A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts two-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity $F=0.889\ifmmode\pm\else\textpm\fi{}0.010$ by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum entanglement.
A linear optics-based scheme to implement various quantum information processing tasks is of paramount importance due to ease of implementation and low noise. Many information-theoretic tasks depend on the successful discrimination of Bell states. A no-go theorem has been proved in literature which tells that it is not possible to perfectly discriminate among the four Bell states by restricting measurement apparatus to linear optical elements. The success probability is only
50%. Through using extra resources such as hyper entanglement, ancillary entanglement, and even a minimum amount of non-linearity complete Bell-state discrimination can be achieved. The success probability for Bell-like state discrimination is only
25%. We find that this can be boosted up to
50% using hyperentanglement in polarization, momentum, or OAM degrees of freedom of the photons which is in contrast to the Bell-state discrimination scenario where
100% can be achieved. Furthermore, we find that by using correlation in time of the photons all four Bell states can be distinguished with
100% success probability while for the Bell-like state discrimination, it strictly lies between
25% and
50% depending on the state parameter with only three Bell-like states being distinguishable. We also observe a similar contrast when we use ancillary entangled photons. While the success probability for all four Bell-state discrimination increases as
1−2N1 where N is the number of ancillary photons for Bell-like states it depends again on the state parameters and can be less than
25% in some cases. Also adding further ancillary photons decreases the success probability. We then show that using non-linear gadgets namely SFG
100% success probability can be achieved even for Bell-like state discrimination.
We show how hyperentanglement allows us to deterministically distinguish between all four polarization Bell states of two photons. In this proof-of-principle experiment, we employ the intrinsic time-energy correlation of photon pairs generated with high temporal definition in addition to the polarization entanglement obtained from parametric down-conversion. For the identification, no nonlinear optical elements or auxiliary photons are needed. The new possibilities this complete Bell measurement offers are demonstrated by realizing an optimal dense coding protocol.
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.
Bell-state projections serve as a fundamental basis for most quantum communication and computing protocols today. However, with current Bell-state measurement schemes based on linear optics, only two of four Bell states can be identified, which means that the maximum success probability of this vital step cannot exceed
50%. Here, we experimentally demonstrate a scheme that amends the original measurement with additional modes in the form of ancillary photons, which leads to a more complex measurement pattern, and ultimately a higher success probability of
62.5%. Experimentally, we achieve a success probability of
(57.9±1.4)%, a significant improvement over the conventional scheme. With the possibility of extending the protocol to a larger number of ancillary photons, our work paves the way towards more efficient realisations of quantum technologies based on Bell-state measurements.
Bell-state projections serve as a fundamental basis for most quantum communication and computing protocols today. However, with current Bell-state measurement schemes based on linear optics, only two of four Bell states can be identified, which means that the maximum success probability of this vital step cannot exceed 50%. Here, we experimentally demonstrate a scheme that amends the original measurement with additional modes in the form of ancillary photons, which leads to a more complex measurement pattern, and ultimately a higher success probability of 62.5%. Experimentally, we achieve a success probability of (57.9 ± 1.4)%, a substantial improvement over the conventional scheme. With the possibility of extending the protocol to a larger number of ancillary photons, our work paves the way toward more efficient realizations of quantum technologies based on Bell-state measurements.