Speaker
Description
We introduce a framework for distributed quantum inference under communication constraints. In our model, $m$ distributed nodes each receive one copy of an unknown $d$-dimensional quantum state $\rho$, before communicating via a constrained communication channel with a central node, which aims to infer some property of $\rho$. This framework generalizes the classical distributed inference framework (Acharya, Canonne, and Tyagi COLT2019), by allowing quantum resources such as quantum communication and shared entanglement. Within this setting, we focus on the fundamental problem of quantum state certification: Given a complete description of some state $\sigma$, decide whether $\rho=\sigma$ or $\|\rho-\sigma\|_1\geq \epsilon$. Additionally, we focus on the case of limited \textit{quantum} communication between distributed nodes and the central node. We show that when each communication channel is limited to only $n_q\leq \log d$ qubits, then the sample complexity of distributed state certification is $\mathcal{O}(\frac{d^2}{2^{n_q}\epsilon^2})$ when public randomness is available to all nodes. Moreover, under the assumption that the channels used by the distributed nodes are \emph{mixedness-preserving}, we prove a matching lower bound. We further demonstrate that shared randomness is necessary to achieve the above complexity, by proving an $\Omega(\frac{d^3}{4^{n_q} \epsilon^2})$ lower bound in the \emph{private-coin} setting under the same assumption as above. Our lower bounds leverage a recently introduced quantum analogue of the celebrated Ingster--Suslina method and generalize arguments from the classical setting. Together, our work provides the first characterization of distributed quantum state certification in the regime of limited quantum communication and establishes a general framework for distributed quantum inference with communication constraints.
| Topic | Theoretical foundations of quantum learning |
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| Additional Topic | Quantum state and process tomography with learning-based approaches |