Quantum weak and modular values in enlarged Hilbert spaces

Ho, Le Bin; Imoto, Nobuyuki

doi:10.1103/physreva.97.012112

Cited by 8 publications

(13 citation statements)

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“…The weak value measurement method using an expanded Hilbert space [31] is derived by modulating the transformed weak value measurement technique described in Fig. 2(c) of Sec.…”

Section: Other Weak Value Measurement Methods In the Proposed Frameworkmentioning

confidence: 99%

“…In previous studies, weak values have been obtained by weak measurements, which involve weak system-probe interactions. However, this is not the only possible method for their determination, and several alternative measurement techniques that do not involve weak system-probe interactions have been recently developed, including those using strong system-probe interactions [25][26][27][28], modular values [29], quantum control interactions [30], an enlarged Hilbert space [31], and coupling-deformed pointer observables [32]. In this work, we propose a framework for measuring weak values common to the conventional weak measurement using a qubit probe and other weak value measurement techniques.…”

Section: Introductionmentioning

confidence: 99%

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A framework for measuring weak values without weak interactions and its diagrammatic representation

Ogawa,

Yasuhiko,

Kobayashi

et al. 2018

Preprint

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Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak measurements, and several methods without weak system-probe interactions have been developed previously. In this work, a framework for measuring weak values is proposed to describe the relationship between various weak measurement techniques in a unified manner. This framework, which uses a probe-controlled system transformation instead of the weak system-probe interaction, improves the understanding of the currently used weak value measurement methods. Furthermore, a diagrammatic representation of the proposed framework is introduced to intuitively identify the complex values obtained in each measurement system. By using this diagram, a new method for measuring weak values with a desired function can be systematically derived. As an example, a scan-free and more efficient direct measurement method of wavefunctions than the conventional techniques using weak measurements is developed.

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“…The weak value measurement method using an expanded Hilbert space [31] is derived by modulating the transformed weak value measurement technique described in Fig. 2(c) of Sec.…”

Section: Other Weak Value Measurement Methods In the Proposed Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A framework for measuring weak values without weak interactions and its diagrammatic representation

Ogawa,

Yasuhiko,

Kobayashi

et al. 2018

Preprint

View full text Add to dashboard Cite

show abstract

“…However, this is not the only possible method for their determination, and several alternative weak value measurement techniques that do not involve weak system-probe interactions have been recently developed, including those using strong system-probe interactions [26][27][28][29], modular values [30], quantum control interactions [31,32], an enlarged Hilbert space [33], coupling-deformed pointer observables [34], and a combination of several strong measurements of the system [35]. It should be noted here that most of them [26][27][28][29][30][31][32][33] and some weak measurement experiments [2][3][4][5][6][7][8][9][10][16][17][18][19][20][21][22][23][24] use qubit systems as the probes. They all have the same measurement procedure of the qubit probes to obtain complex weak values-measuring expectation values of two operators, such as Pauli-X and Pauli-Y.…”

Section: Introductionmentioning

confidence: 99%

“…The weak value measurement method using an expanded Hilbert space [33] is derived by modulating the transformed weak value measurement technique described in figure 2(c) of section 2.2. The complex value derived by this method is y y y y á ñá ñ |…”

mentioning

confidence: 99%

A framework for measuring weak values without weak interactions and its diagrammatic representation

et al. 2019

View full text Add to dashboard Cite

Weak values are typically obtained experimentally by performing weak measurements, which involve weak interactions between the measured system and a probe. However, the determination of weak values does not necessarily require weak measurements, and several methods without weak systemprobe interactions have been developed previously. In this work, a framework for measuring weak values is proposed to describe the relationship between various weak value measurement techniques in a unified manner. This framework, which uses a probe-controlled system transformation instead of the weak system-probe interaction, improves the understanding of the currently used weak value measurement methods. Furthermore, a diagrammatic representation of the proposed framework is introduced to intuitively identify the complex values obtained in each measurement system. By using this diagram, a new method for measuring weak values with a desired function can be systematically derived. As an example, a scan-free and more efficient direct measurement method of wavefunctions than the conventional techniques using weak measurements is developed.

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“…In this Letter, we discuss modular-value-based measurements [29][30][31][32][33] with spin-j coherent pointers [34,35]. They are different from the weak-value-based ones and can allow arbitrary strength interactions between the pointers and sensors.…”

mentioning

confidence: 99%

Modular-value-based metrology with spin coherent pointers

Kondo

2019

Physics Letters A

Self Cite

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Modular values are quantities that described by pre-and postselected states of quantum systems like weak values but are different from them: The associated interaction is not necessary to be weak. We discuss an optimal modular-value-based measurement with a spin coherent pointer: A quantum system is exposed to a field in which strength is to be estimated through its modular value. We consider two cases, with a two-dimensional and a higher-dimensional pointer, and evaluate the quantum Fisher information. The modular-value-based measurement has no merit in the former case, while its sensitivity can be enhanced in the latter case. We also consider the pointer under a phase-flip error. Our study should motivate researchers to apply the modular-value-based measurements for quantum metrology.Introduction.-In the concept of quantum sensing, a physical quantity on a small scale can be measured indirectly via a quantum system, a quantum property, or a quantum phenomenon [1]. The principle of measurements is (i) preparing quantum systems, hereafter called sensors, of which number is L, (ii) exposing to a field of which strength is to be measured for a period of t, and (iii) obtaining a state change before and after the exposure. The change is a measure of the strength of the field. This procedure is repeated T /t times in a total measurement time T . If the sensors are independent, the effective total measurement number N is given as N = LT /t. For fixed T and t, the uncertainty of the estimation is proportional to 1/ √ L, which is known as the standard quantum limit or the shot noise limit [2][3][4][5]. However, if the uncertainty scales as 1/L then it is called the Heisenberg limit [6] which is a fundamental limit.

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Quantum weak and modular values in enlarged Hilbert spaces

Cited by 8 publications

References 54 publications

A framework for measuring weak values without weak interactions and its diagrammatic representation

A framework for measuring weak values without weak interactions and its diagrammatic representation

A framework for measuring weak values without weak interactions and its diagrammatic representation

Modular-value-based metrology with spin coherent pointers

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