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Register a new userMeasurement errors in entanglement-assisted electron microscopy
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Hiroshi Okamoto Dr. Sc.
Publication date
2014
fields
Physics
and research's language is
English
Authors
Hiroshi Okamoto
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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 textbf{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.
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A notorious problem in high-resolution biological electron microscopy is radiation damage to the specimen caused by probe electrons. Hence, acquisition of data with minimal number of electrons is of critical importance. Quantum approaches may represent the only way to improve the resolution in this context, but all proposed schemes to date demand delicate control of the electron beam in highly unconventional electron optics. Here we propose a scheme that involves a flux qubit based on a radio-frequency superconducting quantum interference device (rf-SQUID), inserted in essentially a conventional transmission electron microscope. The scheme significantly improves the prospect of realizing a quantum-enhanced electron microscope for radiation-sensitive specimens.
The present paper is devoted to investigation of the entropy reduction and entanglement-assisted classical capacity (information gain) of continuous variable quantum measurements. These quantities are computed explicitly for multimode Gaussian measurement channels. For this we establish a fundamental property of the entropy reduction of a measurement: under a restriction on the second moments of the input state it is maximized by a Gaussian state (providing an analytical expression for the maximum). In the case of one mode, the gain of entanglement assistance is investigated in detail.
We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. We prove that this measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron scattering. We prove that it does not depend on the azimuthal rotation angle of the second electron spin relative to the first electron spin before scattering. Finally, we specify how to find a spin correlation tensor and the related measure of a quantum entanglement in an experiment with electron-electron scattering.
We show how entanglement shared between encoder and decoder can simplify the theory of quantum error correction. The entanglement-assisted quantum codes we describe do not require the dual-containing constraint necessary for standard quantum error correcting codes, thus allowing us to ``quantize all of classical linear coding theory. In particular, efficient modern classical codes that attain the Shannon capacity can be made into entanglement-assisted quantum codes attaining the hashing bound (closely related to the quantum capacity). For systems without large amounts of shared entanglement, these codes can also be used as catalytic codes, in which a small amount of initial entanglement enables quantum communication.
In this dissertation, I present a general method for studying quantum error correction codes (QECCs). This method not only provides us an intuitive way of understanding QECCs, but also leads to several extensions of standard QECCs, including the operator quantum error correction (OQECC), the entanglement-assisted quantum error correction (EAQECC). Furthermore, we can combine both OQECC and EAQECC into a unified formalism, the entanglement-assisted operator formalism. This provides great flexibility of designing QECCs for different applications. Finally, I show that the performance of quantum low-density parity-check codes will be largely improved using entanglement-assisted formalism.
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