Inherent channel losses during photon transmission limit the efficiency of optical quantum communication. In this paper, we construct a hyperdistillation scheme which can be used to distill the spatial-mode and polarization states of a photon simultaneously from photon loss in a heralded strategy. Exploiting linear-optical devices, the fidelity of a single-photon two qubit in a lossy signal mode can be increased to one with a certain success probability. By using a four-photon entanglement resource, the success probability of the hyperdistillation operation could be improved. The proposed scheme provides a realistic solution to overcome the transmission losses and exhibits unique properties, which shows important applications to quantum information processing.
Inherent channel losses during photon transmission limit the efficiency of optical quantum communication. In this paper, we construct a hyperdistillation scheme which can be used to distill the spatial-mode and polarization states of a photon simultaneously from photon loss in a heralded strategy. Exploiting linear-optical devices, the fidelity of a single-photon two qubit in a lossy signal mode can be increased to one with a certain success probability. By using a four-photon entanglement resource, the success probability of the hyperdistillation operation could be improved. The proposed scheme provides a realistic solution to overcome the transmission losses and exhibits unique properties, which shows important applications to quantum information processing.
We investigate a new approach for achieving hyperdistillation and hyperentanglement purification operations simultaneously on two-photon systems, whose state is described by nonlocal hyperentangled Bell states on both the spatial mode and polarization degree of freedoms. Exploiting linear optics and local entanglement resource, the quantum nondemolition (QND) parity-checking measurement and the heralded two-qubit amplification could are key steps in our scheme. With the QND parity-checking measurement and heralded qubit amplification operations, both the bit-flip (phase-flip) errors caused by decoherence in noisy channels and the vacuum errors caused by the transmission losses can be corrected. We show that the proposed scheme provides a new solution to overcome the problem of photon losses and decoherence simultaneously, which could be achieved with current technologies.
In quantum information processing, the quality of photon system is decreased by the inevitable interaction with environment, which will greatly reduce the efficiency and security of quantum information processing. In this paper, we propose hyperentanglement-assisted hyperdistillation schemes to guarantee the quality of hyper-encoding photon system based on the method of quantum hyper-teleportation, which can increase the success probability of hyperdistillation and reduce the resource consumption. First, we propose a hyperentanglement-assisted single-photon hyperdistillation (HASPHD) scheme for polarization and spatial qubits to get rid of the vacuum state component caused by transmission loss, whose success probability can achieve the optimal one by increasing the efficiency of quantum hyper-teleportation. Subsequently, we present two hyperentanglement-assisted hyperentanglement distillation (HAHED) schemes for photon system to protect hyperentanglement from both transmission loss and quantum channel noise, which can recover the less-entangled mixed state to maximally hyperentangled state for known-parameter and unknown-parameter cases with high success probability and low resource consumption. In these hyperdistillation schemes, the influence of imperfect effects of optical elements can be largely decreased by the quantum hyper-teleportation method. These characters make the hyperentanglement-assisted hyperdistillation schemes have potential application prospects in practical quantum information processing.
Recent years, researchers pay much more attention to hyperentanglement. Protocols to concentrating and purifying hyperentangled photons have been widely discussed using nonliear optics in the past ten years. While, we propose a linear optics scheme supported by a entangled state as a local resource, to implement the hyperentanglement distillation and hyperentanglement purificaiton in one step. In our scheme, the quantum nondemolition (QND) parity-checking measurement in the spatial-mode and polarization DOFs and the qubit amplification could be the key steps. We discuss the decoherence in noisy channel and photon losses simutaneously, which could be feasible with current technologies.
We illustrate an entanglement distillation protocol (EDP) for a mixed photon-ensemble which composed of four kinds of entangled states and vacuum states. Exploiting the linear optics and local entanglement resource (four-qubit entangled GHZ state), we design the nondemolition parity-checking and qubit amplifying (PCQA) setup for photonic polarization degree of freedom which are the key device of our scheme. With the PCQA setup, a high-fidelity entangled photon-pair system can be achieved against the transmission losses and the decoherence in noisy channels. And in the available purification range for our EDP, the fidelity of this ensemble can be improved to the maximal value through iterated operations. Compared to the conventional entanglement purification schemes, our scheme largely reduces the initialization requirement of the distilled mixed quantum system, and overcomes the difficulties posed by inherent channel losses during photon transmission. All these advantages make this scheme more useful in the practical applications of long-distance quantum communication.
High-dimensional hyperentangled states, serving as crucial physical resources in quantum communication, have attracted significant attention due to their exceptional properties (e.g., higher information density) compared to conventional two-dimensional single-degree-of-freedom entanglement. However, practical quantum entanglement systems inevitably suffer from environmental interactions, resulting in their degradation into partially entangled pure states or even mixed states, thereby significantly compromising the efficiency and security of quantum communication. Consequently, improving entanglement preservation in noisy systems emerges as a pivotal challenge in realizing fault-tolerant quantum networks. We propose two universal distillation schemes based on local positive-operator-valued measures (POVMs) for single-copy $(2\ifmmode\times\else\texttimes\fi{}4\ifmmode\times\else\texttimes\fi{}4)$-dimensional hyperentangled photons. These schemes effectively suppress photon vacuum errors induced by transmission losses and are constructed using spatial-mode and polarization-based POVM measurements, respectively. Our results demonstrate that the spatial-mode-based scheme outperforms its polarization-based counterpart in terms of fidelity and success probability. Remarkably, we discover that with appropriate POVM parameters, the fidelity range of amplitude-damped noisy states can be expanded to cover almost all parameter spaces. Due to the universal applicability of POVM measurements, which require neither auxiliary entanglement nor complex detectors and operate on single copies of imperfect states in each purification round, our scheme provides an experimentally feasible solution for distilling high-dimensional hyperentangled photonic states.
Entanglement distillation has many applications in quantum information processing and is an important tool for improving the quality and efficiency of quantum communication, cryptography, computing, and simulation. We propose an entanglement distillation scheme using only one pair of polarization-frequency hyperentangled photons, which can be equivalently viewed as containing two pairs of entangled logical qubits: a pair of polarization-entangled qubits and a pair of frequency-entangled qubits. To perform the required CNOT operation between the two qubits we consider the use of a polarization-dependent frequency converter. Compared to past methods of entanglement distillation that relied on polarization and spatial-mode/energy-time degree of freedom, the utilization of frequency-encoded qubits offers an advantage in that it is immune to bit-flip errors when the channel is linear. After distillation, the fidelity of polarization entanglement can be significantly improved by sacrificing the frequency degree of freedom. Through simulation, we show that high fidelity gains, large yield, and high distillation rate can be achieved. Our distillation scheme is simple to implement with current technologies, compatible with existing telecommunication fiber networks, and is a promising approach for achieving efficient quantum communication.