Exponential advantage in continuous-variable quantum state learning

• URL: http://arxiv.org/abs/2501.17633v1
• Date: Wed, 29 Jan 2025 13:10:37 GMT
• Title: Exponential advantage in continuous-variable quantum state learning
• Authors: Eugen Coroi, Changhun Oh,
• Abstract summary: We consider the task of learning quantum states in bosonic continuous-variable (CV) systems. We present a experimentally feasible protocol that utilizes entangled measurements and reflected states. We establish a rigorous exponential advantage from entangled measurements and access to reflected states in learning CV quantum states.
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• Abstract: We consider the task of learning quantum states in bosonic continuous-variable (CV) systems. We present a concrete experimentally feasible protocol that utilizes entangled measurements and reflected states to enable efficient learning of the characteristic function of CV quantum states with a sample complexity independent of the number of modes $n$. We then prove that any general adaptive learning scheme without entangled measurements requires a sample complexity that is exponential in $n$ to accomplish the same task, demonstrating an exponential advantage provided by entangled measurements. Remarkably, we also prove that any general adaptive entanglement-assisted scheme also requires an exponential sample complexity if access to reflected states is prohibited. Hence, we establish a rigorous exponential advantage from entangled measurements and access to reflected states in learning CV quantum states.

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