Optimal Frames for Polarization State Reconstruction

Foreman, Matthew R.; Favaro, Alberto; Aiello, Andrea

doi:10.1103/physrevlett.115.263901

Cited by 77 publications

(49 citation statements)

References 42 publications

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“…8(b). The equal spacing of vectors around the Bloch sphere gives the device maximum robustness to errors in the tomography procedure [26], by essentially realizing non-local measurements. This can be confirmed by calculating the condition number of the transfer function of the chip, lower 5 values of which correspond to higher robustness of the state reconstruction to measurement errors.…”

Section: Arxiv:170403595v[physicsoptics] 12 Apr 2017mentioning

confidence: 99%

Scalable on-chip quantum state tomography

Titchener

Gräfe

Heilmann

et al. 2016

Frontiers in Optics 2016

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Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing [1][2][3] and the information required to fully describe these systems scales exponentially with qubit number [4]. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements [5], becoming highly resource demanding for large numbers of qubits [6]. Here we propose a novel and scalable method to characterize quantum systems, where the complexity of the measurement process only scales linearly with the number of qubits. We experimentally demonstrate an integrated photonic chip capable of measuring two-and three-photon quantum states with reconstruction fidelity of 99.67%. arXiv:1704.03595v[physics.optics] 12 Apr 2017The standard way to characterize a quantum system is known as quantum state tomography [5,7]. It involves measuring expectation values of a complete set of observables and using these to reconstruct the system's density matrix [8][9][10][11][12][13]. To characterize an N -qubit state, 2 2N different observables are measured [8], thus the measurement apparatus must be reconfigured exponentially many times, which is impractical for large states. Furthermore many of the expectation values measured will be vanishingly small, and thus contribute little useful information. Finally, even if all the measurements can be completed, the task of reconstructing the density matrix from measurement data becomes computationally challenging for high qubit-number states [6].New approaches to quantum state tomography are being developed in an effort to increase its practicality and efficiency. Some approaches seek to avoid unnecessary measurements by assuming that the system is in particular low rank states, such as sparse states [14,15] measurements have increased error robustness relative to using only local qubit measurements, and thus can be completed in less time [19]. The computational burden of inverting large data sets to find the density matrix is reduced with simple real-time optimization algorithms in self guided tomography, or can be completely avoided with systems for direct projection of density matrix parameters [20][21][22]. However all these approaches rely on a common measurement paradigm, whereby different characteristics of a system are measured sequentially, thus they become exponentially complex to implement as the number of parameters in the density matrix scales exponentially with qubit number.Here we present a quantum tomography method with complexity that scales linearly with qubit number. This is achieved by leveraging quantum systems' greatest strength, the simultaneous occupation of exponentially many states, in the measurement process. Instead of preforming a sequence of different measurements on the state, we design a single static measurement system [Fig. 7(a)] that preforms...

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Section: Arxiv:170403595v[physicsoptics] 12 Apr 2017mentioning

confidence: 99%

Scalable on-chip quantum state tomography

Titchener

Gräfe

Heilmann

et al. 2016

Frontiers in Optics 2016

View full text Add to dashboard Cite

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“…2b. The equal spacing of vectors around the Bloch sphere gives the device maximum robustness to errors in the tomography procedure, 29 by essentially realizing non-local measurements. This can be confirmed by calculating the condition number of the transfer function of the chip, lower values of which correspond to higher robustness of the state reconstruction to measurement errors.…”

Section: Resultsmentioning

confidence: 99%

Scalable on-chip quantum state tomography

et al. 2018

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Quantum information systems are on a path to vastly exceed the complexity of any classical device. The number of entangled qubits in quantum devices is rapidly increasing, and the information required to fully describe these systems scales exponentially with qubit number. This scaling is the key benefit of quantum systems, however it also presents a severe challenge. To characterize such systems typically requires an exponentially long sequence of different measurements, becoming highly resource demanding for large numbers of qubits. Here we propose and demonstrate a novel and scalable method for characterizing quantum systems based on expanding a multi-photon state to larger dimensionality. We establish that the complexity of this new measurement technique only scales linearly with the number of qubits, while providing a tomographically complete set of data without a need for reconfigurability. We experimentally demonstrate an integrated photonic chip capable of measuring two-and three-photon quantum states with statistical reconstruction fidelity of 99.71%.

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“…22,23 Ellipsometric measurements are becoming more accurate due to the development of better and improved calibration procedures. [24][25][26][27][28][29][30] When light of high enough intensity falls on a material, its optical response can be nonlinear. The order of optical nonlinearity depends on the incident intensity, symmetry of the material and the orientation of the crystal axis with respect to the propagation direction of light.…”

Section: Introductionmentioning

confidence: 99%

Generalized Stokes vector for three photon process

Shaji

Ismail

Satyanarayana

et al. 2017

J. Nonlinear Optic. Phys. Mat.

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Stokes Mueller formalism is used to measure the optical properties of materials by probing the sensitive changes in the polarization state of light after scattering from the medium. The formalism can be extended to nonlinear scattering processes involving two and three photon processes also. In this paper, we derive the Stokes vector, viz. triple Stokes vector analytically from quantum theory of light for a three photon process. The state of polarization of light, with three simultaneous photons, incident on a material is described by triple Stokes vector, and has 16 components involving cubes of intensities dependence. The response of a material for the scattered light in a three photon process is described by 4 × 16 Mueller matrix. Polarization in Polarization out (PIPO) experiments can be carried out to determine the elements of Mueller matrix. We identify 16 independent points on Poincare sphere and construct triple Stokes vector for each point. Four measurements are done to determine the linear Stokes vector of scattered light, where the 16 polarization states are represented by triple Stokes vector and this determines the Mueller matrix of the sample.

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Optimal Frames for Polarization State Reconstruction

Cited by 77 publications

References 42 publications

Scalable on-chip quantum state tomography

Scalable on-chip quantum state tomography

Scalable on-chip quantum state tomography

Generalized Stokes vector for three photon process

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