arXiv subjects

Zhi-Xi Wang

Publications and source records attributed to Zhi-Xi Wang.

At least 37 records · Page 2Linked to original sources

arXiv2024

Tighter superadditivity relations for $l_{1}$-norm coherence measure

Quantum coherence serves as a crucial physical resource, with its quantification emerging as a focal point in contemporary research. Superadditivity constitutes one of the most fundamental attributes in characterizing the coherence distribution in multipartite quantum systems. In this paper, we provide a way to derive tighter superadditivity inequalities of $l_1$-norm coherence measure for arbitrary multiqubit states. We present a category of superadditivity relations related to the $α$-th ($α\geqslant 2$) power of $l_{1}$-norm coherence $C_{l_{1}}$ under certain conditions. Our results are better than existing ones and are illustrated in detail with examples.

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arXiv2024

Geometric genuine N-partite entanglement measure for arbitrary dimensions

We present proper genuine multipartite entanglement (GME) measures for arbitrary multipartite and dimensional systems. By using the volume of concurrence regular polygonal pyramid we first derive the GME measure of four-partite quantum systems. From our measure it is verified that the GHZ state is more entangled than the W state. Then we study the GME measure for multipartite quantum states in arbitrary dimensions. A well defined GME measure is constructed based on the volume of the concurrence regular polygonal pyramid. Detailed example shows that our measure can characterize better the genuine multipartite entanglements.

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arXiv2024

The quantum uncertainty relations of quantum channels

The uncertainty relation reveals the intrinsic difference between the classical world and the quantum world. We investigate the quantum uncertainty relation of quantum channel in qubit systems. Under two general measurement bases, we first derive the quantum uncertainty relation for quantum channels with respect to the relative entropy of coherence. Then we obtain the quantum uncertainty relation for unitary channels with respect to the $l_1$ norm of coherence. Some examples are given in detail.

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arXiv2024

Dynamics of quantum battery capacity under Markovian channels

We study the dynamics of the quantum battery capacity for the Bell-diagonal states under Markovian channels on the first subsystem. We show that the capacity increases for special Bell-diagonal states under amplitude damping channel. The sudden death of the capacity occurs under depolarizing channel. We also investigate the capacity evolution of Bell-diagonal states under Markovian channels on the first subsystem $n$ times. It is shown that the capacity under depolarizing channel decreases initially, then increases for small $n$ and tend to zero for large $n$. We find that under bit flip channel and amplitude damping channel, the quantum battery capacity of special Bell-diagonal states tends to a constant for large $n$, namely, the frozen capacity occurs. The dynamics of the capacity of the Bell-diagonal states under two independent same type local Markovian channels is also studied.

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arXiv2024

General monogamy relations of the $S^{t}$ and $T^{t}_q$-entropy entanglement measures based on dual entropy

Monogamy of entanglement is the fundamental property of quantum systems. By using two new entanglement measures based on dual entropy, the $S^{t}$-entropy entanglement and $T^{t}_q$-entropy entanglement measures, we present the general monogamy relations in multi-qubit quantum systems. We show that these newly derived monogamy inequalities are tighter than the existing ones. Based on these general monogamy relations, we construct the set of multipartite entanglement indicators for $N$-qubit states, which are shown to work well even for the cases that the usual concurrence-based indicators do not work. Detailed examples are presented to illustrate our results.

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arXiv2024

Tighter Constraints of Multi-Qubit Entanglement in Terms of Nonconvex Entanglement Measures LCREN and LCRENoA

The monogamy property of entanglement is an intriguing feature of multipartite quantum entanglement. Most entanglement measures satisfying the monogamy inequality are turned out to be convex. Whether nonconvex entanglement measures obeys the monogamy inequalities remains less known at present. As a well known measure of entanglement, the logarithmic negativity is not convex. We elucidate the constraints of multi-qubit entanglement based on the logarithmic convex-roof extended negativity (LCREN) and the logarithmic convex-roof extended negativity of assistance (LCRENoA). Using the Hamming weight derived from the binary vector associated with the distribution of subsystems, we establish monogamy inequalities for multi-qubit entanglement in terms of the $α$th-power ($α\geq 4\ln2$) of LCREN, and polygamy inequalities utilizing the $α$th-power ($0 \leq α\leq 2$) of LCRENoA. We demonstrate that these inequalities give rise to tighter constraints than the existing ones. Furthermore, our monogamy inequalities are shown to remain valid for the high dimensional states that violate the CKW monogamy inequality. Detailed examples are presented to illustrate the effectiveness of our results in characterizing the multipartite entanglement distributions.

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arXiv2023

Detecting multipartite entanglement via complete orthogonal basis

We study genuine tripartite entanglement and multipartite entanglement in arbitrary $n$-partite quantum systems based on complete orthogonal basis (COB). While the usual Bloch representation of a density matrix uses three types of generators, the density matrix with COB operators has one uniformed type of generators which may simplify related computations. We take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement and multipartite entanglement. We first convert the general states to simpler forms by using the relationship between general symmetric informationally complete measurements and COB. Then we derive an operational criteria to detect genuine tripartite entanglement. We study multipartite entanglement in arbitrary dimensional multipartite systems. By providing detailed examples, we demonstrate that our criteria can detect more genuine entangled and multipartite entangled states than the previously existing criteria.

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arXiv2023

Variational quantum algorithms for Poisson equations based on the decomposition of sparse Hamiltonians

Solving a Poisson equation is generally reduced to solving a linear system with a coefficient matrix $A$ of entries $a_{ij}$, $i,j=1,2,...,n$, from the discretized Poisson equation. Although the variational quantum algorithms are promising algorithms to solve the discretized Poisson equation, they generally require that $A$ be decomposed into a sum of $O[\text{poly}(\text{log}_2n)]$ simple operators in order to evaluate efficiently the loss function. A tensor product decomposition of $A$ with $2\text{log}_2n+1$ terms has been explored in previous works. In this paper, based on the decomposition of sparse Hamiltonians we greatly reduce the number of terms. We first write the loss function in terms of the operator $σ_x\otimes A$ with $σ_x$ denoting the standard Pauli operator. Then for the one-dimensional Poisson equations with different boundary conditions and for the $d$-dimensional Poisson equations with Dirichlet boundary conditions, we decompose $σ_x\otimes A$ into a sum of at most 7 and $(4d+1)$ Hermitian, one-sparse, and self-inverse operators, respectively. We design explicitly the quantum circuits to evaluate efficiently the loss function. The decomposition method and the design of quantum circuits can also be easily extended to linear systems with Hermitian and sparse coefficient matrices satisfying $a_{i,i+c}=a_{c}$ for $c=0,1,\cdots,n-1$ and $i=0,\cdots,n-1-c$.

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arXiv2023

Detection of entanglement for multipartite quantum states

We study genuine tripartite entanglement and multipartite entanglement of arbitrary $n$-partite quantum states by using the representations with generalized Pauli operators of a density matrices. While the usual Bloch representation of a density matrix uses three types of generators in the special unitary Lie algebra $\mathfrak{su}(d)$, the representation with generalized Pauli operators has one uniformed type of generators and it simplifies computation. In this paper, we take the advantage of this simplicity to derive useful and operational criteria to detect genuine tripartite entanglement. We also obtain a sufficient criterion to detect entanglement for multipartite quantum states in arbitrary dimensions. The new method can detect more entangled states than previous methods as backed by detailed examples.

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arXiv2023

Detection of tripartite entanglement based on principal basis matrix representations

We study the entanglement in tripartite quantum systems by using the principal basis matrix representations of density matrices. Using the Schmidt decomposition and local unitary transformation, we first convert the general states to simpler forms and then construct some special matrices from the correlation tensors of the simplified density matrices. Based on the different linear combinations of these matrices, necessary conditions are presented to detect entanglement of tripartite states. Detailed examples show that our method can detect more entangled states than previous ones.

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arXiv2023

Sharing EPR steering between sequential pairs of observers

The recycling of quantum correlations has attracted widespread attention both theoretically and experimentally. Previous works show that bilateral sharing of nonlocality is impossible under mild measurement strategy and 2-qubit entangled state can be used to witness entanglement arbitrary many times by sequential and independent pairs of observers. However, less is known about the bilateral sharing of EPR steering yet. Here, we aim at investigating the EPR steering sharing between sequential pairs of observers. We show that an unbounded number of sequential Alice-Bob pairs can share the EPR steering as long as the initially shared state is an entangled two-qubit pure state. The claim is also true for particular class of mixed entangled states.

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arXiv2023

Ising Hamiltonians for Constrained Combinatorial Optimization Problems and the Metropolis-Hastings Warm-Starting Algorithm

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis-Hastings warm-starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis-Hastings warm-starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1-depth QAOA.

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arXiv2023

Discrimination of Coherent States via Atom-Field Interaction without Rotation Wave Approximation

The quantum state discrimination is an important part of quantum information processing. We investigate the discrimination of coherent states through Jaynes-Cummings (JC) model interaction between the field and the ancilla without rotation wave approximation (RWA). We show that the minimum failure probability can be reduced as RWA is eliminated from JC model and the non-RWA terms accompanied by the quantum effects of fields (e.g. the virtual photon process in the JC model without RWA) can enhance the state discrimination. The JC model without RWA for unambiguous state discrimination is superior to ambiguous state discrimination, particularly when the number of sequential measurements increases. Unambiguous state discrimination implemented via the non-RWA JC model is beneficial to saving resource cost.

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arXiv2023

Bounds on positive operator-valued measure based coherence of superposition

Quantum coherence is a fundamental feature of quantum physics and plays a significant role in quantum information processing. By generalizing the resource theory of coherence from von Neumann measurements to positive operator-valued measures (POVMs), POVM-based coherence measures have been proposed with respect to the relative entropy of coherence, the $l_1$ norm of coherence, the robustness of coherence and the Tsallis relative entropy of coherence. We derive analytically the lower and upper bounds on these POVM-based coherence of an arbitrary given superposed pure state in terms of the POVM-based coherence of the states in superposition. Our results can be used to estimate range of quantum coherence of superposed states. Detailed examples are presented to verify our analytical bounds.

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arXiv2023

One-Way Deficit and Holevo Quantity of Generalized $n$-qubit Werner State

Originated from the work extraction in quantum systems coupled to a heat bath, quantum deficit is a kind of significant quantum correlations like quantum entanglement. It links quantum thermodynamics with quantum information. We analytically calculate the one-way deficit of the generalized $n$-qubit Werner state. We find that the one-way deficit increases as the mixing probability $p$ increases for any $n$. For fixed $p$, we observe that the one-way deficit increases as $n$ increases. For any $n$, the maximum of one-way deficit is attained at $p=1$. Furthermore, for large $n$ ($2^n \rightarrow \infty$), we prove that the curve of one-way deficit versus $p$ approaches to a straight line with slope $1$. We also calculate the Holevo quantity for the generalized $n$-qubit Werner state, and show that it is zero.

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arXiv2023

Assisted quantum simulation of open quantum systems

Universal quantum algorithms (UQA) implemented on fault-tolerant quantum computers are expected to achieve an exponential speedup over classical counterparts. However, the deep quantum circuits makes the UQA implausible in the current era. With only the noisy intermediate-scale quantum (NISQ) devices in hand, we introduce the quantum-assisted quantum algorithm, which reduces the circuit depth of UQA via NISQ technology. Based on this framework, we present two quantum-assisted quantum algorithms for simulating open quantum systems, which utilize two parameterized quantum circuits to achieve a short-time evolution. We propose a variational quantum state preparation method, as a subroutine to prepare the ancillary state, for loading a classical vector into a quantum state with a shallow quantum circuit and logarithmic number of qubits. We demonstrate numerically our approaches for a two-level system with an amplitude damping channel and an open version of the dissipative transverse field Ising model on two sites.

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arXiv2023

Unified multivariate trace estimation and quantum error mitigation

Calculating the trace of the product of $m$ $n$-qubit density matrices (multivariate trace) is a crucial subroutine in quantum error mitigation and information measures estimation. We propose an unified multivariate trace estimation (UMT) which conceptually unifies the previous qubit-optimal and depth-optimal approaches with tunable quantum circuit depth and the number of qubits. The constructed circuits have $\lceil(m-1)/s\rceil$ or $n\lceil(m-1)/s\rceil$ depth corresponding to $(s+m)n$ or $s+mn$ qubits for $s\in\{1,\cdots,\lfloor m/2\rfloor\}$, respectively. Such flexible circuit structures enable people to choose suitable circuits according different hardware devices. We apply UMT to virtual distillation for achieving exponential error suppression and design a family of concrete circuits to calculate the trace of the product of $8$ and $9$ $n$-qubit density matrices. Numerical example shows that the additional circuits still mitigate the noise expectation value under the global depolarizing channel.

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arXiv2022

Improved iterative quantum algorithm for ground-state preparation

Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. We provide practical guideline on the selection of the learning rate in QGD by finding a fundamental upper bound and establishing a relationship between our algorithm and the first-order approximation of the imaginary time evolution. Furthermore, we adapt a variational quantum state preparation method as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of our algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.

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