Entanglement-enabled advantage for learning a bosonic random displacement channel

Abstract

We show that quantum entanglement can provide an exponential advantage in learning properties of a bosonic continuous-variable (CV) system. The task we consider is estimating a probabilistic mixture of displacement operators acting on $n$ bosonic modes, called a random displacement channel. We prove that if the $n$ modes are not entangled with an ancillary quantum memory, then the channel must be sampled a number of times exponential in $n$ in order to estimate its characteristic function to reasonable precision; this lower bound on sample complexity applies even if the channel inputs and measurements performed on channel outputs are chosen adaptively. On the other hand, we present a simple entanglement-assisted scheme that only requires a number of samples independent of $n$, given a sufficient amount of squeezing. This establishes an exponential separation in sample complexity. We then analyze the effect of photon loss and show that the entanglement-assisted scheme is still significantly more efficient than any lossless entanglement-free scheme under mild experimental conditions. Our work illuminates the role of entanglement in learning continuous-variable systems and points toward experimentally feasible demonstrations of provable entanglement-enabled advantage using CV quantum platforms.

7+28 pages, 3+6 figures

References in corpus (37)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The Quantum Internet
• Advances in Quantum Metrology
• Quantum information with continuous variables
• Gaussian Quantum Information
• Quantum metrology
• Quantum computational advantage using photons
• Encoding a qubit in an oscillator
• Characterizing Quantum Supremacy in Near-Term Devices
• Strong quantum computational advantage using a superconducting quantum processor
• Resolving photon number states in a superconducting circuit
• Quantum advantage in learning from experiments
• Noise tailoring for scalable quantum computation via randomized compiling
• A hybrid on-chip opto-nanomechanical transducer for ultra-sensitive force measurements
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• A quantum-enhanced search for dark matter axions
• Distributed quantum sensing in a continuous variable entangled network
• Information-theoretic bounds on quantum advantage in machine learning
• Distributed Quantum Sensing Using Continuous-Variable Multipartite Entanglement
• Demonstration of a Reconfigurable Entangled Radiofrequency-Photonic Sensor Network
• Gaussian Boson Sampling with Pseudo-Photon-Number Resolving Detectors and Quantum Computational Advantage
• Single-Mode Displacement Sensor
• Quantum-Enhanced continuous-wave stimulated Raman spectroscopy
• Entangled sensor-networks for dark-matter searches
• Quantum advantages for Pauli channel estimation
• Optimal Distributed quantum sensing using Gaussian states
• 43-GHz bandwidth real-time amplitude measurement of 5-dB squeezed light using modularized optical parametric amplifier with 5G technology
• Classical shadow tomography for continuous variables quantum systems
• Ultimate precision limit of noise sensing and dark matter search
• Quantum Metrological Power of Continuous-Variable Quantum Networks
• Distributed quantum phase sensing for arbitrary positive and negative weights
• Tight bounds on Pauli channel learning without entanglement
• Test one to test many: a unified approach to quantum benchmarks
• Efficient verification of bosonic quantum channels via benchmarking
• Efficient Learning of Continuous-Variable Quantum States
• A learning theory for quantum photonic processors and beyond

Cited by in corpus (10)

• Hybrid Oscillator-Qubit Quantum Processors: Instruction Set Architectures, Abstract Machine Models, and Applications
• Learning quantum states of continuous variable systems
• Entanglement-induced provable and robust quantum learning advantages
• Quantum learning advantage on a scalable photonic platform
• Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
• Linear-optical protocols for mitigating and suppressing noise in bosonic systems
• On the query complexity of unitary channel certification
• On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning
• Physical-Layer Machine Learning with Multimode Interferometric Photon Counting
• Detection of nonabsolute separability in quantum states and channels through moments