Fundamental limitations on the recoverability of quantum processes
arXiv:2403.12947 · doi:10.1007/s00023-025-01590-y
Abstract
Quantum information processing and computing tasks can be understood as quantum networks, comprising quantum states and channels and possible physical transformations on them. It is hence pertinent to estimate the change in informational content of quantum processes due to physical transformations they undergo. The physical transformations of quantum states are described by quantum channels, while the transformations of quantum channels are described by quantum superchannels. In this work, we determine fundamental limitations on how well the physical transformation on quantum channels can be undone or reversed, which are of crucial interest to design and benchmark quantum information and computation devices. In particular, we refine (strengthen) the quantum data processing inequality for quantum channels under the action of quantum superchannels. We identify a class of quantum superchannels, which appears to be the superchannel analogue of subunital quantum channels, under the action of which the entropy of an arbitrary quantum channel is nondecreasing. We also provide a refined inequality for the entropy change of quantum channels under the action of an arbitrary quantum superchannel.
Improved presentation (close to published version); For application in quantum thermodynamics, see arXiv:2510.12790
References in corpus (38)
- The Role of Relative Entropy in Quantum Information Theory
- On quantum Renyi entropies: a new generalization and some properties
- The second laws of quantum thermodynamics
- Entropic Uncertainty Relations and their Applications
- The Resource Theory of Quantum States Out of Thermal Equilibrium
- The Quantum Chernoff Bound
- Theoretical framework for quantum networks
- Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
- Quantum advantage with shallow circuits
- Transforming quantum operations: quantum supermaps
- Reversing quantum dynamics with near-optimal quantum and classical fidelity
- Tight uniform continuity bounds for quantum entropies: conditional entropy, relative entropy distance and energy constraints
- Quantum Computation by Communication
- Inequalities for Quantum Entropy: A Review with Conditions for Equality
- The Evolution of Quantum Secure Direct Communication: On the Road to the Qinternet
- Comparison of Quantum Channels by Superchannels
- Strong converse exponents for a quantum channel discrimination problem and quantum-feedback-assisted communication
- Recoverability in quantum information theory
- Unital Quantum Channels - Convex Structure and Revivals of Birkhoff's Theorem
- Universal recovery maps and approximate sufficiency of quantum relative entropy
- Approaches for approximate additivity of the Holevo information of quantum channels
- Monotonicity of the Quantum Relative Entropy Under Positive Maps
- Multiplicativity of completely bounded p-norms implies a new additivity result
- Strengthened Monotonicity of Relative Entropy via Pinched Petz Recovery Map
- Quartic quantum theory: an extension of the standard quantum mechanics
- Theoretical framework for Higher-Order Quantum Theory
- Approximate reversibility in the context of entropy gain, information gain, and complete positivity
- Entropy of a quantum channel
- Efficient universal programmable quantum measurements
- New perspectives on covariant quantum error correction
- Towards a Unified Framework for Approximate Quantum Error Correction
- Causal structures and the classification of higher order quantum computations
- Structure of sufficient quantum coarse-grainings
- Programmability of covariant quantum channels
- Quantum reading capacity: General definition and bounds
- A general theory of comparison of quantum channels (and beyond)
- Quantum Network Discrimination
- Convolution algebra of superoperators and nonseparability witnesses for quantum operations