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Zhu-Jun Zheng

Publications and source records attributed to Zhu-Jun Zheng.

At least 37 records · Page 2Linked to original sources
arXiv2023

Sharing tripartite nonlocality sequentially by arbitrarily many independent observers

There exist bipartite entangled states whose violations of Clauser-Horne-Shimony-Holt (CHSH) Bell inequality can be observed by a single Alice and arbitrarily many sequential Bobs [Phys. Rev. Lett. 125, 090401 (2020)]. Here we consider its analogues for tripartite systems: a tripartite entangled state is shared among Alice, Bob and multiple Charlies. The first Charlie measures his qubit and then passes his qubit to the next Charlie who measures again with other measurements and so on. The goal is to maximize the number of Charlies that can observe some kind of nonlocality with the single Alice and Bob. It has been shown that at most two Charlies could share genuine nonlocality of the Greenberger-Horne-Zeilinger (GHZ) state via the violation of Svetlichny inequality with Alice and Bob [Quantum Inf. Process. 18, 42 (2019) and Phys. Rev. A 103, 032216 (2021)]. In this work, we show that arbitrarily many Charlies can have standard nonlocality (via violations of Mermin inequality) and some other kind of genuine nonlocality (which is known as genuinely nonsignal nonlocality) with the single Alice and single Bob.

quant-ph↗
arXiv2023

Beyond the mixture of generalized Pauli dephasing channels

In recent times, there has been a growing scholarly focus on investigating the intricacies of quantum channel mixing. It has been commonly believed, based on intuition in the literature, that every generalized Pauli channel with dimensionality $d$ could be represented as a convex combination of $(d+1)$ generalized Pauli dephasing channels (see [Phys. Rev. A 103, 022605 (2021)] as a reference). To our surprise, our findings indicate the inaccuracy of this intuitive perspective. This has stimulated our interest in exploring the properties of convex combinations of generalized Pauli channels, beyond the restriction to just $(d+1)$ generalized Pauli dephasing channels. We demonstrate that many previously established properties still hold within this broader context. For instance, any mixture of invertible generalized Pauli channels retains its invertibility. It's worth noting that this property doesn't hold when considering the Weyl channels setting. Additionally, we demonstrate that every Pauli channel (for the case of $d=2$) can be represented as a mixture of $(d+1)$ Pauli dephasing channels, but this generalization doesn't apply to higher dimensions. This highlights a fundamental distinction between qubit and general qudit cases. In contrast to prior understanding, we show that non-invertibility of mixed channels is not a prerequisite for the resulting mapping to constitute a Markovian semigroup.

quant-ph↗
arXiv2023

Quantum key distribution over noisy channels by the testing state method

Quantum key distribution(QKD) might be the most famous application of quantum information theory. The idea of QKD is not difficult to understand but in practical implementations, many problems are needed to be solved, for example, the noise of the channels. Previous works usually discuss the estimate of the channels and employ error-correcting procedures, whose feasibility and efficiency depend on the strength of the noise, or assist with entanglement distillation procedures, which often result in a large consumption of states while not all states can be distilled. This paper aims to study QKD over noisy channels including Pauli noises, amplitude damping noises, phase damping noises, collective noises as well as mixtures of them, in any strength without distillations. We provide a method, called the testing state method, to implement QKD protocols without errors over arbitrarily strength noisy channels. The method can be viewed as an error-correcting procedure, and can also be employed for other tasks.

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arXiv2022

Multipartite concurrence of W-class states based on sub-partite quantum systems

We study the concurrence for arbitrary N-partite W-class states based on the (N-1)-partite partitions of subsystems by taking account to the structures of W-class states. By using the method of permutation and combination we give analytical formula of concurrence and some elegant relations between the multipartite concurrence and the (N-1)-partite concurrence for arbitrary multipartite W-class states. Applying these relations we present better lower bounds of concurrence for multipartite mixed states. An example is given to demonstrate that our lower bounds can detect more entanglements.

quant-ph↗
arXiv2022

Genuine hidden nonlocality without entanglement: from the perspective of local discrimination

Quantum nonlocality without entanglement is a fantastic phenomenon in quantum theory. This kind of quantum nonlocality is based on the task of local discrimination of quantum states. Recently, Bandyopadhyay and Halder [Phys. Rev. A 104, L050201 (2021)] studied the problem: is there any set of orthogonal states which can be locally distinguishable, but under some orthogonality preserving local measurement, each outcome will lead to a locally indistinguishable set. We say that the set with such property has hidden nonlocality. Moreover, if such phenomenon can not arise from discarding subsystems which is termed as local irredundancy, we call it genuine hidden nonlocality. There, they presented several sets of entangled states with genuine hidden nonlocality. However, they doubted the existence of a set without entanglement but with genuine hidden nonlocality. In this paper, we eliminate this doubt by constructing a series of sets without entanglement but whose nonlocality can be genuinely activated. We derive a method to tackle with the local irredundancy problem which is a key tricky for the systems whose local dimensions are composite numbers. As Bandyopadhyay and Halder have been pointed out, sets with genuine hidden nonloclity would lead to some applications on the data hiding.

quant-ph↗
arXiv2021

A hybrid quantum-classical neural network with deep residual learning

Inspired by the success of classical neural networks, there has been tremendous effort to develop classical effective neural networks into quantum concept. In this paper, a novel hybrid quantum-classical neural network with deep residual learning (Res-HQCNN) is proposed. We firstly analysis how to connect residual block structure with a quantum neural network, and give the corresponding training algorithm. At the same time, the advantages and disadvantages of transforming deep residual learning into quantum concept are provided. As a result, the model can be trained in an end-to-end fashion, analogue to the backpropagation in classical neural networks. To explore the effectiveness of Res-HQCNN , we perform extensive experiments for quantum data with or without noisy on classical computer. The experimental results show the Res-HQCNN performs better to learn an unknown unitary transformation and has stronger robustness for noisy data, when compared to state of the arts. Moreover, the possible methods of combining residual learning with quantum neural networks are also discussed.

cs.LG↗
arXiv2021

Quantum k-uniform states for heterogeneous systems from irredundant mixed orthogonal arrays

Quantum multipartite entangled states play significant roles in quantum information processing. By using difference schemes and orthogonal partitions, we construct a series of infinite classes of irredundant mixed orthogonal arrays (IrMOAs) and thus provide positive answers to two open problems. The first is the extension of the method for constructing homogeneous systems from orthogonal arrays (OAs) to heterogeneous multipartite systems with different individual levels. The second is the existence of $k$-uniform states in heterogeneous quantum systems. We present explicit constructions of two and three-uniform states for arbitrary heterogeneous multipartite systems with coprime individual levels, and characterize the entangled states in heterogeneous systems consisting of subsystems with nonprime power dimensions as well. Moreover, we obtain infinite classes of $k$-uniform states for heterogeneous multipartite systems for any $k\geq2$. The non-existence of a class of IrMOAs is also proved.

quant-ph↗
arXiv2020

Necessary conditions for classifying m-separability of multipartite entanglements

We study the norms of the Bloch vectors for arbitrary $n$-partite quantum states. A tight upper bound of the norms is derived for $n$-partite systems with different individual dimensions. These upper bounds are used to deal with the separability problems. Necessary conditions are presented for $\mathbf m$-separable states in $n$-partite quantum systems. Based on the upper bounds, classification of multipartite entanglement is illustrated with detailed examples.

quant-ph↗
arXiv2020

Monogamy relations and upper bounds for the generalized $W$-class states using Rényi-$α$ entropy

We investigate monogamy relations and upper bounds for generalized $W$-class states related to the Rényi-$α$ entropy. First, we present an analytical formula on Rényi-$α$ entanglement (R$α$E) and Rényi-$α$ entanglement of assistance (REoA) of a reduced density matrix for a generalized $W$-class states. According to the analytical formula, we show monogamy and polygamy relations for generalized $W$-class states in terms of R$α$E and REoA. Then we give the upper bounds for generalized $W$-class states in terms of R$α$E. Next, we provide tighter monogamy relations for generalized $W$-class states in terms of concurrence and convex-roof extended negativity and obtain the monogamy relations for R$α$E by the analytical expression between R$α$E and concurrence. Finally, we apply our results into quantum games and present a new bound of the nonclassicality of quantum games restricting to generalized $W$-class states.

quant-ph↗
arXiv2019

Multipartite entanglement of fermionic system in accelerated frames

We investigate the entanglement measures of tripartite W-State and GHZ-state in noninertial frame through the coordinate transformation between Minkowski and Rindler. First it is shown that all three qubits undergo in a uniform acceleration $a$ of W-State, we find that the one-tangle, two-tangle, and $π$-tangle decrease when the acceleration parameter $r$ increases, and the two-tangle cannot arrive to infinity of the acceleration. Next we show that the one qubit goes in a uniform acceleration $a_{1}$ and the other two undergo in a uniform acceleration $a$ of GHZ-state, we find that the two-tangle is equal to zero and $N_{B_I (A_I C_I)} = N_{C_I (A_I B_I)}\neq N_{A_I (B_I C_I)}$, but one-tangle and $π$-tangle never reduce to zero for any acceleration.

quant-ph↗
arXiv2019

Positive-partial-transpose distinguishability for lattice-type maximally entangled states

We study the distinguishability of a particular type of maximally entangled states -- the "lattice states" using a new approach of semidefinite program. With this, we successfully construct all sets of four ququad-ququad orthogonal maximally entangled states that are locally indistinguishable and find some curious sets of six states having interesting property of distinguishability. Also, some of the problems arose from \cite{CosentinoR14} about the PPT-distinguishability of "lattice" maximally entangled states can be answered.

quant-ph↗
arXiv2019

Entanglement detection via general SIC-POVMs

We study separability problem using general symmetric informationally complete measurements and propose separability criteria in $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}$ and $\mathbb{C}^{d_{1}}\otimes\mathbb{C}^{d_{2}}\cdots\otimes\mathbb{C}^{d_{n}}$. Our criteria just require less local measurements and provide experimental implementation in detecting entanglement of unknown quantum states.

quant-ph↗
arXiv2019

Tighter monogamy and polygamy relations using Rényi-$α$ entropy

We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.

quant-ph↗
arXiv2017

Generalized monogamy inequalities of convex-roof extended negativity in $N$-qubit systems

In this paper, we present some generalized monogamy inequalities based on negativity and convex-roof extended negativity (CREN). These monogamy relations are satisfied by the negativity of $N$-qubit quantum systems $ABC_1\cdots C_{N-2}$, under the partitions $AB|C_1\cdots C_{N-2}$ and $ABC_1|C_2\cdots C_{N-2}$. Furthermore, the $W$-class states are used to test these generalized monogamy inequalities.

quant-ph↗
arXiv2017

Lower bound on concurrence for arbitrary-dimensional tripartite quantum systems

In this paper, we study the concurrence of arbitrary dimensional tripartite quantum systems. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of sub-states. A given example show that our lower bound may improve the well known existing lower bounds of concurrence. The significance of our result is to get a lower bound when we study the concurrence of arbitrary dimensional multipartite quantum systems.

quant-ph↗
arXiv2017

Lower bound of multipartite concurrence based on sub-multipartite quantum systems

We study the concurrence of arbitrary dimensional multipartite quantum systems. An explicit analytical lower bound of concurrence for four-partite mixed states is obtained in terms of the concurrences of tripartite mixed states. Detailed examples are given to show that our lower bounds improve the existing lower bounds of concurrence. The approach is generalized to five-partite quantum systems.

quant-ph↗
arXiv2017

Violation of Bell inequalities for multipartite systems

In recent papers, the theory of representations of finite groups has been proposed to analyzing the violation of Bell inequalities. In this paper, we apply this method to more complicated cases. For two partite system, Alice and Bob each make one of $d$ possible measurements, each measurement has $n$ outcomes. The Bell inequalities based on the choice of two orbits are derived. The classical bound is only dependent on the number of measurements $d$, but the quantum bound is dependent both on $n$ and $d$. Even so, when $d$ is large enough, the quantum bound is only dependent on $d$. The subset of probabilities for four parties based on the choice of six orbits under group action is derived and its violation is described. Restricting the six orbits to three parties by forgetting the last party, and guaranteeing the classical bound invariant, the Bell inequality based on the choice of four orbits is derived. Moreover, all the corresponding nonlocal games are analyzed.

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