Direct measurement of a 27-dimensional orbital-angular-momentum state vector

Malik, Mehul; Mirhosseini, Mohammad; Lavery, Martin P. J.; Leach, Jonathan; Padgett, Miles J.; Boyd, Robert W.

doi:10.1038/ncomms4115

Cited by 224 publications

(208 citation statements)

References 39 publications

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“…Weak value has a nature of being a complex number, which lead the weak measurements to provide an ideal method to examine some fundamentals of quantum physics. Quantum paradoxes (Hardy's paradox [17][18][19] and the three-box paradox [20]), quantum correlation and quantum dynamics [21][22][23][24][25][26], quantum state tomography [27][28][29][30][31][32], violation of the generalized Leggett-Garg inequalities [33][34][35][36][37][38] and violation of the initial Heisenberg measurement-disturbance relationship [39,40] are just few examples. In these typ-ical examples, the small effects have been amplified due to the benefit of weak values.…”

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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“…Recently, Lundeen and his colleagues demonstrated weak measurement of the one-dimensional transverse wave function [14]. Since then, state tomography via weak measurement has been applied to several physical systems, such as an average photon trajectory [15,16], a polarization state [17], and an orbital angular momentum state [18]. All of these demonstrations, however, require the experimental configuration to measure two noncommutative operators, such as a position operatorX and its momentum operatorP x , onto the probe state of the weak measurement.…”

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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“…In addition, since QST requires a global reconstruction, it does not provide direct access to coherences (i.e. off-diagonal elements), which are of particular interest in quantum physics.Some recent work has focused on developing a direct approach to measuring quantum states [8][9][10][11][12][13][14][15][16][17][18][19]. Defining features of direct methods are that they can determine the state without complicated computations, and they can do so locally, i.e.…”

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confidence: 99%

Direct Measurement of the Density Matrix of a Quantum System

et al. 2016

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One drawback of conventional quantum state tomography is that it does not readily provide access to single density matrix elements, since it requires a global reconstruction. Here we experimentally demonstrate a scheme that can be used to directly measure individual density matrix elements of general quantum states. The scheme relies on measuring a sequence of three observables, each complementary to the last. The first two measurements are made weak to minimize the disturbance they cause to the state, while the final measurement is strong. We perform this joint measurement on polarized photons in pure and mixed states to directly measure their density matrix. The weak measurements are achieved using two walk-off crystals, each inducing a polarization-dependent spatial shift that couples the spatial and polarization degrees of freedom of the photons. This direct measurement method provides an operational meaning to the density matrix and promises to be especially useful for large dimensional states.Shortly after the inception of the quantum state, Pauli questioned its measurability, and in particular, whether or not a wave function can be obtained from position and momentum measurements [1]. This question, now referred to as the Pauli problem, draws on concepts such as complementarity and measurement in an attempt to demystify the physical significance of the quantum state. Indeed, the task of determining a quantum state is a central issue in quantum physics due to both its foundational and practical implications. For instance, a method to verify the production of complicated states is desirable in quantum information and quantum metrology applications. Moreover, since a state fully characterizes a system, any possible measurement outcome can be predicted once the state is determined.A wave function describes a quantum system that can be isolated from its environment, meaning the two are non-interacting and the system is in a pure state. More generally, open quantum systems can interact with their environment and the two can become entangled. In such cases, or even in the presence of classical noise, the system is in a statistical mixture of states (i.e. mixed state), and one requires a density matrix to fully describe the quantum system. In fact, some regard the density matrix as more fundamental than the wave function because of its generality and its relationship to classical measurement theory [2].The standard way of measuring the density matrix is by using quantum state tomography (QST). In QST, one performs an often overcomplete set of measurements in incompatible bases on identically prepared copies of the state. Then, one fits a candidate state to the measurement results with the help of a reconstruction algorithm [3]. Many efforts have been made to optimize QST [4][5][6][7], but the scalability of the experimental apparatus and the complexity of the reconstruction algorithm renders the task increasingly difficult for large dimensional systems. In addition, since QST requires a global reconstruction, it ...

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Direct measurement of a 27-dimensional orbital-angular-momentum state vector

Cited by 224 publications

References 39 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

Direct Measurement of the Density Matrix of a Quantum System

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