arXiv subjects

Linlin Ye

Publications and source records attributed to Linlin Ye.

8 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 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 $\alpha$ 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 $\alpha$ 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 $\beta_{i}$ 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 $\beta_{i}$, eigenvalues of $A$ and the success probability $P_{s}$, and it decreases with the increase of the probability when $\alpha\in(1,2]$. 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 $\alpha$ 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 $\alpha$ entropy of coherence dynamics of the evolved state in Grover's search algorithm. We prove that the Tsallis relative $\alpha$ 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

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 $\alpha$ 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 $\alpha$ 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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arXiv2025

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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arXiv2016

Understanding the Impacts of Dark Pools on Price Discovery

This paper investigates the impact of dark pools on price discovery (the efficiency of prices on stock exchanges to aggregate information). Assets are traded in either an exchange or a dark pool, with the dark pool offering better prices but lower execution rates. Informed traders receive noisy and heterogeneous signals about an asset's fundamental. We find that informed traders use dark pools to mitigate their information risk and there is a sorting effect: in equilibrium, traders with strong signals trade in exchanges, traders with moderate signals trade in dark pools, and traders with weak signals do not trade. As a result, dark pools have an amplification effect on price discovery. That is, when information precision is high (information risk is low), the majority of informed traders trade in the exchange hence adding a dark pool enhances price discovery, whereas when information precision is low (information risk is high), the majority of the informed traders trade in the dark pool hence adding a dark pool impairs price discovery. The paper reconciles the conflicting empirical evidence and produces novel empirical predictions. The paper also provides regulatory suggestions with dark pools on current equity markets and in emerging markets.

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