arXiv subjects

Zhaoqi Wu

Publications and source records attributed to Zhaoqi Wu.

At least 19 recordsLinked to original sources

arXiv2026

Average metric adjusted skew information of coherence under conical 2-designs generalized equiangular measurements

Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under conical 2-designs generalized equiangular measurements, and prove the equivalence of this measure to the scaled average coherence based on metric adjusted skew information under a set of unitary groups, operator orthonormal bases, and mutually unbiased bases. We also derive two trade-off relations by this measure and solve a conjecture. Furthermore, we give two entanglement criteria by this measure and conical 2-designs generalized equiangular measurement, respectively, and illustrate the effectiveness of them by explicit examples.

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arXiv2026

Coherence and decoherence in generalized and noisy Shor's algorithm

Quantum coherence constitutes a fundamental physical mechanism essential to the study of quantum algorithms. We study the coherence and decoherence in generalized Shor's algorithm where the register $A$ is initialized in arbitrary pure state, or the combined register $AB$ is initialized in any pseudo-pure state, which encompasses the standard Shor's algorithm as a special case. We derive both the lower and upper bounds on the performance of the generalized Shor's algorithm, and establish the relation between the probability of calculating $r$ when the register $AB$ is initialized in any pseudo-pure state and the one when the register $A$ initialized in arbitrary pure state. Moreover, we study the coherence and decoherence in noisy Shor's algorithm and give the lower bound of the probability that we can calculate $r$.

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arXiv2026

Coherence dynamics in Simon's quantum algorithm

Quantum coherence plays a pivotal role in quantum algorithms. We study the coherence dynamics of the evolved states in Simon's quantum algorithm based on Tsallis relative $α$ entropy and $l_{1,p}$ norm. We prove that the coherences of the first register and the second register both rely on the dimension $N$ of the state spaces of the $n$ qubit systems, and increase with the increase of $N$. We show that the oracle operator $O$ does not change the coherence. Moreover, we study the coherence dynamics in the Simon's quantum algorithm and prove that in overall the coherence is in production when $N>4$ and in depletion when $N<4$.

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arXiv2026

Coherence dynamics in quantum algorithm for linear systems of equations

Quantum coherence is a fundamental issue in quantum mechanics and quantum information processing. We explore the coherence dynamics of the evolved states in HHL quantum algorithm for solving the linear system of equation $A\overrightarrow{x}=\overrightarrow{b}$. By using the Tsallis relative $α$ entropy of coherence and the $l_{1,p}$ norm of coherence, we show that the operator coherence of the phase estimation $P$ relies on the coefficients $β_{i}$ obtained by decomposing $|b\rangle$ in the eigenbasis of $A$. We prove that the operator coherence of the inverse phase estimation $\widetilde{P}$ relies on the coefficients $β_{i}$, eigenvalues of $A$ and the success probability $P_{s}$, and it decreases with the increase of the probability when $α\in(1,2]$. Moreover, the variations of coherence deplete with the increase of the success probability and rely on the eigenvalues of $A$ as well as the success probability.

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arXiv2026

Tsallis relative $α$ entropy of coherence dynamics in Grover's search algorithm

Quantum coherence plays a central role in Grover's search algorithm. We study the Tsallis relative $α$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $α$ entropy of coherence decreases with the increase of the success probability, and derive the complementarity relations between the coherence and the success probability. We show that the operator coherence of the first $H^{\otimes n}$ relies on the size of the database $N$, the success probability and the target states. Moreover, we illustrate the relationships between coherence and entanglement of the superposition state of targets, as well as the production and deletion of coherence in Grover iterations.

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arXiv2026

Coherence and entanglement dynamics in Shor's algorithm

Shor's algorithm outperforms its classical counterpart in efficient prime factorization. We explore the coherence and entanglement dynamics of the evolved states within Shor's algorithm, showing that the coherence in each step relies on the dimension of register or the order, and discuss the relations between geometric coherence and geometric entanglement. We investigate how unitary operators induce variations in coherence and entanglement, and analyze the variations of coherence and entanglement within the entire algorithm, demonstrating that the overall effect of Shor's algorithm tends to deplete coherence and produce entanglement. Our research not only deepens the understanding of this algorithm but also provides methodological references for studying resource dynamics in other quantum algorithms.

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arXiv2026

Quantifying magic via quantum $(α,β)$ Jensen-Shannon divergence

Magic states play an important role in fault-tolerant quantum computation, and so the quantification of magic for quantum states is of great significance. In this work, we propose two new magic quantifiers by introducing two versions of quantum $(α,β)$ Jensen-Shannon divergence based on the quantum $(α,β)$ entropy and the quantum $(α,β)$-relative entropy, respectively. We derive many desirable properties for our magic quantifiers, and find that they are efficiently computable in low-dimensional Hilbert spaces. We also show that the initial nonstabilizerness in the input state can boost the magic generating power for our magic quantifiers with appropriate parameter ranges for a certain class of quantum gates. Our magic quantifiers may provide new tools for addressing some specific problems in magic resource theory.

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arXiv2026

Coherence and Imaginarity as Resources in Quantum Circuit Complexity

Quantum circuit complexity quantifies the minimal number of gates needed to realize a unitary transformation and plays a central role in quantum computation. In this work, we investigate the complexity of quantum circuits through coherence and imaginarity resources. We establish a lower bound on the circuit cost by the Tsallis relative $α$ entropy of cohering power, which is shown to be tighter than the one presented by Bu et al.[\textit{Communications in Mathematical Physics} 405, no. 7 (2024):161] under restrictive conditions. As a consequence, we obtain the relationships between the circuit cost and the coherence generating power via probabilistic average in terms of skew information/relative entropy, and present explicit bounds of the circuit cost for typical quantum gates. Moreover, we derive lower bounds on the circuit cost via the imaginaring power of the circuit, induced by the Tsallis relative $α$ entropy and relative entropy. We demonstrate that imaginarity can yield nontrivial constraints on the circuit cost even when coherence-based lower bounds are zero (e.g., for the $T$ gate), which implies that imaginarity may provide advantages under certain circumstances compared with coherence. Our results may help better understand the connections between quantum resources and circuit complexity.

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arXiv2026

Uncertainty relations for unified ($α$,$β$)-relative entropy of coherence under mutually unbiased equiangular tight frames

Uncertainty relations based on quantum coherence is an important problem in quantum information science. We discuss uncertainty relations for averaged unified ($α$,$β$)-relative entropy of coherence under mutually unbiased equiangular tight frames, and derive an interesting result for different parameters. As consequences, we obtain corresponding results under mutually unbiased bases, equiangular tight frames or based on Tsallis $α$- relative entropies and Rényi-$α$ relative entropies. We illustrate the derived inequalities by explicit examples in two dimensional spaces, showing that the lower bounds can be regarded as good approximations to averaged coherence quantifiers under certain circumstances.

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arXiv2026

Quantifying imaginarity of quantum operations

Complex numbers are theoretically proved and experimentally confirmed as necessary in quantum mechanics and quantum information, and a resource theory of imaginarity of quantum states has been established. In this work, we establish a framework to quantify the imaginarity of quantum operations from the perspective of the ability to create or detect imaginarity, following the idea by Theurer {\it et al.} [Phys. Rev. Lett. \textbf{122}, 190405 (2019)] used in coherence theory. We present two types of imaginarity measures of quantum operations based on the norm and the weight, investigate their properties and relations, and derive the analytical formulas of the measure under the trace norm for qubit unitary operations. The results provide new insights into imaginarity of operations and deepen our understanding of dynamical imaginarity.

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arXiv2025

Quantifying coherence of quantum channels based on the generalized $α$-$z$-relative Rényi entropy

By using the Choi-Jamiołkowski isomorphism, we propose a well-defined coherence measure of quantum channels based on the generalized $α$-$z$-relative Rényi entropy. In addition, we present an alternative coherence measure of quantum channels by quantifying the commutativity between the channels and the completely dephasing channels with the generalized $α$-$z$-relative Rényi entropy. Some elegant properties of the measures are illustrated in detail. Explicit formulas of these coherence measures are derived for some detailed typical quantum channels.

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arXiv2025

Coherence monotones of quantum channels based on two generalized quantum relative entropies

By using the Choi-Jamiołkowski isomorphism, we propose two classes of coherence monotones of quantum channels based on the unified $(r,s)$-relative entropy and the sandwiched Rényi relative entropy. Elegant properties of the coherence monotones for quantum channels are explored. Moreover, we present the upper bounds of the coherence monotones and derive the explicit formulas of the coherence monotones for qubit unitary channels.

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arXiv2025

Two imaginarity monotones induced by unified $(α,β)$-relative entropy

Complex numbers play a pivotal role in both mathematics and physics, particularly in quantum mechanics, and are extensively utilized to depict the behavior of microscopic particles. Recognizing the significance of complex numbers, a framework of imaginarity resource theory has recently been established. In this work, we propose two types of imaginarity monotones induced by the unified $(α,β)$-relative entropy and investigate their properties. Moreover, we give explicit examples to illustrate our results.

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arXiv2023

Tighter sum uncertainty relations via $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

We establish tighter uncertainty relations for arbitrary finite observables via $(α,β,γ)$ weighted Wigner-Yanase-Dyson ($(α,β,γ)$WWYD) skew information. The results are also applicable to the $(α,γ)$ weighted Wigner-Yanase-Dyson ($(α,γ)$WWYD) skew information and the weighted Wigner-Yanase-Dyson (WWYD) skew information. We also present tighter lower bounds of quantum channels and unitary channels via $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson ($(α,β,γ)$MWWYD) skew information. Detailed examples are provided to illustrate tightness of our uncertainty relations.

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arXiv2023

Quantum Otto engine with quantum correlations

We theoretically prose and investigate a photo-Otto engine that is working with a single-mode radiation field inside an optical cavity and alternatively driven by a hot and a cold reservoir, where the hot reservoir is realized by sending one of a pair of correlated two-level atoms to pass through the optical cavity, and the cold one is made of a collection of noninteracting boson modes. In terms of the quantum discord of the pair of atoms, we derive the analytical expressions for the performance parameters (power and efficiency) and stability measure (coefficient of variation for power). We show that quantum discord boosts the performance and efficiency of the quantum engine, and even may change the operation mode. We also demonstrate that quantum discord improves the stability of machine by decreasing the coefficient of variation for power which satisfies the generalized thermodynamic uncertainty relation. Finally, we find that these results can be transferred to another photo-Otto engine model, where the optical cavity is alternatively coupled to a hot thermal bosonic bath and to a beam of pairs of the two correlated atoms that play the role of a cold reservoir.

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arXiv2022

Tighter uncertainty relations based on $(α,β,γ)$ modified weighted Wigner-Yanase-Dyson skew information of quantum channels

We use a novel formation to illustrate the ($α,β,γ$) modified weighted Wigner-Yanase-Dyson (($α,β,γ$) MWWYD) skew information of quantum channels. By using operator norm inequalities, we explore the sum uncertainty relations for arbitrary $N$ quantum channels and for unitary channels. These uncertainty inequalities are shown to be tighter than the existing ones by a detailed example. Our results are also applicable to the modified weighted Wigner-Yanase-Dyson (MWWYD) skew information and the ($α,γ$) modified weighted Wigner-Yanase-Dyson (($α,γ$) MWWYD) skew information of quantum channels as special cases.

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arXiv2022

Sum uncertainty relations based on $(α,β,γ)$ weighted Wigner-Yanase-Dyson skew information

We introduce ($α,β,γ$) weighted Wigner-Yanase-Dyson (($α,β,γ$) WWYD) skew information and ($α,β,γ$) modified weighted Wigner-Yanase-Dyson (($α,β,γ$) MWWYD) skew information. We explore the sum uncertainty relations for arbitrary $N$ mutually noncommutative observables based on ($α,β,γ$) WWYD skew information. A series of uncertainty inequalities are derived. We show by detailed example that our results cover and improve the previous ones based on the original Wigner-Yanase (WY) skew information. Finally, we establish new sum uncertainty relations in terms of the ($α,β,γ$) MWWYD skew information for arbitrary $N$ quantum channels.

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arXiv2022

Uncertainty of quantum channels via modified generalized variance and modified generalized Wigner-Yanase-Dyson skew information

Uncertainty relation is a fundamental issue in quantum mechanics and quantum information theory. By using modified generalized variance (MGV), and modified generalized Wigner-Yanase-Dyson skew information (MGWYD), we identify the total and quantum uncertainty of quantum channels. The elegant properties of the total uncertainty of quantum channels are explored in detail. In addition, we present a trade-off relation between the total uncertainty of quantum channels and the entanglement fidelity and establish the relationships between the total uncertainty and entropy exchange/coherent information. Detailed examples are given to the explicit formulas of the total uncertainty and the quantum uncertainty of quantum channels. Moreover, utilizing a realizable experimental measurement scheme by using the Mach-Zehnder interferometer proposed in Nirala et al. (Phys Rev A 99:022111, 2019), we discuss how to measure the total/quantum uncertainty of quantum channels for pure states.

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