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Determining the quantum circuit complexity of a unitary operation is an important problem in quantum computation. By using the mathematical techniques of Riemannian geometry, we investigate the efficient quantum circuits in quantum computation with n qutrits. We show that the optimal quantum circuits are essentially equivalent to the shortest path between two points in a certain curved geometry of SU(3(n)). As an example, three-qutrit systems are investigated in detail.

Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the l 2 norm coherence, conditional von Neumann entropy and Wigner–Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise. [ABSTRACT FROM AUTHOR]

Noise exists inherently in realistic quantum systems and affects the evolution of quantum systems. We investigate the dynamics of quantum networks in noisy environments by using the fidelity of the quantum evolved states and the classical percolation theory. We propose an analytical framework that allows us to characterize the stability of quantum networks in terms of quantum noises and network topologies. The calculation results of the framework determine the maximal time that quantum networks with different network topologies can maintain the ability to communicate under noise. We demonstrate the results of the framework through examples of specific graphs under amplitude damping and phase damping noises. We further consider the capacity of the quantum network in a noisy environment according to the proposed framework. The analytical framework helps us better understand the evolution time of a quantum network and provides a reference for designing large quantum networks. [ABSTRACT FROM AUTHOR]

Finding the ground state of a Hamiltonian system is of great significance in many‐body quantum physics and quantum chemistry. An improved iterative quantum algorithm to prepare the ground state of a Hamiltonian is proposed. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. Practical guideline on the selection of the learning rate in QGD are provided by finding a fundamental upper bound and establishing a relationship between the algorithm and the first‐order approximation of the imaginary time evolution. Furthermore, a variational quantum state preparation method is adapted as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of the algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, the 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. [ABSTRACT FROM AUTHOR]

Monogamy and polygamy relations characterize the quantum correlation distributions among multipartite quantum systems. We investigate the monogamy and polygamy relations satisfied by measures of general quantum correlation. By using the Hamming weight, we derive new monogamy and polygamy inequalities satisfied by the β-th power and the α-th power of general quantum correlations, respectively. We show that these monogamy and polygamy relations are tighter than the existing ones, such as Liu [Int. J. Theor. Phys. 60, 1455–1470 (2021)]. Taking concurrence and the Tsallis-q entanglement of assistance as examples, we show the advantages of our results. [ABSTRACT FROM AUTHOR]

Bohr's complementarity is one central tenet of quantum physics. The paradoxical wave-particle duality of quantum matters and photons has been tested in Young's double-slit (double-path) interferometers. The object exclusively exhibits wave and particle nature, depending measurement apparatus that can be delayed chosen to rule out too-naive interpretations of quantum complementarity. All experiments to date have been implemented in the double-path framework, while it is of fundamental interest to study complementarity in multipath interferometric systems. Here, we demonstrate generalized multipath wave-particle duality in a quantum delayed-choice experiment, implemented by large-scale silicon-integrated multipath interferometers. Single-photon displays sophisticated transitions between wave and particle characters, determined by the choice of quantum-controlled generalized Hadamard operations. We characterise particle-nature by multimode which-path information and wave-nature by multipath coherence of interference, and demonstrate the generalisation of Bohr's multipath duality relation. Our work provides deep insights into multidimensional quantum physics and benchmarks controllability of integrated photonic quantum technology. Wave-particle duality and delayed choice are keys to our understanding of quantum mechanics. Here, leveraging the capabilities of silicon nanophotonics, the authors probe the extension of wave-particle duality from dual-path to multipath case. [ABSTRACT FROM AUTHOR]

We study the detection of multipartite entanglement based on the generalized local uncertainty relations. A sufficient criterion for the entanglement of four-partite quantum systems is presented in terms of the local uncertainty relations. Detailed examples are given to illustrate the advantages of our criterion. The approach is generalized to general multipartite entanglement cases. [ABSTRACT FROM AUTHOR]

Coherence is a fundamental ingredient in quantum physics and a key resource in quantum information processing. The quantification of quantum coherence is of great importance. We present a family of coherence quantifiers based on the Tsallis relative operator entropy. Shannon inequality and its reverse one in Hilbert space operators derived by Furuta [Linear Algebra Appl. 381 (2004) 219] are extended in terms of the parameter of the Tsallis relative operator entropy. These quantifiers are shown to satisfy all the standard criteria for a well-defined measure of coherence and include some existing coherence measures as special cases. Detailed examples are given to show the relations among the measures of quantum coherence. [ABSTRACT FROM AUTHOR]

Genuine multipartite entanglement plays important roles in quantum information processing. The detection of genuine multipartite entanglement has been long time a challenging problem in the theory of quantum entanglement. We propose a criterion for detecting genuine tripartite entanglement of arbitrary dimensional tripartite states based on quantum Fisher information. We show that this criterion is more effective for some states in detecting genuine tripartite entanglement by detailed example. [ABSTRACT FROM AUTHOR]

We study the concurrence of arbitrary-dimensional multipartite quantum states. Analytical lower bounds of concurrence for tripartite quantum states are derived by projecting high-dimensional states to 2 ⊗ 2 ⊗ 2 substates. The results are then generalized to arbitrary multipartite quantum systems. Furthermore, the scheme enables us obtain lower bounds of concurrence for arbitrary four-partite quantum states by projecting high-dimensional states to arbitrary given lower dimensional substates. By detailed examples we show that our results improve the existing lower bounds of concurrence. [ABSTRACT FROM AUTHOR]

Quantum entanglement plays significant roles in quantum information processing. Estimating quantum entanglement is an essential and difficult problem in the theory of quantum entanglement. We study two main measures of quantum entanglement: concurrence and convex-roof extended negativity. Based on the improved separability criterion from the Bloch representation of density matrices, we derive analytical lower bounds of the concurrence and the convex-roof extended negativity for arbitrary dimensional bipartite quantum systems. We show that these bounds are better than some of the existing ones by detailed examples. [ABSTRACT FROM AUTHOR]

The monogamy relations of quantum correlation restrict the sharability of quantum correlations in multipartite quantum states. We show that all measures of quantum correlations satisfy some kind of monogamy relations for arbitrary multipartite quantum states. Moreover, by introducing residual quantum correlations, we present tighter monogamy inequalities that are better than all the existing ones. In particular, for multi-qubit pure states, we also establish new monogamous relations based on the concurrence and concurrence of assistance under the partition of the first two qubits and the remaining ones. [ABSTRACT FROM AUTHOR]

Entanglement polygamy, like entanglement monogamy, is a fundamental property of multipartite quantum states. We investigate the polygamy relations related to the concurrence C and the entanglement of formation E for general n-qubit states. We extend the results in [Phys. Rev. A 90, 024304 (2014)] from the parameter region α ≤ 0 to α ≤ α0, where 0 < α0 ≤ 2 for C, and 0 < α 0 ≤ 2 for E. [ABSTRACT FROM AUTHOR]

We study one-way quantum deficit of two-qubit X states systematically from analytical derivations. An effective approach to compute one-way quantum deficit of two-qubit X states has been provided. Analytical results are presented as for detailed examples. Moreover, we demonstrate the decoherence of one-way quantum deficit under phase damping channel. [ABSTRACT FROM AUTHOR]

The mutually unbiasedness between a maximally entangled basis (MEB) and an unextendible maximally entangled system (UMES) in the bipartite system $\mathbb {C}^{2}\otimes \mathbb {C}^{2^{k}} (k>1)$ are introduced and discussed first in this paper. Then two mutually unbiased pairs of a maximally entangled basis and an unextendible maximally entangled system are constructed; lastly, explicit constructions are obtained for mutually unbiased MEB and UMES in $\mathbb {C}^{2}\otimes \mathbb {C}^{4}$ and $\mathbb {C}^{2}\otimes \mathbb {C}^{8}$, respectively. [ABSTRACT FROM AUTHOR]

One-way quantum deficit and quantum discord are two important measures of quantum correlations. We revisit the relationship between them in two-qubit systems. We investigate the conditions that both one-way quantum deficit and quantum discord have the same optimal measurement ensembles, and demonstrate that one-way quantum deficit can be derived from the quantum discord for a class of X states. Moreover, we give an explicit relation between one-way quantum deficit and entanglement of formation. We show that under phase damping channel both one-way quantum deficit and quantum discord evolve exactly in the same way for four parameter X states. Some examples are presented in details. [ABSTRACT FROM AUTHOR]

Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath (Oppenheim et al. in Phys Rev Lett 89:180402, ). It links quantum correlations with quantum thermodynamics and provides a new standpoint for understanding quantum non-locality. In this paper, we propose a new method to evaluate the one-way deficit for a class of two-qubit states. The dynamic behavior of the one-way deficit under decoherence channel is investigated, and it is shown that the one-way deficit of the $$X$$ states with five parameters is more robust against decoherence than entanglement. [ABSTRACT FROM AUTHOR]

We study mutually unbiased bases in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'}$$ . A systematic way of constructing mutually unbiased maximally entangled bases (MUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^{l}d'} (l\in {\mathbb {Z}}^{+})$$ from MUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd, k\in {\mathbb {Z}}^+)$$ and a general approach to construct mutually unbiased unextendible maximally entangled bases (MUUMEBs) in $${\mathbb {C}}^d\otimes {\mathbb {C}}^{2^ld'} (l \in {\mathbb {Z}}^{+})$$ from MUUMEBs in $${\mathbb {C}}^d \otimes {\mathbb {C}}^{d'}(d'=kd+r, 0

We study maximally entangled bases in bipartite systems $$\mathbb {C}^d \otimes \mathbb {C}^{kd}\ (k\in Z^{+})$$ , which are mutually unbiased. By systematically constructing maximally entangled bases, we present an approach in constructing mutually unbiased maximally entangled bases. In particular, five maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{4}$$ and three maximally entangled bases in $$\mathbb {C}^2 \otimes \mathbb {C}^{6}$$ that are mutually unbiased are presented. [ABSTRACT FROM AUTHOR]

Fidelity and relative entropy are two significant quantities in quantum information theory. We study the quantum fidelity and relative entropy under unitary orbits. The maximal and minimal quantum fidelity and relative entropy between two unitary orbits are explicitly derived. The potential applications in quantum computation and information processing are discussed. [ABSTRACT FROM AUTHOR]

We study certain quantum states for which the PPT criterion is both sufficient and necessary for separability. A class of n× n bipartite mixed states is presented and the conditions of PPT for these states are derived. The separable pure state decompositions of these states are explicitly constructed when they are PPT. [ABSTRACT FROM AUTHOR]

We study the stability of NPT property of an arbitrary pure entangled state under the mixture of arbitrary pure separable states. For bipartite pure states with Schmidt number n ( n>1) which is NPT, we show that this state is still NPT when it is mixed with no more than $\frac {n(n-1)}{2}-1$ arbitrary pure separable states. This result is generalized to multipartite case. [ABSTRACT FROM AUTHOR]

We present an inequality for detecting entanglement and distillability of arbitrary dimensional bipartite systems. This inequality provides a sufficient condition of entanglement for bipartite mixed states, and a necessary and sufficient condition of entanglement for bipartite pure states. Moreover, the inequality also gives a necessary and sufficient condition for distillability. [ABSTRACT FROM AUTHOR]

We present a set of inequalities based on mean values of quantum mechanical observables similar to nonlinear entanglement witnesses for bipartite quantum systems. These inequalities give rise to sufficient and necessary conditions for separability of all bipartite pure states and even some mixed states. In terms of these mean values of quantum mechanical observables, a measurable lower bound of the convex-roof extension of the negativity is derived. [ABSTRACT FROM AUTHOR]

We review some well-known Bell inequalities, the relations between the Bell inequality and quantum separability, and the entanglement distillation of quantum states. Bell inequalities with pseudo Hermitian operators are also discussed. [ABSTRACT FROM AUTHOR]

We study the evolution of quantum entanglement in double cavity systems. The entanglement of cavity atoms induced by entangled pair of photons is investigated. Both entanglement sudden death and entanglement sudden birth phenomena are shown to exist and are analyzed in detail. We also propose a strategy to enhance the entanglement between the atom in one cavity and the photon in another cavity by using quantum Zeno effect. [ABSTRACT FROM AUTHOR]

We study quantum states for which the PPT criterion is both sufficient and necessary for separability. We present a class of 3 × 3 bipartite mixed states and show that these states are separable if and only if they are PPT. [ABSTRACT FROM AUTHOR]

We investigate the separability of arbitrary-dimensional tripartite systems. By introducing a new operator related to transformations on the subsystems, a necessary condition for the separability of tripartite systems is presented. [ABSTRACT FROM AUTHOR]

Abstract: We generalize the Schmidt-correlated states to multipartite systems. The related equivalence under SLOCC, the separability, entanglement witness, entanglement measures of negativity, concurrence and relative entropy are investigated in detail for the generalized Schmidt-correlated states. [Copyright &y& Elsevier]

We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach. It is shown that two bipartite mixed states are equivalent under local unitary transformations if and only if they have the same representation class. Detailed examples are given on calculating representation classes. [ABSTRACT FROM AUTHOR]

Abstract: In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational criterion for the equivalence of two such mixed bipartite states under local unitary transformations is presented. [Copyright &y& Elsevier]

We discuss a kind of generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the generalized concurrence. An analytical expression of the entanglement of formation for a class of high-dimensional quantum mixed states is obtained. [Copyright &y& Elsevier]

Entanglement of formation for a class of higher-dimensional quantum mixed states is studied in terms of a generalized formula of concurrence for N-dimensional quantum systems. As applications, the entanglement of formation for a class of 16×16 density matrices are calculated. [Copyright &y& Elsevier]

Explicit sufficient and necessary conditions for separability of N-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to nonzero eigenvalues of the density matrix is maximally entangled. [Copyright &y& Elsevier]

A study of symplectic forms associated with two-dimensional quantum planes and the quantum sphere in a three-dimensional orthogonal quantum plane is provided. The associated Hamiltonian vector fields and Poissonian algebraic relations are made explicit. [ABSTRACT FROM AUTHOR]

Entanglement is a key issue in the quantum physics which gives rise to resources for achieving tasks that are not possible within the realm of classical physics. Quantum entanglement varies with the evolution of the quantum systems. It is of significance to investigate the entanglement dynamics in terms of quantum channels. We study the entanglement-breaking channels and present the necessary and sufficient conditions for a quantum channel to an entanglement-breaking one for qubit systems. Furthermore, a concept of strong entanglement-breaking channel is introduced. The amendment of entanglement-breaking channels is also studied. [ABSTRACT FROM AUTHOR]

We investigate monogamy relations related to quantum entanglement for n-qubit quantum systems. General monogamy inequalities are presented to the βth(β∈(0,2)) power of concurrence, negativity and the convex-roof extended negativity, as well as the βth(β∈(0,2)) power of entanglement of formation. These monogamy relations are complementary to the existing ones with different regions of parameter β. In additions, new monogamy relations are also derived which include the existing ones as special cases. [ABSTRACT FROM AUTHOR]

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented. [ABSTRACT FROM AUTHOR]

We give a sufficient condition for detecting the entanglement resource for perfect multiqubit teleportation. The criterion involves only local measurements on some complementary observables and can be experimentally implemented. It is also a necessary condition for full separability of multiqubit states. Moreover, by proving the optimality of teleportation witnesses, we solve the open problem in Phys. Rev. A86, 032315 (2012). [ABSTRACT FROM AUTHOR]

Abstract: Let be a bipartite system and a quantum state on , , . Then each quantum operation on the quantum system can induce a quantum ensemble on quantum system . In this Letter, we show that the Holevo quantity of the quantum ensemble can be upper bounded by both subsystem entropies. By using the result, we answer partly a conjecture of Fannes, de Melo, Roga and Życzkowski. [Copyright &y& Elsevier]

We study the optimal entanglement witness with respect to multiqubits W-states. We show such entanglement witnesses can be used to distinguish genuine entangled states, different biseparable states and fully separable states. [Copyright &y& Elsevier]

We give explicit expressions for entanglement measures of Werner states in arbitrary dimensions in terms of concurrence and tangle. We show that an optimal ensemble decomposition for a joint density matrix of a Werner slate can achieve the minimum average concurrence and tangle simultaneously. Furthermore, the same decomposition also altains entanglement of formation for Werner slates. [Copyright &y& Elsevier]