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

Varga, Juan José Miguel, Rebón, Lorena, Solís Prosser, M. A., Neves, L., Ledesma, Silvia Adriana, Claudio Iemmi

Published Jan 1, 2014• 7 citations
OpenAlex

Abstract

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.

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

J J M Varga, L Rebón, M A Solís-Prosser +3 more

We present a method for preparing arbitrary pure states of spatial qudits, namely, D -dimensional ( ) 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 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.

arXiv:1406.3596•Journal of Physics B Atomic Molecular and Optical Physics•Nov 7, 2014•15 citations

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J. J. M. Varga, M. A. Solís-Prosser, Lorena Rebón +4 more

We present a new method for preparing multidimensional spatial qudits by means of a single phase-only spatial light modulator (SLM). This method improves previous ones that use two SLMs, one working in amplitude regime and the other in phase regime. To that end, we addressed diffraction gratings on the slits that define the state and then we performed a spatial filtering in the Fourier plane. The amplitude of the coefficients of the quantum state are determined by the modulation deep of the diffraction gratings, and the relative phase is the mean phase value of the diffraction gratings. This encoding result to be more compact, less expensive and use the photons more efficiently.

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

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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.

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We propose a method for preparing mixed quantum states of arbitrary dimension $D$ ($D\ensuremath{\ge}2$) which are codified in the discretized transverse momentum and position of single photons, once they are sent through an aperture with $D$ slits. Following our previous technique we use a programmable single phase-only spatial light modulator (SLM) to define the aperture and set the complex transmission amplitude of each slit, allowing the independent control of the complex coefficients that define the quantum state. Since these SLMs give us the possibility to dynamically vary the complex coefficients of the state during the measurement time, we can generate not only pure states but also quantum states compatible with a mixture of pure quantum states. Therefore, by using these apertures varying on time according to a probability distribution, we have experimentally obtained $D$-dimensional quantum states with purities that depend on the parameters of the distribution through a clear analytical expression. This fact allows us to easily customize the states to be generated. Moreover, the method offers the possibility of working without changing the optical setup between pure and mixed states, or when the dimensionality of the states is increased. The obtained results show a quite good performance of our method at least up to dimension $D=11$, being the fidelity of the prepared states $F>0.98$ in every case.

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Proposal for automated transformations on single-photon multipath qudits

Roberto D. Baldijão, G. F. Borges, Breno Marques +3 more

We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths by using a stable interferometric network, and filtering out the unwanted diffraction orders. The automation feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations, and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyze how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than is possible with a SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.

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Simulating Universal Quantum Gate Sets on Photonic OAM Qubits: Single-Qubit and Multi-Qubit Operations via Spatial Light Modulator Phase Holography

Saleha Maqsood, Muhammad Kamran, Tahir Malik

Spatial light modulators (SLMs) have emerged as reconfigurable platforms for photonic quantum information processing, offering software-defined control over the orbital angular momentum (OAM) of light encoded in Laguerre-Gaussian (LG) beams. This paper presents a comprehensive simulation and hardware-grounded fidelity analysis of quantum gate operations implemented on the HOLOEYE LC 2012 transmissive SLM. A realistic three-channel noise model comprising 8-bit quantisation noise, twisted-nematic (TN) electronic and thermal noise, and phase-wrap clipping error is obtained from the manufacturer's datasheet without free-parameter fitting, yielding a total noise of $σ_{\text{total}} = 92.4\text{mrad}$. The complete universal single-qubit gate set $\{X, Y, Z, S, T, H\}$ and two-qubit entangling gates $\{\text{CNOT}, \text{CZ}, \text{SWAP}\}$ are simulated on a $512 \times 512$ computational grid. Results show that predicted gate fidelity are in the range of $F = 0.9914\text{--}0.9936$, with fork grating gates limited primarily by TN noise and phase gates achieving higher fidelity owing to zero phase-wrap clipping error. In addition, Bell state preparation via the H-CNOT circuit achieves $F(Φ^+) = 0.9914$ after two SLM interactions. We benchmark our obtained results against six published experimental studies spanning the 78%--99.6% fidelity range. Finally, a wavelength-dependent analysis identifies 450--532 nm operation as the optimal regime for this device.

quant-pharXiv:2606.26088•Jun 25, 2026•0 citations
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 2pi2\\pi 2pi 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.
We present a method for preparing arbitrary pure states of spatial qudits, namely, D -dimensional ( ) 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 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.
We present a new method for preparing multidimensional spatial qudits by means of a single phase-only spatial light modulator (SLM). This method improves previous ones that use two SLMs, one working in amplitude regime and the other in phase regime. To that end, we addressed diffraction gratings on the slits that define the state and then we performed a spatial filtering in the Fourier plane. The amplitude of the coefficients of the quantum state are determined by the modulation deep of the diffraction gratings, and the relative phase is the mean phase value of the diffraction gratings. This encoding result to be more compact, less expensive and use the photons more efficiently.
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.
We propose a method for preparing mixed quantum states of arbitrary dimension DDD ($D\ensuremath{\ge}2$) which are codified in the discretized transverse momentum and position of single photons, once they are sent through an aperture with DDD slits. Following our previous technique we use a programmable single phase-only spatial light modulator (SLM) to define the aperture and set the complex transmission amplitude of each slit, allowing the independent control of the complex coefficients that define the quantum state. Since these SLMs give us the possibility to dynamically vary the complex coefficients of the state during the measurement time, we can generate not only pure states but also quantum states compatible with a mixture of pure quantum states. Therefore, by using these apertures varying on time according to a probability distribution, we have experimentally obtained DDD-dimensional quantum states with purities that depend on the parameters of the distribution through a clear analytical expression. This fact allows us to easily customize the states to be generated. Moreover, the method offers the possibility of working without changing the optical setup between pure and mixed states, or when the dimensionality of the states is increased. The obtained results show a quite good performance of our method at least up to dimension D=11D=11D=11, being the fidelity of the prepared states F>0.98F>0.98F>0.98 in every case.
We propose a method for implementing automated state transformations on single-photon multipath qudits encoded in a one-dimensional transverse spatial domain. It relies on transferring the encoding from this domain to the orthogonal one by applying a spatial phase modulation with diffraction gratings, merging all the initial propagation paths by using a stable interferometric network, and filtering out the unwanted diffraction orders. The automation feature is attained by utilizing a programmable phase-only spatial light modulator (SLM) where properly designed diffraction gratings displayed on its screen will implement the desired transformations, including, among others, projections, permutations, and random operations. We discuss the losses in the process which is, in general, inherently nonunitary. Some examples of transformations are presented and, considering a realistic scenario, we analyze how they will be affected by the pixelated structure of the SLM screen. The method proposed here enables one to implement much more general transformations on multipath qudits than is possible with a SLM alone operating in the diagonal basis of which-path states. Therefore, it will extend the range of applicability for this encoding in high-dimensional quantum information and computing protocols as well as fundamental studies in quantum theory.
Spatial light modulators (SLMs) have emerged as reconfigurable platforms for photonic quantum information processing, offering software-defined control over the orbital angular momentum (OAM) of light encoded in Laguerre-Gaussian (LG) beams. This paper presents a comprehensive simulation and hardware-grounded fidelity analysis of quantum gate operations implemented on the HOLOEYE LC 2012 transmissive SLM. A realistic three-channel noise model comprising 8-bit quantisation noise, twisted-nematic (TN) electronic and thermal noise, and phase-wrap clipping error is obtained from the manufacturer's datasheet without free-parameter fitting, yielding a total noise of σtotal=92.4mradσ_{\text{total}} = 92.4\text{mrad}σtotal​=92.4mrad. The complete universal single-qubit gate set {X,Y,Z,S,T,H}\{X, Y, Z, S, T, H\}{X,Y,Z,S,T,H} and two-qubit entangling gates {CNOT,CZ,SWAP}\{\text{CNOT}, \text{CZ}, \text{SWAP}\}{CNOT,CZ,SWAP} are simulated on a 512×512512 \times 512512×512 computational grid. Results show that predicted gate fidelity are in the range of F=0.9914–0.9936F = 0.9914\text{--}0.9936F=0.9914–0.9936, with fork grating gates limited primarily by TN noise and phase gates achieving higher fidelity owing to zero phase-wrap clipping error. In addition, Bell state preparation via the H-CNOT circuit achieves F(Φ+)=0.9914F(Φ^+) = 0.9914F(Φ+)=0.9914 after two SLM interactions. We benchmark our obtained results against six published experimental studies spanning the 78%--99.6% fidelity range. Finally, a wavelength-dependent analysis identifies 450--532 nm operation as the optimal regime for this device.