Scan-free direct measurement of an extremely high-dimensional photonic state

Shi, Zhimin; Mirhosseini, Mohammad; Margiewicz, Jessica; Malik, Mehul; Rivera, Freida; Zhu, Ziyi; Boyd, Robert W.

doi:10.1364/optica.2.000388

Cited by 77 publications

(67 citation statements)

References 46 publications

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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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confidence: 99%

Direct Measurement of the Density Matrix of a Quantum System

et al. 2016

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“…In addition, weak values are used for the precise measurement of the magnitudes of weak system-probe interactions [11][12][13][14][15] because they can exceed the eigenvalues of the observables. Furthermore, weak values are utilized for the direct measurement of complex functions such as wavefunctions and pseudo-probability distributions of the initial state of the system [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…Furthermore, using the transformation rule of the diagram, a new weak value measurement method that has a desired function, such as measurement precision and a simple experimental setup, can be systematically derived, regardless of the type of physical systems. As an example, this transformation rule is applied to a direct measurement method of wavefunctions using weak measurement [16] to develop a scan-free and more efficient method than the conventional techniques using weak measurements [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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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 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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“…(c) The trace distance is half the Euclidean distance between the measured and theory states on the Poincaré sphere, and it is always less than 0.049 (i.e., 4.9%). PRL 117, 120401 (2016) P H Y S I C A L R E V I E W L E T T E R S week ending 16 SEPTEMBER 2016 various physical systems [13,17,18]. Quantum state tomography typically requires Oðd 2 Þ measurements in OðdÞ bases and finds the full density matrix at once.…”

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confidence: 99%

Mapping Out the State of a Quantum System

Jordan

2016

Physics

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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. DOI: 10.1103/PhysRevLett.117.120401 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 its 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 noninteracting 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., a 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, si...

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Scan-free direct measurement of an extremely high-dimensional photonic state

Cited by 77 publications

References 46 publications

Direct Measurement of the Density Matrix of a Quantum System

Direct Measurement of the Density Matrix of a Quantum System

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

Mapping Out the State of a Quantum System

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