Quantum Representation Learning Beyond Pairwise Fidelity

• URL: http://arxiv.org/abs/2609.01797v1
• Date: Tue, 01 Sep 2026 19:07:37 GMT
• Title: Quantum Representation Learning Beyond Pairwise Fidelity
• Abstract summary: We show that a transition-probability-only learning interface can possess exact continuous blind directions in certain quantum-state families.<n>In relational quartets derived from toric-code and double-semion states, this fidelity-blind signal encodes inequivalent modular data despite identical pairwise fidelities.
• Score: 0.26856688022781555
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum contrastive, metric, and self-supervised learning often expose encoded quantum states to the learner through transition probabilities, especially fidelity. Quantum states are known to possess higher-order relational invariants, but their consequences for learned representations remain unclear. Here we show that a transition-probability-only learning interface can possess exact continuous blind directions in certain quantum-state families. We recover this missing information with a batch operator, built from coherent overlap amplitudes and negative masking, where its second moment $q_-$ retains four-state interference. Moreover, $q_-$ is directly measurable through two-copy interference and can enter variational learning via methods like parameter shift. In relational quartets derived from toric-code and double-semion states, this fidelity-blind signal encodes inequivalent modular data despite identical pairwise fidelities. Finally, in a four-photon benchmark with preparation drift, augmenting all six pairwise fidelities at two orthogonal probes with the corresponding normalized $q_-$ reduces the mean out-of-distribution phase error by $86\%$ at equal total shot budget. These results establish multistate relational observables as measurable, trainable, and physically consequential signals for quantum representation learning beyond pairwise fidelity.

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