On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning

• URL: http://arxiv.org/abs/2507.11089v1
• Date: Tue, 15 Jul 2025 08:32:36 GMT
• Title: On the Fundamental Resource for Exponential Advantage in Quantum Channel Learning
• Authors: Minsoo Kim, Changhun Oh,
• Abstract summary: We distinguish between two fundamental resources provided by quantum memory -- entanglement and ancilla qubits.<n>We show that while a large amount of entanglement is not necessary, the dimension of the quantum memory is a crucial resource.
• Score: 3.3894236476098185
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum resources enable us to achieve an exponential advantage in learning the properties of unknown physical systems by employing quantum memory. While entanglement with quantum memory is recognized as a necessary qualitative resource, its quantitative role remains less understood. In this work, we distinguish between two fundamental resources provided by quantum memory -- entanglement and ancilla qubits -- and analyze their separate contributions to the sampling complexity of quantum learning. Focusing on the task of Pauli channel learning, a prototypical example of quantum channel learning, remarkably, we prove that vanishingly small entanglement in the input state already suffices to accomplish the learning task with only a polynomial number of channel queries in the number of qubits. In contrast, we show that without a sufficient number of ancilla qubits, even learning partial information about the channel demands an exponentially large sample complexity. Thus, our findings reveal that while a large amount of entanglement is not necessary, the dimension of the quantum memory is a crucial resource. Hence, by identifying how the two resources contribute differently, our work offers deeper insight into the nature of the quantum learning advantage.

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