Tomography of spatial mode detectors

Bobrov, I. B.; Kovlakov, E. V.; Markov, A. A.; Straupe, S. S.; Kulik, S. P.

doi:10.1364/oe.23.000649

Cited by 11 publications

(8 citation statements)

References 37 publications

(45 reference statements)

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“…However, a typical measurement device does not register a continuous and infinite range of values, and it is thus necessary to consider discretized measurements. A most common approach is the selection of a finite set of transverse spatial modes labeled by discrete mode indexes [26][27][28][29], for which MUB measurements are attainable by the use of phase holograms [6]. Free-space [30], multi-core fibers [31] or on-chip [32] path encoding as well as time-bin [33] are also interesting techniques with potencial for high-dimensionality.…”

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confidence: 99%

Mutual Unbiasedness in Coarse-Grained Continuous Variables

et al. 2018

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The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.Introduction. The ability to measure a system in an infinite number of non-commuting bases distinguishes the quantum world from classical physics. Wave-particle duality and more generally the complementarity principle are directly rooted in this feature of quantum mechanics. Though one can measure a quantum system in several distinct bases, uncertainty relations limit the amount of information that can be obtained. It is well known that projection onto an eigenstate of one basis reduces the information that can be obtained through or inferred about subsequent measurement in a different basis. The information is minimum for mutually unbiased bases (MUBs), for which all outcomes of the second measurement are equally likely, so that total uncertainty is always substantial (the sharpest uncertainty relations [1]) and most insensitive to input states [2]. MUBs play an important role in complementarity [3], quantum cryptography [4] and quantum tomography [5,6], are useful for certifying quantum randomness [7], and for detecting quantum correlations such as entanglement [8][9][10] and steering [11][12][13][14][15][16][17][18].

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confidence: 99%

Mutual Unbiasedness in Coarse-Grained Continuous Variables

et al. 2018

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“…[69][70][71][72][73][74][75][76][77] We caution the varied notions of QDT, which include the estimation of certain physical parameters (such as the quantum efficiency and dark-count rate) describing the given quantum-measurement set, 78 or the calibration of commuting outcomes. 11,[79][80][81][82] In this section, we consider the most general (C)QDT of a set of M positive outcomes {Π j } that are mutually noncommutative. Standard QDT without any compressive elements clearly requires O(d 2 ) mutually linearly-independent input states to characterize the POVM.…”

Section: Compressive Quantum Detector Tomographymentioning

confidence: 99%

Modern compressive tomography for quantum information science

Teo

Sánchez-Soto

2021

Int. J. Quantum Inform.

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This review serves as a concise introductory survey of modern compressive tomography developed since 2019. These are schemes meant for characterizing arbitrary low-rank quantum objects, be it an unknown state, a process or detector, using minimal measuring resources (hence compressive) without any a priori assumptions (rank, sparsity, eigenbasis, etc.) about the quantum object. This paper contains a reasonable amount of technical details for the quantum-information community to start applying the methods discussed here. To facilitate the understanding of formulation logic and physics of compressive tomography, the theoretical concepts and important numerical results (both new and cross-referenced) shall be presented in a pedagogical manner.

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“…Indeed, in such a * All data and source code are available online at [1]. scenario the experimenter faces careful calibration of the measurement setup, or in other words quantum detector tomography [6,7,18], which works reliably if known probe states can be prepared [19][20][21][22].…”

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confidence: 99%

“…Such calibration is essentially tomography on its right. For example, the reconstruction of measurement operators is known as detector tomography [6,7,18,35,36] and requires ideal preparation of calibration states. The most straightforward approach is calibration of the measurement setup with some closeto-ideal and easy to prepare test states, or calibration of the preparation setup with known and close-to-ideal measurements.…”

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confidence: 99%

Experimental neural network enhanced quantum tomography

et al. 2020

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Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state preparation and the measurement apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to state-preparation-and-measurement (SPAM) errors degrading reconstruction performance. Here we develop and experimentally implement a machine learning based protocol reducing SPAM errors. We trained a supervised neural network to filter the experimental data and hence uncovered salient patterns that characterize the measurement probabilities for the original state and the ideal experimental apparatus free from SPAM errors. We compared the neural network state reconstruction protocol with a protocol treating SPAM errors by process tomography, as well as to a SPAM-agnostic protocol with idealized measurements. The average reconstruction fidelity is shown to be enhanced by 10% and 27%, respectively. The presented methods apply to the vast range of quantum experiments which rely on tomography.arXiv:1904.05902v2 [quant-ph]

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Tomography of spatial mode detectors

Cited by 11 publications

References 37 publications

Mutual Unbiasedness in Coarse-Grained Continuous Variables

Mutual Unbiasedness in Coarse-Grained Continuous Variables

Modern compressive tomography for quantum information science

Experimental neural network enhanced quantum tomography

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