We used quantum process tomography to investigate and identify the function of a nonideal two-qubit quantum-state filters subject to various degree of decoherence. We present a simple decoherence model that explains the experimental results and point out that a beamsplitter followed by a post-selection process is not, as commonly believed, a singlet-state filter. In the ideal case it is a triplet-state filter.
Using a Hong-Ou-Mandel interferometer, we apply the techniques of quantum process tomography to characterize errors and decoherence in a prototypical two-photon operation, a singlet-state filter. The quantum process tomography results indicate a large asymmetry in the process and also the required operation to correct for this asymmetry. Finally, we quantify errors and decoherence of the filtering operation after this modification.
We review an experimental technique used to correct state preparation and measurement errors on gate-based quantum computers, and discuss its rigorous justification. Within a specific biased quantum measurement model, we prove that nonideal measurement of an arbitrary $n$-qubit state is equivalent to ideal projective measurement followed by a classical Markov process $Γ$ acting on the output probability distribution. Measurement errors can be removed, with rigorous justification, if $Γ$ can be learned and inverted. We show how to obtain $Γ$ from gate set tomography (R. Blume-Kohout et al., arX…
Several Bayesian estimation based heuristics have been developed to perform quantum state tomography (QST). Their ability to quantify uncertainties using region estimators and include a priori knowledge of the experimentalists makes this family of methods an attractive choice for QST. However, specialized techniques for pure states do not work well for mixed states and vice versa. In this paper, we present an adaptive particle filter (PF) based QST protocol which improves the scaling of fidelity compared to nonadaptive Bayesian schemes for arbitrary multi-qubit states. This is due to the proto…
We present and demonstrate a method for optical homodyne tomography based on the inverse Radon transform. Different from the usual filtered back-projection algorithm, this method uses an appropriate polynomial series to expand the Wigner function and the marginal distribution and discretize Fourier space. We show that this technique solves most technical difficulties encountered with kernel deconvolution based methods and reconstructs overall better and smoother Wigner functions. We also give estimators of the reconstruction errors for both methods and show improvement in noise handling proper…
We present a novel quantum tomographic reconstruction method based on Bayesian inference via the Kalman filter update equations. The method not only yields the maximum likelihood/optimal Bayesian reconstruction, but also a covariance matrix expressing the measurement uncertainties in a complete way. From this covariance matrix the error bars on any derived quantity can be easily calculated. This is a first step towards the broader goal of devising an omnibus reconstruction method that could be adapted to any tomographic setup with little effort and that treats measurement uncertainties in a st…
Photons carrying orbital angular momentum (OAM) are excellent qudits and are widely used in several applications, such as long distance quantum communication, $d$-dimensional teleportation and high-resolution imaging and metrology. All these protocols rely on quantum tomography to characterise the OAM state, which currently requires complex measurements involving spatial light modulators and mode filters. To simplify the measurement and characterisation of OAM states, here we apply a recent tomography protocol [Asadian et al., \pra {\bf 94}, 010301 (2016)]. Our scheme for OAM tomography in $d$…
The implementation of optimal statistical inference protocols for high-dimensional quantum systems is often computationally expensive. To avoid the difficulties associated with optimal techniques, here I propose an alternative approach to quantum estimation and detection based on Volterra filters. Volterra filters have a clear hierarchy of computational complexities and performances, depend only on finite-order correlation functions, and are applicable to systems with no simple Markovian model. These features make Volterra filters appealing alternatives to optimal nonlinear protocols for the i…
Conditional quantum optical processes enable a wide range of technologies from generation of highly non-classical states to implementation of quantum logic operations. The process fidelity that can be achieved in a realistic implementation depends on a number of system parameters. Here we experimentally examine Fock-state filtration, a canonical example of a broad class of conditional quantum operations acting on a single optical field mode. This operation is based upon interference of the mode to be manipulated with an auxiliary single-photon state at a beam splitter, resulting in the entangl…
We theoretically and experimentally investigate conditional enhancement of overall coherence of quantum states by probabilistic quantum operations that apply to the input state a quantum filter diagonal in the basis of incoherent states. We identify the optimal filters that for a given probability of successful filtering maximize the output coherence. We verify the performance of the studied quantum filters in a proof-of-principle experiment with linear optics, where a pair of two-level quantum systems is represented by polarization states of two photons. We comprehensively characterize the im…
We report an experiment that uses the environmental selection, a key concept in the recent theory of quantum Darwinism, as a mechanism to realize the entanglement filter, a useful quantum information device that filters out certain entangled states. In the experiment, the environment of two qubits is controlled to favor an entangled state and kill other competing components in the input state. The initial state has vanishing entanglement, but the state surviving after interaction with the environment is close to a maximally entangled state, with an entanglement fidelity of $(94.7\pm 1.9)%$ mea…
We propose a scheme for both distilling and quantifying entanglement, applicable to individual copies of an arbitrary unknown two-qubit state. It is realized in a usual two-qubit interferometry with local filtering. Proper filtering operation for the maximal distillation of the state is achieved, by erasing single-qubit interference, and then the concurrence of the state is determined directly from the visibilities of two-qubit interference. We compare the scheme with full state tomography.
Tomography of a quantum state is usually based on positive operator-valued measure (POVM) and on their experimental statistics. Among the available reconstructions, the maximum-likelihood (MaxLike) technique is an efficient one. We propose an extension of this technique when the measurement process cannot be simply described by an instantaneous POVM. Instead, the tomography relies on a set of quantum trajectories and their measurement records. This model includes the fact that, in practice, each measurement could be corrupted by imperfections and decoherence, and could also be associated with …
We develop an enhanced technique for characterizing quantum optical processes based on probing unknown quantum processes only with coherent states. Our method substantially improves the original proposal [M. Lobino et al., Science 322, 563 (2008)], which uses a filtered Glauber-Sudarshan decomposition to determine the effect of the process on an arbitrary state. We introduce a new relation between the action of a general quantum process on coherent state inputs and its action on an arbitrary quantum state. This relation eliminates the need to invoke the Glauber-Sudarshan representation for sta…
We demonstrate a Fock-state filter which is capable of preferentially blocking single photons over photon pairs. The large conditional nonlinearities are based on higher-order quantum interference, using linear optics, an ancilla photon, and measurement. We demonstrate that the filter acts coherently by using it to convert unentangled photon pairs to a path-entangled state. We quantify the degree of entanglement by transforming the path information to polarisation information, applying quantum state tomography we measure a tangle of T=(20+/-9)%.
Accessing electronic entanglement via photo-assisted two-electron tomography
Univ Lyon, Ens de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique（里昂大学，巴黎高等师范学院里昂分校，克洛德·贝尔纳里昂大学，法国国家科学研究中心，物理实验室）；Laboratoire de Physique de l’Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris（巴黎高等师范学院物理实验室，巴黎文理研究大学，法国国家科学研究中心，索邦大学，巴黎大学）；Laboratoire PhLam (UMR 8523), Université de Lille（PhLam实验室（联合研究单位8523），里尔大学）
Precisely engineered mechanical oscillators keep time, filter signals, and sense motion, making them an indispensable part of today's technological landscape. These unique capabilities motivate bringing mechanical devices into the quantum domain by interfacing them with engineered quantum circuits. Proposals to combine microwave-frequency mechanical resonators with superconducting devices suggest the possibility of powerful quantum acoustic processors. Meanwhile, experiments in several mechanical systems have demonstrated quantum state control and readout, phonon number resolution, and phonon-…
Deep Quantum Labs（深度量子实验室）；Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；M. V. Lomonosov Moscow State University（莫斯科国立罗蒙诺索夫大学）；University of Milan-Bicocca（米兰比可卡大学）
Quantum tomography is currently ubiquitous for testing any implementation of a quantum information processing device. Various sophisticated procedures for state and process reconstruction from measured data are well developed and benefit from precise knowledge of the model describing state preparation and the measurement apparatus. However, physical models suffer from intrinsic limitations as actual measurement operators and trial states cannot be known precisely. This scenario inevitably leads to state-preparation-and-measurement (SPAM) errors degrading reconstruction performance. Here we dev…
