Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1707.03306 · Physical Review A

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

Quimey Pears Stefano, Lorena Rebón, Silvia Adriana Ledesma, Claudio Iemmi

Published Dec 22, 2017• 22 citations
arXivHTMLPDF

Abstract

We present a proof-of-principle demonstration of a method to characterize any pure spatial qudit of arbitrary dimension $d$, which is based on the classic phase-shift interferometry technique. In the proposed scheme a total of only $4d$ measurement outcomes are needed, implying a significant reduction with respect to the standard schemes for quantum-state tomography which require on the order of ${d}^{2}$. By using this technique, we have experimentally reconstructed a large number of states ranging from $d=2$ up to 14 with mean fidelity values higher than 0.97. For that purpose the qudits were codified in the discretized transverse-momentum position of single photons, once they are sent through an aperture with $d$ slits. We provide an experimental implementation of the method based in a Mach-Zehnder interferometer, which allows one to reduce the number of measurement settings to four since the $d$ slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstruction of the unknown state from the outcome frequencies of $4d\ensuremath{-}3$ fixed projectors independently of the encoding or the nature of the quantum system, allowing one to implement the reconstruction method in a general experiment.

DOI
10.1103/physreva.96.062328

Related papers

Determination of spatial quantum states by using point diffraction interferometry

Quimey Pears Stefano, Lorena Rebón, Claudio Iemmi

Abstract We present a method to reconstruct pure spatial qudits of arbitrary dimension d , which is based on a point diffraction interferometer. In the proposed scheme, the quantum states are codified in the discretized transverse position of a photon field, once they are sent through an aperture consisting in d rectangular regions, with an extra region that provides a phase reference. To characterize these photonic quantum states, the complete phase wavefront is reconstructed through a phase-shifting technique. Combined with a multipixel detector, the acquisition can be parallelized, and only four interferograms are required to reconstruct any pure qudit, independently of the dimension d . We tested the method experimentally, for reconstructing states of dimension d = 6 randomly chosen. A mean fidelity values of 0.95 is obtained. Additionally, we develop an experimental scheme that allows to estimate phase aberrations affecting the wavefront upon propagation, and thus improve the quantum state estimation. In that regard, we present a proof-of-principle demonstration that shows the possibility to correct the influence of turbulence in a free-space communication, recovering mean fidelity values comparable to the propagation free of turbulence.

arXiv:2005.09963•Journal of Optics•Sep 24, 2020•1 citation

Parallelized projective measurements for spatial photonic qudits estimation

Stefano, Quimey Pears, Rebón, Lorena, Claudio Iemmi

We present a quantum state tomography method that enables the reconstruction of \emph{arbitrary} $d-$dimensional quantum states encoded in the discretized transverse momentum of photons, by using \emph{only} $d+1$ experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are \emph{spatially multiplexed} on the interference pattern of the projected state. Using the proposed scheme we performed, as a proof-of-principle, an experimental reconstruction of $d=6-$dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from $42$ to only $7$.

arXiv:2506.15820•Jun 18, 2025•0 citations

Parallelized projective measurements for spatial photonic qudits estimation

Quimey Pears Stefano, Lorena Rebón, Claudio Iemmi

We present a quantum state tomography method that enables the reconstruction of arbitrary d−dimensional quantum states encoded in the discretized transverse momentum of photons, by using only d+1 experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are spatially multiplexed on the interference pattern of the projected state. Using the proposed scheme, we performed, as a proof-of-principle, an experimental reconstruction of d=6−dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from 42 to only 7.

Optics Letters•Aug 28, 2025•1 citation

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

Quimey Pears Stefano, Lorena Rebón, Silvia Adriana Ledesma +1 more

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, which represents an improvement with respect to other similar methods and contributes to answering the question of how many observables are needed to uniquely determine any pure state.

arXiv:1903.05709•Optics Letters•May 10, 2019•12 citations

Optimized generation of spatial qudits by using a pure phase spatial light modulator

Varga, Juan José Miguel, Rebón, Lorena, Solís Prosser, M. A. +3 more

We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional ($D\\geqslant 2$) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D. The amplitude information was codified by introducing phase gratings inside each slit, and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process, we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried out. In this scheme, the amplitudes are set by appropriate phase gratings addressed at the SLM, while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete $2\\pi $ modulation is obtained by shifting the grating by one period; hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analyses are performed for qudits with D = 3 and D = 7.

•Jan 1, 2014•7 citations

Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator

M. A. Solís-Prosser, Augusto Arias, J. J. M. Varga +4 more

Spatial qudits are D-dimensional (D ≥ 2) quantum systems carrying information encoded in the discretized transverse momentum and position of single photons. We present a proof-of-principle demonstration of a method for preparing arbitrary pure states of such systems by using a single phase-only spatial light modulator (SLM). The method relies on the encoding of the complex transmission function corresponding to a given spatial qudit state onto a preset diffraction order of a phase-only grating function addressed at the SLM. Fidelities of preparation above 94% were obtained with this method, which is simpler, less costly, and more efficient than those that require two SLMs for the same purpose.

arXiv:1311.4122•Optics Letters•Nov 11, 2013•50 citations
We present a proof-of-principle demonstration of a method to characterize any pure spatial qudit of arbitrary dimension ddd, which is based on the classic phase-shift interferometry technique. In the proposed scheme a total of only 4d4d4d measurement outcomes are needed, implying a significant reduction with respect to the standard schemes for quantum-state tomography which require on the order of d2{d}^{2}d2. By using this technique, we have experimentally reconstructed a large number of states ranging from d=2d=2d=2 up to 14 with mean fidelity values higher than 0.97. For that purpose the qudits were codified in the discretized transverse-momentum position of single photons, once they are sent through an aperture with ddd slits. We provide an experimental implementation of the method based in a Mach-Zehnder interferometer, which allows one to reduce the number of measurement settings to four since the ddd slits can be measured simultaneously. Furthermore, it can be adapted to consider the reconstruction of the unknown state from the outcome frequencies of 4d\ensuremath−34d\ensuremath{-}34d\ensuremath−3 fixed projectors independently of the encoding or the nature of the quantum system, allowing one to implement the reconstruction method in a general experiment.
Abstract We present a method to reconstruct pure spatial qudits of arbitrary dimension d , which is based on a point diffraction interferometer. In the proposed scheme, the quantum states are codified in the discretized transverse position of a photon field, once they are sent through an aperture consisting in d rectangular regions, with an extra region that provides a phase reference. To characterize these photonic quantum states, the complete phase wavefront is reconstructed through a phase-shifting technique. Combined with a multipixel detector, the acquisition can be parallelized, and only four interferograms are required to reconstruct any pure qudit, independently of the dimension d . We tested the method experimentally, for reconstructing states of dimension d = 6 randomly chosen. A mean fidelity values of 0.95 is obtained. Additionally, we develop an experimental scheme that allows to estimate phase aberrations affecting the wavefront upon propagation, and thus improve the quantum state estimation. In that regard, we present a proof-of-principle demonstration that shows the possibility to correct the influence of turbulence in a free-space communication, recovering mean fidelity values comparable to the propagation free of turbulence.
We present a quantum state tomography method that enables the reconstruction of \emph{arbitrary} d−d-d−dimensional quantum states encoded in the discretized transverse momentum of photons, by using \emph{only} d+1d+1d+1 experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are \emph{spatially multiplexed} on the interference pattern of the projected state. Using the proposed scheme we performed, as a proof-of-principle, an experimental reconstruction of d=6−d=6-d=6−dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from 424242 to only 777.
We present a quantum state tomography method that enables the reconstruction of arbitrary d−dimensional quantum states encoded in the discretized transverse momentum of photons, by using only d+1 experimental settings. To this end, we identify a family of bases with the property that the outcomes of a projective measurement are spatially multiplexed on the interference pattern of the projected state. Using the proposed scheme, we performed, as a proof-of-principle, an experimental reconstruction of d=6−dimensional states, for which a complete set of mutually unbiased bases does not exist. We obtained fidelity values above 0.97 for both pure and mixed states, reducing the number of experimental settings from 42 to only 7.
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, which represents an improvement with respect to other similar methods and contributes to answering the question of how many observables are needed to uniquely determine any pure state.
We present a method for preparing arbitrary pure states of spatial qudits, namely, D-dimensional (Dgeqslant2D\\geqslant 2Dgeqslant2) quantum systems carrying information in the transverse momentum and position of single photons. For this purpose, a set of D slits with complex transmission are displayed on a spatial light modulator (SLM). In a recent work we have shown a method that requires a single phase-only SLM to control independently the complex coefficients which define the quantum state of dimension D. The amplitude information was codified by introducing phase gratings inside each slit, and the phase value of the complex transmission was added to the phase gratings. After a spatial filtering process, we obtained in the image plane the desired qudit state. Although this method has proven to be a good alternative to compact the previously reported architectures, it presents some features that could be improved. In this paper we present an alternative scheme to codify the required phase values that minimizes the effects of temporal phase fluctuations associated to the SLM where the codification is carried out. In this scheme, the amplitudes are set by appropriate phase gratings addressed at the SLM, while the relative phases are obtained by a lateral displacement of these phase gratings. We show that this method improves the quality of the prepared state and provides very high fidelities of preparation for any state. An additional advantage of this scheme is that a complete $2\\pi $ modulation is obtained by shifting the grating by one period; hence the encoding is not limited by the phase modulation range achieved by the SLM. Numerical simulations, that take into account the phase fluctuations, show high fidelities for thousands of qubit states covering the whole Bloch sphere surface. Similar analyses are performed for qudits with D = 3 and D = 7.
Spatial qudits are D-dimensional (D ≥ 2) quantum systems carrying information encoded in the discretized transverse momentum and position of single photons. We present a proof-of-principle demonstration of a method for preparing arbitrary pure states of such systems by using a single phase-only spatial light modulator (SLM). The method relies on the encoding of the complex transmission function corresponding to a given spatial qudit state onto a preset diffraction order of a phase-only grating function addressed at the SLM. Fidelities of preparation above 94% were obtained with this method, which is simpler, less costly, and more efficient than those that require two SLMs for the same purpose.