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.

• The paper shows that using entangled states achieves an exponential reduction in sample complexity compared to entanglement-free methods for bosonic displacement channels.
• The paper employs two-mode squeezed vacuum states and Bell measurements to maintain constant sample complexity regardless of the number of bosonic modes.
• The paper demonstrates that the entanglement-enabled advantage persists under realistic noise conditions such as photonic loss and phase noise.

An Entanglement-Enabled Separation in Learning Bosonic Random Displacement Channels

The paper entitled "Entanglement-enabled advantage for learning a bosonic random displacement channel" presents a rigorous analysis of the exponential advantage provided by quantum entanglement in learning bosonic continuous-variable (CV) random displacement channels. The authors examine a task wherein the goal is to estimate a probabilistic mixture of displacement operators acting on multiple bosonic modes, which define the random displacement channel. They demonstrate that if the bosonic modes are not entangled with an ancillary quantum memory, the channel must be sampled a number of times exponential in the number of modes to accurately estimate its characteristic function. This lower bound holds even under adaptive channel input and output measurement schemes. In contrast, when assisted by entangled states, the sample complexity remains constant, independent of the number of modes.

Results and Implications

The authors present a compelling case for the use of entanglement in reducing the sample complexity associated with learning quantum channels in CV systems. In a conventional entanglement-free scenario, the sample complexity increases exponentially with the number of modes, posing significant challenges for practical implementation. This exponential complexity is rooted in the fact that entanglement-free methods cannot fully exploit non-commutative properties inherent in displacement operators.

An entanglement-assisted approach leveraging two-mode squeezed vacuum (TMSV) states and Bell measurements provides an exponential reduction in sample complexity, particularly when the squeezing parameters scale logarithmically with the number of modes. This setup achieves a constant sample complexity, representing a major theoretical and practical benefit when scaling up quantum systems. Additionally, even under realistic experimental conditions with photonic loss, the authors show that this entanglement-assisted separation is substantial, suggesting feasibility in near-term quantum experiments.

The authors derive both upper and lower bounds on sample complexity, establishing a clear separation based on the quantum resources used. Analyzing realistic noise conditions such as photon loss, phase noise, and crosstalk, they show that this advantage persists under experimental setups feasible with current technology.

Theoretical and Practical Impact

From a theoretical standpoint, this paper contributes significantly to our understanding of quantum learning tasks, particularly in the arena of CV quantum systems. It extends methodologies used for discrete variable systems to CV scenarios, providing insights into the intrinsic benefits of using entangled quantum memories. This paradigm can inspire future studies on quantum models that exhibit memory advantages, enhancing our understanding of quantum-classical separations in learning tasks.

From a practical standpoint, the work underscores the strategic advantage of embedding entanglement in quantum information processing for the efficient characterization of continuous-variable channels. This has potential implications for quantum network design, error correction, sensor networks, and other quantum technologies utilizing bosonic modes. The results suggest quantum technologies based on CV systems can leverage these entanglement-enabled advantages in tasks ranging from sensing to communication.

Future Prospects in Quantum Artificial Intelligence

This research has implications for the future development of AI utilizing quantum technologies, specifically in improving sample efficiency which is pivotal for scaling quantum AI models. As quantum hardware continues to advance, leveraging entanglement could result in substantial performance improvements in machine learning tasks that involve state or channel discrimination in CV systems. As technology progresses allowing for greater integration of quantum and classical systems, these advantages could be practically realized, propelling advances in quantum-enhanced AI and machine learning.

In summary, the work constitutes a substantial theoretical advancement by establishing a rigorous entanglement-induced separation in learning CV quantum channels, with significant experimental implications for the future of quantum technologies and quantum-enhanced machine learning.