Quantum computers promise ultrafast performance of certain tasks 1 . Experimentally appealing, measurement-based quantum computation (MBQC) 2 requires an entangled resource called a cluster state 3 , with long computations requiring large cluster states. Previously, the largest cluster state consisted of 8 photonic qubits 4 or light modes 5 , while the largest multipartite entangled state of any sort involved 14 trapped ions 6 . These implementations involve quantum entities separated in space, and in general, each experimental apparatus is used only once. Here, we circumvent this inherent inefficiency by multiplexing light modes in the time domain. We deterministically generate and fully characterise a continuous-variable cluster state 7,8 containing more than 10,000 entangled modes. This is, by 3 orders of magnitude, the largest entangled state ever created to date. The entangled modes are individually addressable wavepackets of light in two beams. Furthermore, we present an efficient scheme for MBQC on this cluster state based on sequential applications of quantum teleportation.Originally formulated as a demonstration as to why quantum mechanics must be incomplete in the famous 1935 Einstein-Podolsky-Rosen (EPR) paradox 9 , entanglement is now recognized as a signature feature of quantum physics 10 , and it plays a central role in various quantum information processing (QIP) protocols 1,11 . For example, the bipartite entangled state known as an EPR state 9 is a resource for quantum teleportation (QT), whereby a quantum state is transferred from one location to another without physical transfer of the quantum information 12-14 .Measurement-based quantum computation (MBQC) 2,7,8,[15][16][17][18] , which is based on the QT of information and logic gates, requires the special class of multipartite entangled resource states known as cluster states 3 . The number of entangled quantum entities and their entanglement structure (represented by a graph) determines the resource space available for computation.Ultra-large-scale QIP (which could be based on MBQC) will require ultra-large-scale entangled 2 states 2,7,8 .In the vast majority of optical experiments, quantum modes are distinguished from each other by their spatial location. This leads to an inherent lack of scalability as each additional entangled party requires an increase in laboratory equipment and dramatically increases the complexity of the optical network 19,20 . Further, due to the probabilistic nature of photon pair generation, demonstrations involving the postselection of photonic qubits 4,15,16 suffer from dramatically reduced event success rates with each additional qubit.One method to overcome this problem of scalability is to deterministically encode the modes within one beam. Entanglement between quadrature-phase amplitudes in continuouswave laser beams has been deterministically created and exploited in QIP 5,13,14,[17][18][19][21][22][23] , even though the quantum correlations are finite. Previous attempts to deterministically create cluster ...

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The Einstein-Podolsky-Rosen (EPR) paradox [1] established a link between entanglement [2,3] and nonlocality in quantum mechanics [4]. EPR steering [5][6][7][8] is the nonlocality associated with the EPR paradox and has traditionally only been investigated between two parties [9][10][11][12][13][14][15]. Here, we present the first experimental observations of multipartite EPR steering, and of the genuine tripartite continuous variable entanglement of three mesoscopic optical systems [16][17][18]. We explore different linear optics networks -each one with optimised asymmetries -that create multipartite steerable states containing different numbers of quantised optical modes (qumodes). By introducing asymmetric loss on a 7-qumode state, we characterize 8 regimes of directional steering, showing that N + 1 regimes exist for an N -qumode state. Further, we reveal the directional monogamy of steering, and experimentally demonstrate continuous variable one-sided semi device-independent quantum secret sharing [19]. Our methods establish principles for the development of multiparty quantum communication protocols with asymmetric observers, and can be extended to qubits, whether photonic [12][13][14][15][16]20], atomic [21], superconducting [22], or otherwise.Schrödinger introduced the term "steering" to describe the nonlocality apparent in the EPR paradox, and pointed out that these states involve a quantum property called "entanglement" [2,5]. Wiseman et al [6,7] have formalised the meaning of steering in terms of violations of local hidden state models, and revealed that the EPR paradox is a manifestation of quantum steering. In simple terms, quantum steering dictates that measurements made by one observer can apparently "steer" (alter) the state of another observer at a different location.The observation of multipartite EPR steering has not been possible until recently as the framework necessary to understand the concept has only just been developed [6][7][8]23]. The motivation to expand this framework arises from considerations of real-world quantum networks, such as the quantum internet [24], for which security and privacy are of paramount importance. Here, we expand on the theoretical framework and derive optimised criteria to detect multipartite EPR steering using linear optical circuits. The criteria involve the canonical position and momentum observables, which are realised in our experiment as highly efficient quadrature phase amplitude measurements. Following the criteria, we present the first experimental investigation of multipartite EPR steering, including demonstration of directional monogamy relations which give bounds on the way steering is distributed among the different parties. Further, we demonstrate the principle of one-sided deviceindependent quantum secret sharing and in doing so confirm for the first time the continuous variable genuine tripartite entanglement of three optical modes. For bipartite EPR states, there are 3 different regimes: 2-way, 1-way, and no-way steering [25,26]. In general, for...