Weak and strong measurement of a qubit using a switching-based detector

Sahel Ashhab, J. Q. You, Franco Nori

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytical results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.

Original languageEnglish
Article number032317
JournalPhysical Review A - Atomic, Molecular, and Optical Physics
Volume79
Issue number3
DOIs
Publication statusPublished - 3 Mar 2009
Externally publishedYes

Fingerprint

detectors
energy
probes

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

Cite this

Weak and strong measurement of a qubit using a switching-based detector. / Ashhab, Sahel; You, J. Q.; Nori, Franco.

In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 79, No. 3, 032317, 03.03.2009.

Research output: Contribution to journalArticle

@article{13e9540449fa4ce1be61e091a2f77dfc,
title = "Weak and strong measurement of a qubit using a switching-based detector",
abstract = "We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytical results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.",
author = "Sahel Ashhab and You, {J. Q.} and Franco Nori",
year = "2009",
month = "3",
day = "3",
doi = "10.1103/PhysRevA.79.032317",
language = "English",
volume = "79",
journal = "Physical Review A - Atomic, Molecular, and Optical Physics",
issn = "1050-2947",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Weak and strong measurement of a qubit using a switching-based detector

AU - Ashhab, Sahel

AU - You, J. Q.

AU - Nori, Franco

PY - 2009/3/3

Y1 - 2009/3/3

N2 - We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytical results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.

AB - We analyze the operation of a switching-based detector that probes a qubit's observable that does not commute with the qubit's Hamiltonian, leading to a nontrivial interplay between the measurement and free-qubit dynamics. In order to obtain analytical results and develop intuitive understanding of the different possible regimes of operation, we use a theoretical model where the detector is a quantum two-level system that is constantly monitored by a macroscopic system. We analyze how to interpret the outcome of the measurement and how the state of the qubit evolves while it is measured. We find that the answers to the above questions depend on the relation between the different parameters in the problem. In addition to the traditional strong-measurement regime, we identify a number of regimes associated with weak qubit-detector coupling. An incoherent detector whose switching time is measurable with high accuracy can provide high-fidelity information, but the measurement basis is determined only upon switching of the detector. An incoherent detector whose switching time can be known only with low accuracy provides a measurement in the qubit's energy eigenbasis with reduced measurement fidelity. A coherent detector measures the qubit in its energy eigenbasis and, under certain conditions, can provide high-fidelity information.

UR - http://www.scopus.com/inward/record.url?scp=63249116237&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63249116237&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.79.032317

DO - 10.1103/PhysRevA.79.032317

M3 - Article

VL - 79

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032317

ER -