Mechanical systems facilitate the development of a new generation of hybrid quantum technology comprising electrical, optical, atomic and acoustic degrees of freedom [1]. Entanglement is the essential resource that defines this new paradigm of quantum enabled devices. Continuous variable (CV) entangled fields, known as Einstein-Podolsky-Rosen (EPR) states, are spatially separated two-mode squeezed states that can be used to implement quantum teleportation and quantum communication [2]. In the optical domain, EPR states are typically generated using nondegenerate optical amplifiers [3] and at microwave frequencies Josephson circuits can serve as a nonlinear medium [4][5][6]. It is an outstanding goal to deterministically generate and distribute entangled states with a mechanical oscillator. Here we observe stationary emission of path-entangled microwave radiation from a parametrically driven 30 micrometer long silicon nanostring oscillator, squeezing the joint field operators of two thermal modes by 3.40(37) dB below the vacuum level. This mechanical system correlates up to 50 photons/s/Hz giving rise to a quantum discord that is robust with respect to microwave noise [7]. Such generalized quantum correlations of separable states are important for quantum enhanced detection [8] and provide direct evidence for the non-classical nature of the mechanical oscillator without directly measuring its state [9]. This noninvasive measurement scheme allows to infer information about otherwise inaccessible objects with potential implications in sensing, open system dynamics and fundamental tests of quantum gravity. In the near future, similar on-chip devices can be used to entangle subsystems on vastly different energy scales such as microwave and optical photons. *
Continuous-time quantum walks can be used to solve the spatial search problem, which is an essential component for many quantum algorithms that run quadratically faster than their classical counterpart, in Oð ffiffiffi n p Þ time for n entries. However, the capability of models found in nature is largely unexplored-e.g., in one dimension only nearest-neighbor Hamiltonians have been considered so far, for which the quadratic speedup does not exist. Here, we prove that optimal spatial search, namely with Oð ffiffiffi n p Þ run time and high fidelity, is possible in one-dimensional spin chains with long-range interactions that decay as 1=r α with distance r. In particular, near unit fidelity is achieved for α ≈ 1 and, in the limit n → ∞, we find a continuous transition from a region where optimal spatial search does exist (α < 1.5) to where it does not (α > 1.5). Numerically, we show that spatial search is robust to dephasing noise and that, for reasonable chain lengths, α ≲ 1.2 should be sufficient to demonstrate optimal spatial search experimentally with near unit fidelity.
Linear ion trap chains are a promising platform for quantum computation and simulation. The XY model with long-range interactions can be implemented with a single side-band Mølmer-Sørensen scheme, giving interactions that decay as 1/rα, where α parameterises the interaction range. Lower α leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing α causes an increased generation of coherent phonons and appears to dephase the effective XY interaction model. We characterise and show how to correct for this effect completely, allowing lower α interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal O(√N) time, for N ions. Finally, we introduce a O(√N) quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.
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