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arXiv:2501.12655

Linear-optical four-dimensional Bell state measurement with two-photon interference

Zhi Zeng

Published Jan 22, 2025• 0 citations
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Abstract

We theoretically investigate the distinguishability of a set of mutually orthogonal four-dimensional Bell states of photon system in path degree of freedom using only linear optics, resorting to the two-photon interference. With quantum interference effect, we find that the 16 four-dimensional Bell states can be classified into 7 groups, which can support the transmission of $log_2 7 = 2.81$ bits classical information with just sending one photon in the quantum superdense coding protocol. When an auxiliary two-dimensional polarization entanglement is introduced, the 16 four-dimensional Bell states then can be classified into 12 groups, which can promote the channel capacity to $log_2 12 = 3.58$ bits with encoding one photon. Our results are significant for photonic superdense coding, and can be useful for other quantum information technologies involved linear-optical high-dimensional Bell state measurement.

DOI
10.48550/arxiv.2501.12655

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We theoretically investigate the distinguishability of a set of mutually orthogonal four-dimensional Bell states of photon system in path degree of freedom using only linear optics, resorting to the two-photon interference. With quantum interference effect, we find that the 16 four-dimensional Bell states can be classified into 7 groups, which can support the transmission of log27=2.81log_2 7 = 2.81log2​7=2.81 bits classical information with just sending one photon in the quantum superdense coding protocol. When an auxiliary two-dimensional polarization entanglement is introduced, the 16 four-dimensional Bell states then can be classified into 12 groups, which can promote the channel capacity to log212=3.58log_2 12 = 3.58log2​12=3.58 bits with encoding one photon. Our results are significant for photonic superdense coding, and can be useful for other quantum information technologies involved linear-optical high-dimensional Bell state measurement.
We theoretically investigate the distinguishability of a set of mutually orthogonal four-dimensional Bell states of photon system in path degree of freedom using only linear optics, resorting to the two-photon interference. With quantum interference effect, we find that the 16 four-dimensional Bell states can be classified into seven groups, which can support the transmission of log 2 7=2.81bits classical information with just sending one photon in the quantum superdense coding protocol. When an auxiliary two-dimensional polarization entanglement is introduced, the 16 four-dimensional Bell states then can be classified into 12 groups, which can promote the channel capacity to log 2 12=3.58bits with encoding one photon. Moreover, both of these two approaches can be easily realized with the current technology. Our results are significant for photonic superdense coding and can be useful for other quantum information technologies involved in linear-optical high-dimensional Bell state measurement.
With the assistance of auxiliary two-dimensional polarization entanglement, we theoretically present an efficient Bell state measurement (BSM) method for photonic four-dimensional entanglement in the path degree of freedom, in which just simple linear optical elements and common single-photon detectors are utilized. With this approach, the 16 mutually orthogonal four-dimensional path Bell states can be classified into eight distinguishable groups, which allows the transmission of 3 bits of classical information by just sending one photon in our quantum superdense coding protocol. Compared with previous quantum dense coding protocols that are also based on linear-optical BSM, our protocol has certain advantages and will be useful for other quantum communication protocols based on high-dimensional entanglement.
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We present a technique for hyperentangled Bell-state analysis that only relies on linear optics and is assisted by auxiliary entangled states. This technique can be used to implement hyperdense coding with an experimentally realizable two-photon state hyperentangled in polarization and two longitudinal-momentum degrees of freedom. The 16 hyperentangled states in the first two degrees of freedom are classified into 12 groups with the help of the third degree of freedom. This allows the transmission of 3.58 bits/photon via our hyperdense coding scheme. We also generalize our technique to nnn-qubit hyperentangled Bell-state analysis assisted by additional auxiliary entangled states. We show that given nnn degrees of freedom, the 4n{4}^{n}4n hyperentangled Bell states can be separated via linear optics into ${x}_{k}={2}^{n+k+1}\ensuremath{-}{2}^{2k}$ groups with the help of $k\phantom{\rule{4pt}{0ex}}(k\ensuremath{\le}n)$ ancillary entangled states. When k=nk=nk=n, all 4n{4}^{n}4n hyperentangled states can be distinguished. Our results are useful for quantum information processing based on hyperentanglement.
The orbital angular momentum (OAM) carried by twisted photons provides a promising playground for high-dimensional quantum information processing. While Bell-state measurement is the cornerstone for various quantum information applications, the deterministic discrimination of the complete high-dimensional Bell states with linear optics remains relatively unexplored in the OAM state space. Here, we demonstrate a theoretical scheme for the complete four-dimensional OAM Bell-state measurement by using the single-photon hyperentangled state analyzer, in which the auxiliary two-dimensional polarization entanglement and two-dimensional path entanglement are utilized. Our scheme offers an alternative route toward enhancing the channel capacity in quantum communication and increasing the robustness against deleterious noise in practical experiments with twisted photons.