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arXiv:2604.24291

Catalytic Enhancement of Coherence Fraction in Noisy Quantum Channels and Characterization of Strictly Incoherent Operations

Priyabrata Char, Dipayan Chakraborty, Indrani Chattopadhyay, Debasis Sarkar

quant-phSubmitted Apr 27, 2026• Announced Apr 28, 2026• 0 citations
v1 · Apr 27, 2026v2 · May 17, 2026
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Abstract

In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state $ρ_s'$ as the input to a quantum channel $Λ$, instead of the original state $ρ_s$, can yield an output state $Λ(ρ_s')$ whose coherence fraction exceeds that of $Λ(ρ_s)$. We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map $\mathcal{E}$ to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.

Comments
12 pages, 4 figures, Comments welcome

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In realistic quantum information processing tasks, quantum states are inevitably affected by environmental noise, leading to decoherence and degradation of useful quantum resources. The coherence fraction, which serves as an important figure of merit for several quantum protocols, may decrease significantly after the action of a noisy channel. Such degradation can result in unsatisfactory performance in real-world applications. In this work, we investigate whether catalysis can be used to pre-process the input state to enhance the coherence fraction of an output state from a quantum channel. Specifically, we study whether using a processed state ρs′ρ_s'ρs′​ as the input to a quantum channel ΛΛΛ, instead of the original state ρsρ_sρs​, can yield an output state Λ(ρs′)Λ(ρ_s')Λ(ρs′​) whose coherence fraction exceeds that of Λ(ρs)Λ(ρ_s)Λ(ρs​). We analyze the conditions under which such an improvement is possible. We also provide a practical application of our setup for the phase discrimination task. Furthermore, we establish a necessary and sufficient condition for an incoherent state preserving CPTP(Completely Positive Trace Preserving) map E\mathcal{E}E to be a particular type of Strictly Incoherent Operation (SIO). This characterization provides a new structural understanding of SIO and clarifies its role in coherence manipulation. Our results offer practical insights into coherence preservation and enhancement in noisy quantum processes and may be useful for optimizing quantum information protocols under realistic conditions. We also provide numerical examples to support our claims.
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Coherent information quantifies the transmittable quantum information through a channel and is directly linked to the channel's quantum capacity. In a monitored quantum circuit, regarded as a quantum channel, extensive and positive coherent information is sustained at low measurement rates, protected by the scrambling dynamics. However, noise suppresses coherent information, driving it to zero or negative values. Here, we show that incorporating quantum-enhanced operations facilitates reliable quantum information transmission even in the presence of noise, as evidenced by a phase transition in coherent information from a recoverable phase with positive values to an irrecoverable phase with negative values. We provide both analytical understanding and numerical evidence demonstrating this transition, which is modulated by the relative frequencies of noise and quantum-enhanced operations. Additionally, we propose a resource-efficient protocol to characterize this phase transition in experiments, effectively avoiding postselection by utilizing every run of the quantum circuit. This approach bridges the gap between theoretical insights and practical implementation, making the phase transition feasible to demonstrate on realistic noisy intermediate-scale quantum devices.
In quantum technologies, quantum channels are essential for transmitting quantum states. Quantum channels usually introduce noise, thereby reducing the information in a state. These are mathematically described by completely positive trace-preserving linear maps that represent the generic evolution of quantum systems and are also special cases of Hermitian-preserving trace-preserving (HPTP) linear maps. Concatenating a quantum channel with another quantum channel makes it noisier and degrades its information and resource preservability. In this work, we demonstrate a physically meaningful way to compare a pair of quantum channels using Hermitian-preserving trace-preserving linear maps. Precisely, given a pair of quantum channels Λ1,Λ2Λ_1, Λ_2Λ1​,Λ2​ and an arbitrary unknown input state, we show that the output state of the quantum channel Λ2Λ_2Λ2​ from the pair can be uniquely identified from the output statistics of the other channel Λ1Λ_1Λ1​ from the pair, using some POVM, iff Λ2Λ_2Λ2​ can be obtained from Λ1Λ_1Λ1​ by concatenating it with a Hermitian-preserving trace-preserving linear map that is not necessarily positive. In such cases, Λ2Λ_2Λ2​ may not always be obtained from Λ1Λ_1Λ1​ through post-processing. The relation between these channels is a preorder, and we study its characterization in this work. In other words, we provide an operational interpretation of this preorder induced by HPTP linear maps in a communication scenario. Furthermore, we characterize the difficulty of implementing Λ2Λ_2Λ2​ given that Λ1Λ_1Λ1​ has already been implemented via a quantifier, namely, physical implementability. We also illustrate the implications of our results for the incompatibility of quantum devices through an example. In short, we provide valuable insights about the relevance of Hermitian-preserving trace-preserving linear maps in physically motivated settings.
A general property of quantum coherence is its non-increasing behavior during any incoherent quantum operation, such as an incoherent quantum channel in a noisy environment. We address that thermal coherence can mitigate these losses by offering relative improvements for different quantum models considering the ferromagnetic and antiferromagnetic properties. It is possible to obtain the thermal coherence of density operators obtained by the actions of the Hamiltonians, even for higher temperatures and certain values of the other parameters compared to other models. By adjusting the parameters, it is maximized such that the state of the output is maximally coherent. These make it possible to create maximal coherence in realizing any quantum information task in a noisy environment.
Quantum computers promise transformative speedups, but environmental noise destroys their fragile states. Conventional quantum error correction (QEC) encodes information redundantly across physical qubits, yet fails above a threshold of about 1% and incurs polynomial qubit overhead. A recent theorem from the resource theory of coherence shows that catalytic covariant operations amplify coherence at an unbounded rate, but this result has never been cast as an operational protocol. The challenge is to turn an asymptotic theorem into a recovery scheme that works at any noise strength with realistic resources. Here we show that catalytic coherence amplification can be cast as an error-correction primitive, Catalytic Quantum Error Correction (CQEC), which recovers a known target state from noisy copies without any error magnitude threshold whenever the target's coherent modes are preserved. In an effective model of the recovery map, fidelity exceeds 0.99 across 200 noise configurations spanning d = 4-64; the catalyst cost drops from the constructive bound n* ~ d^4 e^(2 gamma) to 32 copies at matched fidelity (10^4- to 10^9-fold) via a pipeline of dynamical decoupling, Clifford twirling, and recursive swap-test purification. A first explicitly CPTP, exactly covariant joint-channel implementation validates genuine recovery under dephasing at small dimension (0.54 -> 0.77) while showing that shallow circuits consume the catalyst, quantifying the model-vs-channel gap. These results turn an abstract resource-theoretic statement into a concrete protocol candidate complementary to stabilizer- and purification-based QEC; an open-source package reproducing the benchmarks accompanies this work (arXiv:2603.25774, https://github.com/deeptell-inc/cqec).