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arXiv:2306.04364 · Physics Open

Transformation of Bell states using linear optics

Sarika Mishra, Ravindra Pratap Singh

Published Dec 8, 2023• 8 citations

Abstract

Bell states form a complete set of four maximally polarization entangled two-qubit quantum state. Being a key ingredient of many quantum applications such as entanglement based quantum key distribution protocols, superdense coding, quantum teleportation, entanglement swapping etc, Bell states have to be prepared and measured. Spontaneous parametric down-conversion (SPDC) is the easiest way of preparing Bell states and a desired Bell state can be prepared from any entangled photon pair through single-qubit logic gates. In this paper, we present the generation of complete set of Bell states, only by applying unitary transformations of half-wave plate (HWP) on the initial Bell state. The initial Bell state is prepared using a combination of a nonlinear crystal and a beam-splitter (BS) and the rest of the Bell states are created by applying single-qubit logic gates on the entangled photon pairs using HWPs. Our results can be useful in many quantum applications, especially in superdense coding where control over basis of maximally entangled state is required.

DOI: 10.1016/j.physo.2023.100199

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Bell states form a complete set of four maximally polarization entangled two-qubit quantum state. Being a key ingredient of many quantum applications such as entanglement based quantum key distribution protocols, superdense coding, quantum teleportation, entanglement swapping etc, Bell states have to be prepared and measured. Spontaneous parametric down-conversion (SPDC) is the easiest way of preparing Bell states and a desired Bell state can be prepared from any entangled photon pair through single-qubit logic gates. In this paper, we present the generation of complete set of Bell states, only by applying unitary transformations of half-wave plate (HWP) on the initial Bell state. The initial Bell state is prepared using a combination of a nonlinear crystal and a beam-splitter (BS) and the rest of the Bell states are created by applying single-qubit logic gates on the entangled photon pairs using HWPs. Our results can be useful in many quantum applications, especially in superdense coding where control over basis of maximally entangled state is required.

Bell states are fundamental resources in quantum optics, underpinning a range of applications in quantum computation and communication. However, many experimental sources focus on generating a single Bell state, limiting their utility for protocols that require the full set of maximally entangled states. In this work, we present a polarization-entangled photon-pair source based on spontaneous parametric down-conversion in a periodically poled potassium titanyl phosphate crystal integrated into a Sagnac loop interferometer. Our source initially generates one Bell state, which is then transformed into the complete set of Bell states through the application of phase and bit flips using phase plates. We characterize the entanglement quality of all generated states via two-photon interference measurements, quantum state tomography, and evaluation of the Bell parameter. Our results show spectral brightness of 0.15 kHz/mW/nm with interference visibilities of ∼98% (H/V basis) and ∼96% (A/D basis) and state fidelity of ∼0.97 across all Bell states, with all states demonstrating a clear violation of the Clauser–Horne–Shimony–Holt inequality (S≥2.6). This approach offers a practical solution for obtaining all four Bell states with high efficiency from a single source, which could facilitate more versatile implementations in quantum information processing.

We present a theoretical and experimental study of preparing maximally entangled two-photon polarization states, or Bell states, using femtosecond-pulse-pumped spontaneous parametric down-conversion (SPDC). First, we show how the inherent distinguishability in femtosecond-pulse-pumped type-II SPDC can be removed by using an interferometric technique without spectral and amplitude postselection. We then analyze the recently introduced Bell-state preparation scheme using type-I SPDC. Theoretically, both methods offer the same results, however, type-I SPDC provides experimentally superior methods of preparing Bell states in femtosecond-pulse-pumped SPDC. Such a pulsed source of highly entangled photon pairs is useful in quantum communications, quantum cryptography, quantum teleportation, etc.

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

Nowadays, the nonlinear optical process of spontaneous parametric down-conversion is considered as the canonical approach for creating entangled-photon pairs. We consider three pairs of entangled photons emitted by the parametric down-conversion source, and introduce a setup for evolving these photons based on linear optics, which is composed of several polarizing beam splitters, beam splitters, and half wave plates. By using the parametric down-conversion source and the setup, we carefully design an efficient scheme for preparing six-photon hyperentangled states in both the polarization and the spatial degrees of freedom. Because we use almost all possible behaviors of the three pairs of entangled photons, the present scheme is efficient for creating six-photon hyperentangled states. Next, in the regime of weak nonlinearity we design a quantum nondemolition detection to distinguish the two cases of photons in two special spatial modes. It is worth pointing out that our scheme is much easier to realize, since the strength of the nonlinearities in the process of quantum nondemolition detection can be restricted to the scalable orders of magnitude in practicality.