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Register a new userDeterministic distribution of multipartite entanglement and steering in a quantum network by separable states
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As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are created among independent users during the distribution process. More specifically, the quantum server prepares separable squeezed states and applies classical displacements on them before spreading out, and users simply perform local beam-splitter operations and homodyne measurements after they receive separable states. We show that the distributed Gaussian entanglement and steerability are robust against channel loss. Furthermore, one-way Gaussian steering is achieved among users that is useful for further directional or highly asymmetric quantum information processing.
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Three distant labs A, B and C, having no prior entanglement can establish a shared GHZ state, when one of them say A sends two particles to B and C for their local actions. The mediating particles remain separable from each other and from the particles of A, B and C. We prove that in this way, GHZ states are shared with a probability $frac{1}{7}$. We also show how separable particles can be mediated to establish arbitrary $d-$ dimensional Bell states between distant labs. Our method is constructive and allows generaization of GHZ sharing between any number of parties and in any dimension. The proposed method may facilitate the construction of multi-node quantum networks and many other processes which use multi-partite entangled states.
The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as a definition of genuine multipartite quantum steering, give a method to detect entanglement in a scenario in between the standard entanglement and fully device-independent scenarios, and provide a basis for semi-device-independent cryptographic applications in quantum networks.
Quantum entanglement is a key resource for quantum computation and quantum communication cite{Nielsen2010}. Scaling to large quantum communication or computation networks further requires the deterministic generation of multi-qubit entanglement cite{Gottesman1999,Duan2001,Jiang2007}. The deterministic entanglement of two remote qubits has recently been demonstrated with microwave photons cite{Kurpiers2018,Axline2018,Campagne2018,Leung2019,Zhong2019}, optical photons cite{Humphreys2018} and surface acoustic wave phonons cite{Bienfait2019}. However, the deterministic generation and transmission of multi-qubit entanglement has not been demonstrated, primarily due to limited state transfer fidelities. Here, we report a quantum network comprising two separate superconducting quantum nodes connected by a 1 meter-long superconducting coaxial cable, where each node includes three interconnected qubits. By directly connecting the coaxial cable to one qubit in each node, we can transfer quantum states between the nodes with a process fidelity of $0.911pm0.008$. Using the high-fidelity communication link, we can prepare a three-qubit Greenberger-Horne-Zeilinger (GHZ) state cite{Greenberger1990,Neeley2010,Dicarlo2010} in one node and deterministically transfer this state to the other node, with a transferred state fidelity of $0.656pm 0.014$. We further use this system to deterministically generate a two-node, six-qubit GHZ state, globally distributed within the network, with a state fidelity of $0.722pm0.021$. The GHZ state fidelities are clearly above the threshold of $1/2$ for genuine multipartite entanglement cite{Guhne2010}, and show that this architecture can be used to coherently link together multiple superconducting quantum processors, providing a modular approach for building large-scale quantum computers cite{Monroe2014,Chou2018}.
Distribution and distillation of entanglement over quantum networks is a basic task for Quantum Internet applications. A fundamental question is then to determine the ultimate performance of entanglement distribution over a given network. Although this question has been extensively explored for bipartite entanglement-distribution scenarios, less is known about multipartite entanglement distribution. Here we establish the fundamental limit of distributing multipartite entanglement, in the form of GHZ states, over a quantum network. In particular, we determine the multipartite entanglement distribution capacity of a quantum network, in which the nodes are connected through lossy bosonic quantum channels. This setting corresponds to a practical quantum network consisting of optical links. The result is also applicable to the distribution of multipartite secret key, known as common key, for both a fully quantum network and trusted-node based quantum key distribution network. Our results set a general benchmark for designing a network topology and network quantum repeaters (or key relay in trusted nodes) to realize efficient GHZ state/common key distribution in both fully quantum and trusted-node-based networks. We show an example of how to overcome this limit by introducing a network quantum repeater. Our result follows from an upper bound on distillable GHZ entanglement introduced here, called the recursive-cut-and-merge bound, which constitutes major progress on a longstanding fundamental problem in multipartite entanglement theory. This bound allows for determining the distillable GHZ entanglement for a class of states consisting of products of bipartite pure states.
We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this criterion, we need to solve a set of equations, actually it is easy to solve these quations analytically if the density matrix of the given quantum state has few nonzero eigenvalues.
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