Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
Energy-constrained diamond norm with applications to the uniform continuity of continuous variable channel capacities
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abstract
The channels, and more generally superoperators acting on the trace class operators of a quantum system naturally form a Banach space under the completely bounded trace norm (aka diamond norm). However, it is well-known that in infinite dimension, the norm topology is often "too strong" for reasonable applications. Here, we explore a recently introduced energy-constrained diamond norm on superoperators (subject to an energy bound on the input states). Our main motivation is the continuity of capacities and other entropic quantities of quantum channels, but we also present an application to the continuity of one-parameter unitary groups and certain one-parameter semigroups of quantum channels.
fields
quant-ph 3years
2026 3verdicts
UNVERDICTED 3representative citing papers
An extension of the central limit theorem to bosonic quantum channels recovers the classical and state versions while supplying uncertainty relations and energy-constrained capacity lower bounds for linear bosonic channels.
In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.
citing papers explorer
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Quantum state isomorphism problems for groups
Quantum state isomorphism under group actions is BQP-hard for pure states across nontrivial groups and QSZK-complete for mixed states with finite groups; Pauli group version is BQP-complete and Clifford is GI-hard, ruling out efficient quantum algorithms for abelian mixed-state HS unless QSZK=BQP.
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Central Limit Theorem for Bosonic Quantum Channels
An extension of the central limit theorem to bosonic quantum channels recovers the classical and state versions while supplying uncertainty relations and energy-constrained capacity lower bounds for linear bosonic channels.
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Entanglement and circuit complexity in finite-depth random linear optical networks
In finite-depth random linear optical circuits, entanglement grows at most diffusively and robust circuit complexity scales similarly, with depth bounds ensuring near-maximal subsystem entanglement and closeness to Haar unitaries.