We analyze the geometrical properties of trace-preserving Pauli maps. Using the Choi-Jamio\l{}kowski isomorphism, we express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the Pauli map. We analytically compute the volumes of positive, trace-preserving Pauli maps and Pauli channels. In particular, we find the relative volumes of the entanglement-breaking Pauli channels as well as the channels that can be generated by a time-local generator. Finally, we show what part of the Pauli channels are $\mathrm{P}$ - and $\mathrm{CP}$ -divisible, which is related to the notion of Markovianity.We analyze the geometrical properties of trace-preserving Pauli maps. Using the Choi-Jamio\l{}kowski isomorphism, we express the Hilbert-Schmidt line and volume elements in terms of the eigenvalues of the Pauli map. We analytically compute the volumes of positive, trace-preserving Pauli maps and Pauli channels. In particular, we find the relative volumes of the entanglement-breaking Pauli channels as well as the channels that can be generated by a time-local generator. Finally, we show what part of the Pauli channels are $\mathrm{P}$- and $\mathrm{CP}$-divisible, which is related to the notion of Markovianity.

arXiv:1909.07722Physical Review ADec 23, 201912 citations

L’effet Pauli

Joe McEvoy, Oscar Zarate

EDP Sciences eBooksNov 4, 20200 citations

Realization of the Pauli gate based on superposition of the composite solitons via cold atomic medium

LI Wenzhuo, QIN Lu, ZHANG Yingying +6 more

多态量子逻辑门为提高信息编码维度和增强光场调控能力提供了新思路。我们提出通过复合孤子叠加实现三态量子泡利(Pauli)门的方案。本文考虑倒Ψ型五能级冷原子系统，利用奇异微扰展开法推导出三分量耦合非线性薛定谔(nonlinear Schrödinger,NLS)方程。量子态的单个量子比特由NLS方程的精确复合孤子解的分量定义。通过适当的旋转操作，在单个量子比特上实现Pauli-X、Pauli-Y和Pauli-Z操作。进一步以暗-亮-亮型三分量复合孤子作为单个量子比特，分析其自由传播及门操作。结果表明，Pauli-X门可实现分量间交换，Pauli-Y门在分量交换过程中引入相位调制，Pauli-Z门实现相位翻转。本文利用三分量复合孤子叠加态实现三态逻辑操作，为多态量子逻辑门和多通道光信息处理提供了新方案。多态量子逻辑门为提高信息编码维度和增强光场调控能力提供了新思路。我们提出通过复合孤子叠加实现三态量子泡利(Pauli)门的方案。本文考虑倒Ψ型五能级冷原子系统，利用奇异微扰展开法推导出三分量耦合非线性薛定谔(nonlinear Schrödinger,NLS)方程。量子态的单个量子比特由NLS方程的精确复合孤子解的分量定义。通过适当的旋转操作，在单个量子比特上实现Pauli-X、Pauli-Y和Pauli-Z操作。进一步以暗-亮-亮型三分量复合孤子作为单个量子比特，分析其自由传播及门操作。结果表明，Pauli-X门可实现分量间交换，Pauli-Y门在分量交换过程中引入相位调制，Pauli-Z门实现相位翻转。本文利用三分量复合孤子叠加态实现三态逻辑操作，为多态量子逻辑门和多通道光信息处理提供了新方案。

Acta Physica SinicaSep 4, 20260 citations

Pauli Propagation for Imaginary-Time Evolution

Rafael Gómez-Lurbe, Armando Pérez

We extend the Pauli Propagation framework to imaginary-time evolution and introduce imaginary-time Pauli Propagation (ITPP), an operator-based algorithm for approximating thermal and ground-state properties directly in the Pauli basis. We derive explicit imaginary-time propagation rules for Pauli strings and analyze the main approximation errors arising from Trotterization and Pauli-space truncation, including bounds that account for the non-unitary nature of the evolution. Benchmarking ITPP on the one-dimensional transverse field Ising model, we find that the method performs best in the high-temperature regime, where thermal states admit a compressed Pauli-basis approximation, while the required number of Pauli terms grows rapidly as the system approaches the ground-state limit. We further compare with tensor network simulations and study finite-temperature scalability through the number of retained Pauli terms required to reach a fixed target accuracy. These results establish ITPP as a complementary framework for imaginary-time simulation and suggest that combining imaginary-time and real-time Pauli Propagation could provide a pathway toward simulating more general non-unitary and open quantum system dynamics within a unified Pauli-based framework.We extend the Pauli Propagation framework to imaginary-time evolution and introduce imaginary-time Pauli Propagation (ITPP), an operator-based algorithm for approximating thermal and ground-state properties directly in the Pauli basis. We derive explicit imaginary-time propagation rules for Pauli strings and analyze the main approximation errors arising from Trotterization and Pauli-space truncation, including bounds that account for the non-unitary nature of the evolution. Benchmarking ITPP on the one-dimensional transverse field Ising model, we find that the method performs best in the high-temperature regime, where thermal states admit a compressed Pauli-basis approximation, while the required number of Pauli terms grows rapidly as the system approaches the ground-state limit. We further compare with tensor network simulations and study finite-temperature scalability through the number of retained Pauli terms required to reach a fixed target accuracy. These results establish ITPP as a complementary framework for imaginary-time simulation and suggest that combining imaginary-time and real-time Pauli Propagation could provide a pathway toward simulating more general non-unitary and open quantum system dynamics within a unified Pauli-based framework.

quant-pharXiv:2601.14400New Journal of PhysicsJan 22, 20260 citations

Non-Markovianity induced by Pauli-twirling

Joris Kattemölle, Balázs Gulácsi, Guido Burkard

Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the $\sqrt{X}$ -gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.Noise forms a central obstacle to effective quantum information processing. Recent experimental advances have enabled the tailoring of noise properties through Pauli twirling, transforming arbitrary noise channels into Pauli channels. This underpins theoretical descriptions of fault-tolerant quantum computation and forms an essential tool in noise characterization and error mitigation. Pauli-Lindblad channels have been introduced to aptly parameterize quasi-local Pauli errors across a quantum register, excluding negative Pauli-Lindblad parameters relying on the Markovianity of the underlying noise processes. We point out that caution is required when parameterizing channels as Pauli-Lindblad channels with nonnegative parameters. For this, we study the effects of Pauli twirling on Markovianity. We use the notion of Markovianity of a channel (rather than that of an entire semigroup) and prove a general Pauli channel is non-Markovian if and only if at least one of its Pauli-Lindblad parameters is negative. Using this, we show that Markovian quantum channels often become non-Markovian after Pauli twirling. The Pauli-twirling induced non-Markovianity necessitates the use of negative Pauli-Lindblad parameters for a correct noise description in experimentally realistic scenarios. An important example is the implementation of the $\sqrt{X}$-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.

quant-pharXiv:2602.08464npj Quantum InformationFeb 10, 20260 citations

\mathrm{P}

- and

\mathrm{CP}

-divisible, which is related to the notion of Markovianity.

\sqrt{X}

-gate under standard Markovian noise. As such, our results have direct implications for quantum error mitigation protocols that rely on accurate noise characterization.