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Higher-Order Quantum Operations

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arxiv 2503.09693 v1 pith:7W6XY4FD submitted 2025-03-12 quant-ph

Higher-Order Quantum Operations

classification quant-ph
keywords quantumoperationshigher-orderopenunicodex2014applicationarchitectures
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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An operational description of quantum phenomena concerns developing models that describe experimentally observed behaviour. $\textit{Higher-order quantum operations}\unicode{x2014}$quantum operations that transform quantum operations$\unicode{x2014}$are fundamental to modern quantum theory, extending beyond basic state preparations, evolutions, and measurements described by the Born rule. These operations naturally emerge in quantum circuit architectures, correlated open dynamics, and investigations of quantum causality, to name but a few fields of application. This Review Article provides both a pedagogical introduction to the framework of higher-order quantum operations and a comprehensive survey of current literature, illustrated through physical examples. We conclude by identifying open problems and future research directions in this rapidly evolving field.

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Cited by 14 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    quant-ph 2026-07 conditional novelty 7.0

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    Develops two protocols for probabilistic storage-and-retrieval of unitary superchannels, with staircase backstitch reaching unit success probability asymptotically as query number grows, plus a universal inversion protocol.

  5. Entanglement in quantum channel discrimination: sometimes less is more

    quant-ph 2026-05 unverdicted novelty 7.0

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    quant-ph 2026-04 unverdicted novelty 7.0

    Higher-order quantum map types form a distributive lattice of regular subtypes where signalling relations are determined by type function evaluations and structure poset rank parity, with normal forms derived from max...

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    A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibi...

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    quant-ph 2026-07 conditional novelty 6.0

    A continuous-variable link product for quantum circuit fragments is defined, with an efficient Gaussian covariance-matrix algorithm and demonstrations on non-Markovian and agent-environment processes.

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  11. Blind-spots of Randomized Benchmarking Under Temporal Correlations

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  12. GPU-accelerated semidefinite programming for causal games

    quant-ph 2026-06 unverdicted novelty 5.0

    GPU-accelerated see-saw SDP exploration finds no improvement in GYNI winning probability for local dimensions 6-8 over the d=5 value of approximately 0.6218.

  13. Trade-off between complexity and energy in quantum phase estimation

    quant-ph 2025-11 unverdicted novelty 5.0

    A new framework establishes a trade-off between energy cost and complexity in quantum phase estimation, locating a sweet spot for co-optimization at desired precision.

  14. Verifying Quantum Memory in the Dynamics of Spin Boson Models

    quant-ph 2025-05 unverdicted novelty 5.0

    Local quantum memory criteria applied via matrix product operator methods show that single-intervention process tensors generally predict quantum memory at low temperatures in spin-boson models, while dynamical maps d...