/10.1088/1367-2630/11/8/083017

}

TY - JOUR

T1 - The information about the state of a qubit gained by a weakly coupled detector

AU - Ashhab, Sahel

AU - You, J. Q.

AU - Nori, Franco

PY - 2009/8/13

Y1 - 2009/8/13

N2 - We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.

AB - We analyze the information that one can learn about the state of a quantum two-level system, i.e. a qubit, when probed weakly by a nearby detector. In particular, we focus on the case when the qubit Hamiltonian and the qubit's operator being probed by the detector do not commute. Because the qubit's state keeps evolving while being probed and because the measurement data is mixed with detector-related background noise, one might expect the detector to fail in this case. We show, however, that under suitable conditions and by proper analysis of the measurement data useful information about the state of the qubit can be extracted. It turns out that the measurement basis is stochastically determined every time the experiment is repeated. We analyze in detail the probability distributions that govern the choice of measurement bases. We also analyze the information acquisition rate and show that it is largely unaffected by the apparent conflict between the measurement and intrinsic qubit dynamics. We discuss the relation between our analysis and the stochastic master equation that describes the evolution of the qubit's state under the influence of measurement and decoherence. In particular, we write down a stochastic equation that encompasses the usual stochastic master equation for the evolution of the qubit's density matrix and additionally contains the measurement information that can be extracted from the observed signal.

UR - http://www.scopus.com/inward/record.url?scp=69249088955&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=69249088955&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/11/8/083017

DO - 10.1088/1367-2630/11/8/083017

M3 - Article

AN - SCOPUS:69249088955

VL - 11

JO - New Journal of Physics

JF - New Journal of Physics

SN - 1367-2630

M1 - 083017

ER -