The extraordinary correlation seen in entangled states in space-like separated regions is one of the most intriguing aspects of quantum states. Practical utility of entanglement as a resource for quantum key distribution, dense coding, or teleportation generally requires maximally entangled states. In practice, entanglement quality degrades substantially due to channel noise. The problem may be mitigated by entanglement distillation. The simplest distillation protocol is enforced by local filtering operations and classical communication. The local filtering operations are merely generalized positive operator valued measures utilizing additional degrees of freedom (DoFs) as ancillary qubits. In this work, we experimentally show that filtering on a single channel (unilateral) is equally effective as filtering on both channels (bilateral) for distillation of pure non-maximally entangled bipartite states. This result holds for a non-maximally entangled multi-qubit Greenberger-Horne-Zeilinger (GHZ) like states as well, as they show a straightforward extension of the Bell state structure. Further, we provide a theoretical comparison of the efficacy of unilateral and bilateral filtering for the case of mixed states resulting from local depolarizing noise introduced either in one or both of the non-maximally entangled pairs. Surprisingly, when noise is introduced in either one of the channels, we find that unilateral filtering on the noise-free channel outperforms the filtering on the noisy channel and bilateral filtering on both channels. We also find that bilateral filtering is more effective when both channels are noisy. A reduction in the number of local operations, in general, has the advantage of reducing the complexity of the experimental apparatus and the reduction of measurement related errors.
The extraordinary correlation seen in entangled states in space-like separated regions is one of the most intriguing aspects of quantum states. Practical utility of entanglement as a resource for quantum key distribution, dense coding, or teleportation generally requires maximally entangled states. In practice, entanglement quality degrades substantially due to channel noise. The problem may be mitigated by entanglement distillation. The simplest distillation protocol is enforced by local filtering operations and classical communication. The local filtering operations are merely generalized positive operator valued measures utilizing additional degrees of freedom (DoFs) as ancillary qubits. In this work, we experimentally show that filtering on a single channel (unilateral) is equally effective as filtering on both channels (bilateral) for distillation of pure non-maximally entangled bipartite states. This result holds for a non-maximally entangled multi-qubit Greenberger-Horne-Zeilinger (GHZ) like states as well, as they show a straightforward extension of the Bell state structure. Further, we provide a theoretical comparison of the efficacy of unilateral and bilateral filtering for the case of mixed states resulting from local depolarizing noise introduced either in one or both of the non-maximally entangled pairs. Surprisingly, when noise is introduced in either one of the channels, we find that unilateral filtering on the noise-free channel outperforms the filtering on the noisy channel and bilateral filtering on both channels. We also find that bilateral filtering is more effective when both channels are noisy. A reduction in the number of local operations, in general, has the advantage of reducing the complexity of the experimental apparatus and the reduction of measurement related errors.
Entanglement is at the heart of quantum theory and is responsible for various quantum-enabling technologies. In practice, during its preparation, storage, and distribution to the intended recipients, this valuable quantum resource may suffer from noisy interactions that reduce its usefulness for the desired information-processing tasks. Conventional schemes of entanglement distillation aim to alleviate this problem by performing collective operations on multiple copies of these decohered states and sacrificing some of them to recover Bell pairs. However, for this scheme to work, the states to be distilled should already contain a large enough fraction of maximally entangled states before these collective operations. Not all entangled quantum states meet this premise. Here, by using the paradigmatic family of two-qutrit Werner states as an exemplifying example, we experimentally demonstrate how one may use single-copy local filtering operations to meet this requirement and to recover the quantumness hidden in these higher-dimensional states. Among others, our results provide the first proof-of-principle experimental certification of the Bell-nonlocal properties of these intriguing entangled states, the activation of their usefulness for quantum teleportation, dense coding, and an enhancement of their quantum steerability, and hence usefulness for certain discrimination tasks. Our theoretically established lower bounds on the steering robustness of these states, when they admit a symmetric quasiextension or a bosonic symmetric extension, and when they show hidden dense-codability, may also be of independent interest.
Hyperentanglement has a higher information density than conventional single-degree-of-freedom entanglement, which has attracted much attention due to its fascinating applications in quantum communication. However, since the inevitable interactions between quantum entangled systems and the environment will drive hyperentangled systems into less hyperentangled states or even mixed hyperentangled states, the efficiency and security of quantum communication will be greatly depressed. The currently existing distillation protocols are not universal, i.e., they only work for the lossy hyperentangled states in specific systems. In this paper, based on local positive-operator-valued measures (POVMs), we present a distillation protocol for lossy hyperentangled photonic Bell and Greenberger-Horne-Zeilinger (GHZ) states. The intrinsic property of our protocol is twofold, i.e., the POVM nature of the protocol guarantees that the protocol is a universal one, and the distillation operation on only one of the two degrees of freedom (DOFs) can enhance the fidelity of the system in both DOFs. Furthermore, in the implementation level, our hyperentanglement distillation protocol (HEDP) has other two merits: no auxiliary local entanglement resources and sophisticated single-photon detectors are required, and only one copy of the lossy state will be operated in each distillation round, which show that our HEDPs are relatively simple and feasible.
In this work, we study how to distill two typical multipartite entangled noisy states, the amplitude-damped W state and the amplitude-damped Greenberger-Horne-Zeilinger state. Unlike the currently existing multipartite entanglement purification schemes, our scheme is a single-copy-based scheme, i.e., only one noisy state is needed in each distillation round, and the complicated multilateral controlled-not (cnot) operations are replaced by measurements of local positive-operator-valued measures (POVMs). The results show that local POVM measurements on one copy of the noisy state can project the initial state onto a new state with higher entanglement and nonlocality. In this scheme, although the final state can violate the multipartite Bell inequality, the corresponding initial noisy state does not violate it, which means that this distillation scheme can reveal the hidden genuine multipartite nonlocality of these initial states. For the case of the amplitude-damped W state, if the POVM parameters are appropriately chosen, the fidelity of the output state can approach 1.0 for all the initial states with fidelity bigger than zero. So this single-copy-based multipartite entanglement distillation scheme has a wide range of distillable fidelities, and it is much simpler than the two-copy- or multiple-copy-based schemes. Furthermore, if the POVM measurement is carried out only on some member qubits rather than all of them, the distillation scheme can succeed too, which will greatly decrease the implementation complexity of the scheme. So this multipartite entanglement distillation scheme may be implementable in some physical system.
Multipartite Einstein-Podolsky-Rosen (EPR) steering admits multipartite entanglement in the presence of uncharacterized verifiers, enabling practical applications in semi-device-independent protocols. Such applications generally require stronger steerability, while the unavoidable noise weakens steerability and consequently degrades the performance of quantum information processing. Here, we propose the local filtering operation that can maximally distill genuine tripartite EPR steering from N copies of three-qubit generalized Greenberger-Horne-Zeilinger states, in the context of two semi-device-independent scenarios. The optimal filtering operation is determined by the maximization of assemblage fidelity. Analytical and numerical results indicate the advantage of the proposed filtering operation when N is finite and the steerability of initial assemblages is weak. Experimentally, a proof-of-principle demonstration of two-copy distillation is realized with the optical system. The advantage of the optimal local filtering operation is confirmed by the distilled assemblage in terms of higher assemblage fidelity with perfectly genuine tripartite steerable assemblages, as well as the greater violation of the inequality to witness genuine tripartite steerable assemblages. Our results benefit the distillation of multipartite EPR steering in practice, where the number of copies of initial assemblages is generally finite.
Entanglement distillation is the process of concentrating entanglement from a given quantum state. We present a technique for distillation of bipartite polarization entanglement using interferometry. This technique can be optimized to extract maximal entanglement from any pure or mixed entangled state. A model for this method is presented, and, in particular, we present experimental results for pure states when using polarizing Mach-Zehnder interferometers. These experimentally distilled states always demonstrate an increased violation of Bell's inequality.
Quantum communication relies on the existence of high quality quantum channels to exchange information. In practice, however, all communication links are affected by noise from the environment. Here we investigate the ability of quantum channels to perform quantum communication tasks by restricting the participants to use only local operations and one-way classical communication (one-way LOCC) along with the available quantum channel. In particular, a channel can be used to distill a highly entangled state between two parties, which further enables quantum or private communication. In this work, we invoke the framework of superchannels to study the distillation of a resourceful quantum state, such as a maximally entangled state or a private state, using multiple instances of a point-to-point quantum channel. We use the idea ofk-extendibility to obtain a semidefinite relaxation of the set of one-way LOCC superchannels and define a class of entanglement measures for quantum channels that decrease monotonically under such superchannels; therefore these measures, dubbed collectively the “unextendible entanglement of a channel”, yield upper bounds on several communication-theoretic quantities of interest in the regimes of resource distillation and zero error.We then generalize the formalism ofk-extendibility to bipartite superchannels, thus obtaining functions that are monotone under two-extendible superchannels. This allows us to analyze probabilistic distillation of ebits or secret key bits from a bipartite state when using a resourceful quantum channel. Moreover, we propose semidefinite programs to evaluate several of these quantities, providing a computationally feasible method of comparison between quantum channels for resource distillation.