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Register a new userCompressed sensing of twisted photons
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Added by
Luis L. Sanchez. Soto
Publication date
2018
fields
Physics
and research's language is
English
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The ability to completely characterize the state of a quantum system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing inspired method to ascertain any rank-deficient qudit state, which we experimentally encode in photonic orbital angular momentum. We efficiently reconstruct these qudit states from a few scans with an intensified CCD camera. Since it requires only a few intensity measurements, our technique would provide an easy and accurate way to identify quantum sources, channels, and systems.
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In the light of the progress in quantum technologies, the task of verifying the correct functioning of processes and obtaining accurate tomographic information about quantum states becomes increasingly important. Compressed sensing, a machinery derived from the theory of signal processing, has emerged as a feasible tool to perform robust and significantly more resource-economical quantum state tomography for intermediate-sized quantum systems. In this work, we provide a comprehensive analysis of compressed sensing tomography in the regime in which tomographically complete data is available with reliable statistics from experimental observations of a multi-mode photonic architecture. Due to the fact that the data is known with high statistical significance, we are in a position to systematically explore the quality of reconstruction depending on the number of employed measurement settings, randomly selected from the complete set of data, and on different model assumptions. We present and test a complete prescription to perform efficient compressed sensing and are able to reliably use notions of model selection and cross-validation to account for experimental imperfections and finite counting statistics. Thus, we establish compressed sensing as an effective tool for quantum state tomography, specifically suited for photonic systems.
Long-range correlated errors can severely impact the performance of NISQ (noisy intermediate-scale quantum) devices, and fault-tolerant quantum computation. Characterizing these errors is important for improving the performance of these devices, via calibration and error correction, and to ensure correct interpretation of the results. We propose a compressed sensing method for detecting two-qubit correlated dephasing errors, assuming only that the correlations are sparse (i.e., at most s pairs of qubits have correlated errors, where s << n(n-1)/2, and n is the total number of qubits). In particular, our method can detect long-range correlations between any two qubits in the system (i.e., the correlations are not restricted to be geometrically local). Our method is highly scalable: it requires as few as m = O(s log n) measurement settings, and efficient classical postprocessing based on convex optimization. In addition, when m = O(s log^4(n)), our method is highly robust to noise, and has sample complexity O(max(n,s)^2 log^4(n)), which can be compared to conventional methods that have sample complexity O(n^3). Thus, our method is advantageous when the correlations are sufficiently sparse, that is, when s < O(n^(3/2) / log^2(n)). Our method also performs well in numerical simulations on small system sizes, and has some resistance to state-preparation-and-measurement (SPAM) errors. The key ingredient in our method is a new type of compressed sensing measurement, which works by preparing entangled Greenberger-Horne-Zeilinger states (GHZ states) on random subsets of qubits, and measuring their decay rates with high precision.
Compressed sensing is a processing method that significantly reduces the number of measurements needed to accurately resolve signals in many fields of science and engineering. We develop a two-dimensional (2D) variant of compressed sensing for multidimensional electronic spectroscopy and apply it to experimental data. For the model system of atomic rubidium vapor, we find that compressed sensing provides significantly better resolution of 2D spectra than a conventional discrete Fourier transform from the same experimental data. We believe that by combining powerful resolution with ease of use, compressed sensing can be a powerful tool for the analysis and interpretation of ultrafast spectroscopy data.
Real-time sensing of ultra-wideband radio-frequency signal with high frequency resolution is challenging, which is confined by the sampling rate of electronic analog-to-digital converter and the capability of digital signal processing. By combining quantum mechanics with compressed sensing, quantum compressed sensing is proposed for wideband radio-frequency signal frequency measurement. By using an electro-optical crystal as a sensor which modulates the wave function of the coherent photons with the signal to be measured. The frequency spectrum could be recovered by detecting the modulated sparse photons with a low time-jitter single-photon detector and a time-to-digital converter. More than 50 GHz real-time analysis bandwidth is demonstrated with the Fourier transform limit resolution. The further simulation shows it can be extended to more than 300 GHz with the present technologies.
We report on an experiment in which orbital angular momentum of light is mapped at the single-photon level into and out of a cold atomic ensemble. Based on the dynamic electromagnetically-induced transparency protocol, the demonstrated optical memory enables the reversible mapping of Laguerre-gaussian modes with preserved handedness of the helical phase structure. The demonstrated capability opens the possibility to the storage of qubits encoded as superpositions of orbital angular momentum states and to multi-dimensional light-matter interfacing.
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