Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry

Stefano, Quimey Pears; Rebón, Lorena; Ledesma, Salvador; Iemmi, Claudio

doi:10.1103/physreva.96.062328

Cited by 22 publications

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“…Recently [25], we have reported a quantum tomography method to reconstruct any pure photonic spatial qudit of arbitrary dimension from a set of only 4d measurement outcomes, in case of a fixed measurement settings, or 4d − 3 when the procedure is performed in an adaptive way. In that work, the qudits were codified in the discretized transverse momentum of single photons (slit states) [26].…”

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“…This interferometer is used to implement the threestep Phase Shifting Interferometry technique (PSI) [27], which is ideally suited to find the phase of a light wave-arXiv:1903.05709v1 [quant-ph] 13 Mar 2019 front. As the method allows to reconstruct the whole wavefront from the interference pattern, the 4d measurement outcomes can be obtained in parallel by means of an image detector, reducing the measurement settings to only four, independently of the dimension d of the quantum system [25]. This measurement scheme is extremely efficient, and work properly for spatial qudits where it is straightforward to parallelize the measurements.…”

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Set of 4d–3 observables to determine any pure qudit state

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We present a tomographic method which requires only 4d − 3 measurement outcomes to reconstruct any pure quantum state of arbitrary dimension d. Using the proposed scheme we have experimentally reconstructed a large number of pure states of dimension d = 7, obtaining a mean fidelity of 0.94. Moreover, we performed numerical simulations of the reconstruction process, verifying the feasibility of the method for higher dimensions. In addition, the a priori assumption of purity can be certified within the same set of measurements, what represents an improvement with respect to other similar methods and contributes to answer the question of how many observables are needed to uniquely determine any pure state. 20020170100564BA).

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Set of 4d–3 observables to determine any pure qudit state

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“…Experimental demonstration of high-dimensional quantum communication advantage.-We present an experimental demonstration of the advantages of single-system quantum communication in the considered CCPs for d = 6, ..., 10. In our experiment, d-dimensional quantum systems are encoded into the linear transverse momentum of single photons transmitted by programmable diffractive apertures, which nowadays is a standard technique used for high-dimensional quantum information processing [44][45][46][47][48][49][50][51][52][53][54].…”

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High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

et al. 2018

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Quantum resources can improve communication complexity problems (CCPs) beyond their classical constraints. One quantum approach is to share entanglement and create correlations violating a Bell inequality, which can then assist classical communication. A second approach is to resort solely to the preparation, transmission and measurement of a single quantum system; in other words quantum communication. Here, we show the advantages of the latter over the former in high-dimensional Hilbert space. We focus on a family of CCPs, based on facet Bell inequalities, study the advantage of high-dimensional quantum communication, and realise such quantum communication strategies using up to ten-dimensional systems. The experiment demonstrates, for growing dimension, an increasing advantage over quantum strategies based on Bell inequality violation. For sufficiently high dimensions, quantum communication also surpasses the limitations of the post-quantum Bell correlations obeying only locality in the macroscopic limit. Surprisingly, we find that the advantages are tied to the use of measurements that are not rank-one projective. We provide an experimental semi-device-independent falsification of such measurements in Hilbert space dimension six.Introduction.-Communication complexity problems (CCPs) are tasks in which distant parties hold local data, the collection of which is needed for a computation of their interest. To make the computation possible, the parties communicate with each other. However, the amount of communication is limited and therefore not all data can be sent. The CCP consist in parties adopting an efficient communication strategy which allows them to perform the desired computation with a probability as high as possible. Efficient use of quantitatively limited communication is a broadly relevant matter [1], which provides fundamental insights on physical limitations [2,3].The ability to process information depends on the choice of the physical system into which the information is encoded [4]. Consequently, quantum entities without a classical counterpart can be regarded as tools for quantum information processing. The most famous example is entanglement. In a quantum CCP, parties may share an entangled state on which they perform local measurements, generating strongly correlated data which violates a Bell inequality. That data can then be used to assist a classical communication strategy [5]. In fact, Bell inequalities have been systematically linked to CCPs [6-8], and their violation enables better-than-classical communication efficiencies [7][8][9][10][11][12][13][14][15].Nevertheless, quantum theory presents also a second approach to CCPs: substituting classical communication with quantum communication. The justification for such a substitution relies on the Holevo theorem [16] which implies that no more information can be extracted from quantum d-level system than from a classical d-level system. Hence, in a quantum communication strategy, information is encoded in a quantum state of a specified Hilbe...

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“…Traditionally, the total number of measurement outcomes is considered as a resource. Thus, there is a search for QT methods relying on a smaller number of measurement outcomes [51][52][53][54]. Standard quantum tomography for a single qudit is based on the measurement of a D-dimensional representation of the D 2 − 1 generators of the SU(D) group, which leads to a total number of measurement outcomes of 2D 2 − D [55].…”

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Experimental quantum tomography assisted by multiply symmetric states in higher dimensions

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High-dimensional quantum information processing has become a mature field of research with several different approaches being adopted for the encoding of D-dimensional quantum systems. Such progress has fueled the search of reliable quantum tomographic methods aiming for the characterization of these systems, being most of these methods specifically designed for a given scenario. Here, we report on a new tomographic method based on multiply symmetric states and on experimental investigations to study its performance in higher dimensions. Unlike other methods, it is guaranteed to exist in any dimension and provides a significant reduction in the number of measurement outcomes when compared to standard quantum tomography. Furthermore, in the case of odd dimensions, the method requires the least possible number of measurement outcomes. In our experiment we adopt the technique where high-dimensional quantum states are encoded using the linear transverse momentum of single photons and are controlled by spatial light modulators. Our results show that fidelities of 0.984 ± 0.009 with ensemble sizes of only 1.5 × 10 5 photons in dimension D = 15 can be obtained in typical laboratory conditions, thus showing its practicability in higher dimensions.

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Determination of any pure spatial qudits from a minimum number of measurements by phase-stepping interferometry

Cited by 22 publications

References 30 publications

Set of 4d–3 observables to determine any pure qudit state

Set of 4d–3 observables to determine any pure qudit state

High-Dimensional Quantum Communication Complexity beyond Strategies Based on Bell’s Theorem

Experimental quantum tomography assisted by multiply symmetric states in higher dimensions

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