We present a scheme for small-displacement measurements using high-order Hermite-Gauss modes and balanced homodyne detection. We demonstrate its use with experimental results of displacement measurements using fundamental transverse mode TEM00 and first order transverse mode TEM10 as signal modes. The results show a factor of 1.41 improvement in measurement precision with the TEM10 mode compared with that with the TEM00 mode. This scheme has potential applications in precision metrology, atomic force microscopy, and optical imaging.

We present an original self-error-rejecting photonic qubit transmission scheme for both the polarization and spatial states of photon systems transmitted over collective noise channels. In our scheme, we use simple linear-optical elements, including half-wave plates, 50:50 beam splitters, and polarization beam splitters, to convert spatial-polarization modes into different time bins. By using postselection in different time bins, the success probability of obtaining the uncorrupted states approaches 1/4 for single-photon transmission, which is not influenced by the coefficients of noisy channels. Our self-error-rejecting transmission scheme can be generalized to hyperentangled N-photon systems and is useful in practical high-capacity quantum communications with photon systems in two degrees of freedom.

Quantum secure direct communication (QSDC) is a powerful technique of transmitting confidential information directly and securely based on the pre-established secure quantum channel and block transmission. Here we propose an efficient QSDC protocol using the complete Bell-state measurement (CBSM) resorting to linear optical elements and temporal-polarization hyperentanglement. In this protocol, the polarized entangled photons are utilized as the information carrier, and all the detection events of CBSM can be identified with common single-photon detectors instead of photon number resolving detectors due to the introduction of temporal degree of freedom (DOF). Moreover, since all the two-photon detection events in CBSM are effective and can be preserved with the efficiency of 100% rather than 50% in the previous QSDC, the quantum efficiency of QSDC can be doubled by encoding more messages on entangled photon pairs.

Quantum error detection relies primarily on precise measurement of qubit parity, a fundamental operation in quantum information processing. Here, we introduce a resilient parity-controlled gate tailored for detecting quantum errors within a 2D Rydberg atom array. Our method enables the discrimination between even and odd parities of virtually excited control atoms by tracking the dynamic evolution of an auxiliary atom. Using spin-exchange dipolar interactions of Rydberg states and single-and two-photon driving between ground states and Rydberg states, our method speeds up Rydberg-parity measurements by a large amount compared to previous methods. In practical application, we explore three-qubit repetition codes, standard surface codes featuring stabilizers in the forms ZZZZ and XXXX, as well as rotated surface codes in the XZZX configuration, facilitating the measurement of stabilizers with a single-shot readout. We carry out thorough numerical simulations to evaluate the feasibility of our strategy, considering potential experimental imperfections such as undesired interactions between Rydberg states, fluctuations in atomic positions, dephasing noise, and laser amplitude inhomogeneities. Particular emphasis is placed on ensuring the reliability and advantages of the physical mechanisms of the parity meter. These results affirm the robustness and viability of our protocol, positioning it as a promising candidate for quantum error detection employing the Rydberg atom system in the foreseeable future.

Channel noise is the main issue which reduces the efficiency of quantum communication. Here we present an efficient scheme for quantum key distribution against collective-rotation channel noise using polarization and transverse spatial mode of photons. Exploiting the two single-photon Bell states and two-photon hyperentangled Bell states in the polarization and the transverse spatial mode degrees of freedom (DOFs), the mutually unbiased bases can be encoded for logical qubits against the collective-rotation noise. Our scheme shows noiseless subspaces can be made up of two DOFs of two photons instead of multiple photons, which will reduce the resources required for noiseless subspaces and depress the photonic loss sensitivity. Moreover, the two single-photon Bell states and two-photon hyperentangled Bell states are symmetrical to the two photons, which means the relative order of the two photons is not required in our scheme, so the receiver only needs to measure the state of each photon, which makes our protocol easy to execute in experiment than the previous works.