Polynomial approximation of non-Gaussian unitaries by counting one photon at a time

In quantum computation with continous-variable systems, quantum advantage can only be achieved if some non-Gaussian resource is available. Yet, non-Gaussian unitary evolutions and measurements suited for computation are challenging to realize in the lab. We propose and analyze two methods to apply a polynomial approximation of any unitary operator diagonal in the amplitude quadrature representation, including non-Gaussian operators, to an unknown input state. Our protocols use as a primary non-Gaussian resource a single-photon counter. We use the fidelity of the transformation with the target one on Fock and coherent states to assess the quality of the approximate gate.Comment: 11 pages, 7 figure

Random coding for sharing bosonic quantum secrets

We consider a protocol for sharing quantum states using continuous variable systems. Specifically we introduce an encoding procedure where bosonic modes in arbitrary secret states are mixed with several ancillary squeezed modes through a passive interferometer. We derive simple conditions on the interferometer for this encoding to define a secret sharing protocol and we prove that they are satisfied by almost any interferometer. This implies that, if the interferometer is chosen uniformly at random, the probability that it may not be used to implement a quantum secret sharing protocol is zero. Furthermore, we show that the decoding operation can be obtained and implemented efficiently with a Gaussian unitary using a number of single-mode squeezers that is at most twice the number of modes of the secret, regardless of the number of players. We benchmark the quality of the reconstructed state by computing the fidelity with the secret state as a function of the input squeezing.Comment: Updated figure 1, added figure 2, closer to published versio

Microglia Control Neuronal Network Excitability via BDNF Signalling

Microglia-neuron interactions play a crucial role in several neurological disorders characterized by altered neural network excitability, such as epilepsy and neuropathic pain. While a series of potential messengers have been postulated as substrates of the communication between microglia and neurons, including cytokines, purines, prostaglandins, and nitric oxide, the specific links between messengers, microglia, neuronal networks, and diseases have remained elusive. Brain-derived neurotrophic factor (BDNF) released by microglia emerges as an exception in this riddle. Here, we review the current knowledge on the role played by microglial BDNF in controlling neuronal excitability by causing disinhibition. The efforts made by different laboratories during the last decade have collectively provided a robust mechanistic paradigm which elucidates the mechanisms involved in the synthesis and release of BDNF from microglia, the downstream TrkB-mediated signals in neurons, and the biophysical mechanism by which disinhibition occurs, via the downregulation of the K+-Cl− cotransporter KCC2, dysrupting Cl−homeostasis, and hence the strength of GABAA- and glycine receptor-mediated inhibition. The resulting altered network activity appears to explain several features of the associated pathologies. Targeting the molecular players involved in this canonical signaling pathway may lead to novel therapeutic approach for ameliorating a wide array of neural dysfunctions