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arXiv:1805.11286 · Optics Express

Informationally symmetrical Bell state preparation and measurement

Yong‐Su Kim, Tanumoy Pramanik, Young‐Wook Cho, Ming Yang, Sang-Wook Han, Sang‐Yun Lee, Min-Sung Kang, Sung Moon

Published Oct 26, 2018• 30 citations
arXivHTMLPDF

Abstract

Bell state measurement (BSM) plays crucial roles in photonic quantum information processing. The standard linear optical BSM is based on Hong-Ou-Mandel interference where two photons meet and interfere at a beamsplitter (BS). However, a generalized two-photon interference is not based on photon-photon interaction, but interference between two-photon probability amplitudes. Therefore, it might be possible to implement BSM without interfering photons at a BS. Here, we investigate a linear optical BSM scheme which does not require two photon overlapping at a BS. By unleashing the two photon coexistence condition, it can be symmetrically divided into two parties. The symmetrically dividable property suggests an informationally symmetrical BSM between remote parties without a third party. We also present that our BSM scheme can be used for Bell state preparation between remote parties without a third party. Since our BSM scheme can be easily extended to multiple photons, it can be useful for various quantum communication applications.

DOI
10.1364/oe.26.029539

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Rotation-symmetric cat (RS-cat) codes are a bosonic-code platform for quantum information processing, combining finite-energy realizability with robustness against photon loss through their discrete rotational symmetry. For applications in long-distance quantum communication and fusion-based quantum computation (FBQC), efficient Bell state measurement (BSM) is a key primitive. In this work, we consider a BSM protocol for RS-cat codes using only a half beam splitter (HBS) and photon-number-resolving detectors (PNRDs). By exploiting the characteristic photon-number structure induced by the discrete rotational symmetry of RS-cat codes, our protocol extracts both photon-number modulo and phase information for Bell-state discrimination. We show that, under ideal loss-free conditions, the proposed BSM protocol becomes deterministic for arbitrary symmetry order NNN for sufficiently large amplitudes ααα. We further numerically evaluate the success probability under photon loss and identify the loss regime in which higher-order RS-cat codes provide an advantage. Finally, we show that post-selection can enhance the success probability.
Fault tolerance is essential for scalable quantum technologies and is enabled by quantum error-correction codes. Bell-state measurements (BSMs) are a fundamental building block for modern quantum technologies such as measurement-based quantum computation and fusion-based quantum computation, as well as quantum networks. Therefore, performing BSMs on error-corrected qubits is a necessary step for achieving fault tolerance in these applications. In this work, we realise a logical BSM using linear optics, based on a two-qubit repetition code, an instance of a quantum parity code that allows detection of bit-flip errors, and experimentally achieve a mean success probability of (70.8 +/- 0.4)%. While standard linear-optical BSMs are fundamentally limited to a maximum success probability of 50%, this increased success probability enables higher secure key rates in quantum communication and facilitates the generation of large graph states for quantum computation. Since fault-tolerant schemes require error-correction codes regardless, this improvement comes at no additional resource overhead. Our results demonstrate that error-correction codes can be used to surpass the linear-optics limit of BSMs, which is an important step towards practical, fault-tolerant, and scalable photonic quantum technologies.
Bell state measurement (BSM) plays an important role in quantum information processing. However, a complete BSM cannot be achieved with linear optics with current technology. In this paper, we present a scheme for realizing single-photon BSM via a one-dimensional photonic quantum random walk. In our scheme, the maximally entangled states with polarization and path degrees of freedom are used as Bell states; then a complete BSM based on quantum random walk can be implemented in single-photon Hilbert space. Detecting single-photon count at different positions can provide unambiguous discrimination of all four Bell states to verify our scheme. Furthermore, we also discuss how to apply our BSM scheme to the proposed single-photon cryptography system.
Quantum logic coding efficiently enhances the noise immunity of quantum systems. A quantum logical qubit using multiple degrees of freedom (DOFs) of a photon is concise, and it can reduce resource consumption compared with a quantum logical qubit using multiple photons in one DOF. In this study, two logical Bell state measurement schemes are proposed for photon systems in momentum and polarization DOFs with linear optical elements, namely, momentum polarization logical Bell state measurement assisted by W-state and self-assisted momentum polarization logical Bell state measurement. In the first scheme, parity measurements on momentum and polarization DOFs are performed simultaneously using an auxiliary four-photon W-state. The even-parity logical Bell states can be distinguished by photon detector results, resulting in a success rate of 12.5%. The second scheme does not require an auxiliary entangled photon state, and the even-parity logical Bell states can be completely distinguished by simple linear optical elements and photon detector results with a success rate of 50%. These two linear optical momentum polarization logical Bell state measurement schemes are easier to implement experimentally than the nonlinear optical schemes, and their applications in quantum communication protocols are crucial.