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Optics Express

Minimal state tomography of spatial qubits using a spatial light modulator

Wanderson M. Pimenta, Breno Marques, Marcio Carvalho, Mariana R. Barros, J. G. Fonseca, José Ferraz, Marcelo Terra Cunha, Sebastião Pádua

Published Nov 8, 2010• 30 citations
Publisher

Abstract

We report minimal quantum state tomography with spatial qubits created by a pair of parametric down converted twin-photons passing through a double-slit. A novel experimental setup is used, which includes a Spatial Light Modulator, as a fundamental tool, to reconstruct the state density matrix. The theory needed to perform a minimal quantum tomography is described. The density matrix is experimentally obtained for the two-qubit photonic states in spatial variables.

DOI
10.1364/oe.18.024423

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We report minimal quantum state tomography with spatial qubits created by a pair of parametric down converted twin-photons passing through a double-slit. A novel experimental setup is used, which includes a Spatial Light Modulator, as a fundamental tool, to reconstruct the state density matrix. The theory needed to perform a minimal quantum tomography is described. The density matrix is experimentally obtained for the two-qubit photonic states in spatial variables.
In a recent letter [Phys. Rev. Lett. 94, 100501 (2005)], we presented a scheme for generating pure entangled states of spatial qudits using transverse correlations of parametric down-converted photons. Here we show how the modication of this scheme can be used to generate mixed states and we investigate the state determination for composite systems of two spatial qubits, motivated by the fact that quantum information protocols may be easier to be implemented for this case. By means of local operations on the twin photons we were able to perform the quantum tomography process to reconstruct the density matrix of a mixed state of two spatial qubits.
An experimental demonstration of two-qutrit state tomography via one-qutrit symmetric informationally complete positive operator-valued measure (SIC-POVM) is presented. A two-qutrit state is encoded in the transversal paths of a spontaneous parametric down-converted photon pair. A spatial light modulator allows us to implement the necessary 81 POVM elements to reconstruct the state. The quality of the reconstruction is evaluated by comparing independent measurements with the predicted results calculated with the reconstructed state. Entanglement in the system is calculated via negativity and generalized robustness from the two-qutrit reconstructed density operator.
We present an experimental study of the nonclassical correlations of a pair of spatial qubits formed by passing two down-converted photons through a pair of double slits. After confirming the entanglement generated in our setup by quantum tomography using separate measurements of the slit images and the interference patterns, we show that the complete Hilbert space of the spatial qubits can be accessed by measurements performed in a single plane between the image plane and the focal plane of a lens. Specifically, it is possible to obtain both the which-path and the interference information needed for quantum tomography in a single scan of the transversal distribution of photon coincidences. Since this method can easily be extended to multidimensional systems, it may be a valuable tool in the application of spatial qudits to quantum-information processes.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possible paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.
Quantum tomography is an essential experimental tool for testing any quantum technology implementation. Transverse spatial quantum states of light play a key role in many experiments in the field of quantum information as well as in free-space optical communications. In this paper we propose and experimentally demonstrate the tomography of spatial quantum states with a deformable mirror. It may be used to significantly outperform the conventional method with a spatial light modulator in terms of speed and efficiency, at the same time providing polarization insensitive operation.
Quantum state tomography (QST), the process through which the density matrix of a quantum system is characterized from measurements of specific observables, is a fundamental pillar in the fields of quantum information and computation. In this work, we propose a simple QST method to reconstruct the density matrix of two qubits encoded in the polarization and path degrees of freedom of a single photon, which can be realized with a single linear-optical setup. We demonstrate that the density matrix can be fully described in terms of the Stokes parameters related to the two possibles paths of the photon, together with a quantum version of the two-point Stokes parameters introduced here. Our findings put forward photonic circuits for the investigation of the dynamics of open quantum systems.