Theory of “Weak Value" and Quantum Mechanical Measurements

Shikano, Yutaka

doi:10.5772/32810

Cited by 20 publications

(26 citation statements)

References 190 publications

(231 reference statements)

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“…The successful postselection probability tends to decrease in order to have successful amplification effect. For more details about weak measurement and weak value, one can consult these reviews [41][42][43].…”

Section: Introductionmentioning

confidence: 99%

Advantages of nonclassical pointer states in postselected weak measurements

et al. 2015

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We investigate, within the weak measurement theory, the advantages of non-classical pointer states over semi-classical ones for coherent, squeezed vacuum, and Schröinger cat states. These states are utilized as pointer state for the system operatorÂ with propertyÂ 2 =Î, whereÎ represents the identity operator. We calculate the ratio between the signal-to-noise ratio (SNR) of non-postselected and postselected weak measurements. The latter is used to find the quantum Fisher information for the above pointer states. The average shifts for those pointer states with arbitrary interaction strength are investigated in detail. One key result is that we find the postselected weak measurement scheme for non-classical pointer states to be superior to semi-classical ones. This can improve the precision of measurement process.

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Section: Introductionmentioning

confidence: 99%

Advantages of nonclassical pointer states in postselected weak measurements

et al. 2015

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“…Although each outcome of weak measurement includes a large uncertainty, the averaged value in multiple trials can build up a significant value, called a weak value, without state collapse. This feature makes weak measurement an ideal tool for examining the fundamentals of quantum physics, such as quantum correlation and quantum dynamics; for instance, see the reviews [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

2014

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We propose a stereographical-visualization scheme for a polarization state by two-dimensional imaging of a weak value with a single setup. The key idea is to employ Laguerre-Gaussian modes or an optical vortex beam for a probe state in weak measurement. Our scheme has the advantage that we can extract information on the polarization state from the single image in which the zero-intensity point of the optical vortex beam corresponds to a stereographic projection point of the Poincaré sphere. We experimentally perform single-setup weak measurement to validate the stereographical relationship between the polarization state on the Poincaré sphere and the location of the zero-intensity point.

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“…Throughout this paper, we omit the preselection sub-index whenever it is clear from the context. Weak values are intrinsically complex which has already proved useful in characterizing the mathematically observable-independent probability space [23], several quantum paradoxes [24], the quantum state [25][26][27][28][29][30][31], and unobservable quantities such as the geometric phase [32][33][34][35] and the non-Hermitian operator [36]; see also the review papers [37][38][39][40]. We show that one may also take advantage of the complex feature of the weak values in assessing the amount of entanglement with a single measurement set-up.…”

Section: Introductionmentioning

confidence: 99%

Quantification of concurrence via weak measurement

2017

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Since entanglement is not an observable per se, measuring its value in practice is a difficult task. Here we propose a protocol for quantifying a particular entanglement measure, namely concurrence, of an arbitrary two-qubit pure state via a single fixed measurement set-up by exploiting so-called weak measurements and the associated weak values together with the properties of the LaguerreGaussian modes. The virtue of our technique is that it is generally applicable for all two-qubit systems and does not involve simultaneous copies of the entangled state. We also propose an explicit optical implementation of the protocol.

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Theory of “Weak Value" and Quantum Mechanical Measurements

Cited by 20 publications

References 190 publications

Advantages of nonclassical pointer states in postselected weak measurements

Advantages of nonclassical pointer states in postselected weak measurements

Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam

Quantification of concurrence via weak measurement

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