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Single-qubit measurements are typically insufficient for inferring arbitrary quantum states of a multi-qubit system. We show that if the system can be fully controlled by driving a single qubit, then utilizing a local random pulse is almost always sufficient for complete quantum-state tomography. Experimental demonstrations of this principle are presented using a nitrogen-vacancy (NV) center in diamond coupled to a nuclear spin, which is not directly accessible. We report the reconstruction of a highly entangled state between the electron and nuclear spin with fidelity above 95%, by randomly driving and measuring the NV-center electron spin only. Beyond quantum-state tomography, we outline how this principle can be leveraged to characterize and control quantum processes in cases where the system model is not known.
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Semiconductor quantum dots are probably the preferred choice for interfacing anchored, matter spin qubits and flying photonic qubits. While full tomography of a flying qubit or light polarization is in general straightforward, matter spin tomography is a challenging and resource-consuming task. Here we present a novel all-optical method for conducting full tomography of quantum-dot-confined spins. Our method is applicable for electronic spin configurations such as the conduction-band electron, the valence-band hole, and for electron-hole pairs such as the bright and the dark exciton. We excite the spin qubit using short resonantly tuned, polarized optical pulse, which coherently converts the qubit to an excited qubit that decays by emitting a polarized single-photon. We perform the tomography by using two different orthogonal, linearly polarized excitations, followed by time-resolved measurements of the degree of circular polarization of the emitted light from the decaying excited qubit. We demonstrate our method on the dark exciton spin state with fidelity of 0.94, mainly limited by the accuracy of our polarization analyzers.
Quantum tomography is an essential experimental tool for testing any quantum technology implementations. 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 letter 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 (SLM) in terms of speed and efficiency, at the same time providing polarization insensitive operation.
We perform state tomography of an itinerant squeezed state of the microwave field prepared by a Josephson parametric amplifier (JPA). We use a second JPA as a pre-amplifier to improve the quantum efficiency of the field quadrature measurement (QM) from 2% to 36 +/- 4%. Without correcting for the detection inefficiency we observe a minimum quadrature variance which is 69 +/- 8% of the variance of the vacuum. We reconstruct the states density matrix by a maximum likelihood method and infer that the squeezed state has a minimum variance less than 40% of the vacuum, with uncertainty mostly caused by calibration systematics.
We introduce the concept of quantum field tomography, the efficient and reliable reconstruction of unknown quantum fields based on data of correlation functions. At the basis of the analysis is the concept of continuous matrix product states, a complete set of variational states grasping states in quantum field theory. We innovate a practical method, making use of and developing tools in estimation theory used in the context of compressed sensing such as Prony methods and matrix pencils, allowing us to faithfully reconstruct quantum field states based on low-order correlation functions. In the absence of a phase reference, we highlight how specific higher order correlation functions can still be predicted. We exemplify the functioning of the approach by reconstructing randomised continuous matrix product states from their correlation data and study the robustness of the reconstruction for different noise models. We also apply the method to data generated by simulations based on continuous matrix product states and using the time-dependent variational principle. The presented approach is expected to open up a new window into experimentally studying continuous quantum systems, such as encountered in experiments with ultra-cold atoms on top of atom chips. By virtue of the analogy with the input-output formalism in quantum optics, it also allows for studying open quantum systems.
Quantum State Tomography is the task of determining an unknown quantum state by making measurements on identical copies of the state. Current algorithms are costly both on the experimental front -- requiring vast numbers of measurements -- as well as in terms of the computational time to analyze those measurements. In this paper, we address the problem of analysis speed and flexibility, introducing textit{Neural Adaptive Quantum State Tomography} (NA-QST), a machine learning based algorithm for quantum state tomography that adapts measurements and provides orders of magnitude faster processing while retaining state-of-the-art reconstruction accuracy. Our algorithm is inspired by particle swarm optimization and Bayesian particle-filter based adaptive methods, which we extend and enhance using neural networks. The resampling step, in which a bank of candidate solutions -- particles -- is refined, is in our case learned directly from data, removing the computational bottleneck of standard methods. We successfully replace the Bayesian calculation that requires computational time of $O(mathrm{poly}(n))$ with a learned heuristic whose time complexity empirically scales as $O(log(n))$ with the number of copies measured $n$, while retaining the same reconstruction accuracy. This corresponds to a factor of a million speedup for $10^7$ copies measured. We demonstrate that our algorithm learns to work with basis, symmetric informationally complete (SIC), as well as other types of POVMs. We discuss the value of measurement adaptivity for each POVM type, demonstrating that its effect is significant only for basis POVMs. Our algorithm can be retrained within hours on a single laptop for a two-qubit situation, which suggests a feasible time-cost when extended to larger systems. It can also adapt to a subset of possible states, a choice of the type of measurement, and other experimental details.
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