Measurement errors in entanglement-assisted electron microscopy

Abstract

The major resolution-limiting factor in cryoelectron microscopy of unstained biological specimens is radiation damage by the very electrons that are used to probe the specimen structure. To address this problem, an electron microscopy scheme that employs quantum entanglement to enable phase measurement precision beyond the standard quantum limit has recently been proposed [Phys. Rev. A 85, 043810]. Here we identify and examine in detail measurement errors that will arise in the scheme. An emphasis is given to considerations concerning inelastic scattering events because in general schemes assisted with quantum entanglement are known to be highly vulnerable to lossy processes. We find that the amount of error due both to elastic and inelastic scattering processes are acceptable provided that the electron beam geometry is properly designed. I IntroductionIn cryoelectron microscopy, unstained biological specimens are rapidly vitrified at cryogenic temperatures [1,2]. Consequently, artefacts due to heavymetal staining, desiccation, and other sample preparation processes are no longer an issue. However, the frozen, hydrated biological specimen, consisting mostly of light elements, scatters electrons weakly. Hence biological specimens generally are weak phase objects associated with low image contrast [3]. In this setting, the resolution is limited by radiation damage by the probe electrons [4] to approximately 5-10 nm in the case of single objects [5]. This leaves much to be desired because 2 nm resolution would be needed to identify molecules in frozen vitrified slices of the cell in cryoelectron tomography [6], or 0.8 nm resolution would be required to observe the secondary structure of a single protein molecule. The reason why radiation damage limits the resolution is that the 'safe' electron dose, which does not cause sizable damage to the specimen, is so small that the low-contrast image is dominated by shot noise. Shot noise is a manifestation of the particle nature of the electron and hence is fundamental.Several approaches to address the radiation damage problem are known. First, methods based on averaging, such as two-dimensional crystallography [7] and single-particle analysis [8], represent an established branch of methodology in structural biology. In favorable cases, these methods essentially attained atomic resolution [9]. However, in order to average out the noise, this approach requires at least thousands of copies of the molecule of interest without much structural variance and hence is not suited for soft or unique objects. Second, the advent of in-focus phase contrast electron microscopy [10,11,12] enabled researchers to see weak phase objects much clearer than hitherto possible. The reason is that it provides a well-behaving phase contrast transfer function (CTF) that does not fall to zero at low resolutions and does not oscillate at high resolutions. However, this method does not go beyond the standard quantum limit, as will be mentioned. Third and finally, the use of low acceleration vo...

Advantages of Multi-photon Detection Revealed by Fisher Information In Resolving Incoherent Sources

“…The high order correlation function can effectively depict the overlapped area between the sources. When the emitted light from the sources is coherented, the resolving ability can be enhanced by the factor of N with the * yshzhang@ustc.edu.cn help of detecting N -photon entangled states [16]. With incoherent light sources, the intensity of first order detecting is the summation of the each light's intensity [11,12].…”

Resilient quantum electron microscopy

“…There have recently been proposals of quantum electron microscopy (QEM) schemes that seek to approach the Heisenberg limit, where N ≃ δθ −1 . These proposals are based on either repeated use of single electrons [3][4][5][6][7][8][9][10], or the use of entanglement between electrons and superconducting qubits [11][12][13]. Both methods accumulate the small phase θ onto a quantum object k times, resulting in a phase kθ after k electron-passing events through the specimen, which is then measured.…”

“…Moreover, the thickness of the "damage layer" generated by gallium focused ion beam milling on the resultant specimen surface "could probably be kept to around 5nm" [24]. A previous estimation of QEM performance, which considered inelastic scattering processes, assumed t = 17.5 nm [13]. The acceptable specimen thickness should obviously be greater for wide applicability of QEM possibly into ECT.…”