Search

Monogamy of entanglement is the fundamental property and inherent nature of quantum systems. We study the monogamy properties of two fidelity based entanglement measures, the Bures measure of entanglement and the geometric measure of entanglement. Stronger monogamy relations are presented for the α th ( α ≥ 2 ) power and the β th ( 0 ≤ β ≤ η , η ≥ 1 ) power of these two entanglement measures. Moreover, for the case of the γ th ( γ < 0 ) power, we give the corresponding upper bounds for the two entanglement measures. Detailed examples are provided to illustrate that our newly established monogamy relations are stronger than the previous ones. [ABSTRACT FROM AUTHOR]

Variational quantum circuits are one of the promising ways to exploit the advantages of quantum computing in the noisy intermediate-scale quantum technology era. The design of the quantum circuit architecture might greatly affect the performance capability of the quantum algorithms. The quantum architecture search is the process of automatically designing quantum circuit architecture, aiming at finding the optimal quantum circuit composition architecture by the algorithm for a given task, so that the algorithm can learn to design the circuit architecture. Compared to manual design, quantum architecture search algorithms are more effective in finding quantum circuits with better performance capabilities. In this paper, based on the deep reinforcement learning, we propose an approach for quantum circuit architecture search. The sampling of the circuit architecture is learnt through reinforcement learning-based controller. Layer-based search is also used to accelerate the computational efficiency of the search algorithm. Applying to data classification tasks, we show that the method can search for quantum circuit architectures with better accuracies. Moreover, the circuit has a smaller number of quantum gates and parameters. [ABSTRACT FROM AUTHOR]

We study the polygamy of arbitrary quantum correlation measures Q for tripartite quantum systems. Both sufficient and necessary conditions for Q to be polygamous in terms of the α th power of Q are explicitly derived. Moreover, analytical polygamy conditions for any quantum correlation measure Q have been also presented with respect to certain subsets of quantum states. Detailed examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Based on the reduced density matrices of a generalized W-class (GW) state with respect to arbitrary partitions, we investigate the monogamy and polygamy inequalities of concurrence and concurrence of assistance (CoA), respectively. For a partially coherent superposition of a GW state and a vacuum under any partitions, we present monogamy and polygamy inequalities of the convex-roof extended negativity and the convex-roof extended negativity of assistance, respectively. We prove that these monogamy and polygamy inequalities are tighter than the existing ones. The finer characterization of the entanglement distribution is illustrated by detailed examples. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The Wigner–Yanase skew information stands for the uncertainty about the information on the values of observables not commuting with the conserved quantity. The Wigner–Yanase skew information-based uncertainty relations can be regarded as a complementarity to the conceptual Heisenberg uncertainty principle. We present tight uncertainty relations in both product and summation forms for two quantum channels based on the Wigner–Yanase skew information. We show that our uncertainty inequalities are tighter than the existing ones. [ABSTRACT FROM AUTHOR]

Monogamy and polygamy of quantum correlations are the fundamental properties of quantum systems. We study the monogamy and polygamy relations satisfied by any quantum correlations in multipartite quantum systems. General monogamy relations are presented for the α th (0 ≤ α ≤ γ , γ ≥ 2) power of quantum correlation, and general polygamy relations are given for the β th (β ≥ δ , 0 ≤ δ ≤ 1) power of quantum correlation. We show that these newly derived monogamy and polygamy inequalities are tighter than the existing ones. By applying these results to specific quantum correlations such as concurrence and the square of convex-roof extended negativity of assistance (SCRENoA), the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given to illustrate the advantages of our results. [ABSTRACT FROM AUTHOR]

The variance of quantum channels involving a mixed state gives a hybrid of classical and quantum uncertainties. We seek certain decomposition of variance into classical and quantum parts in terms of the Wigner–Yanase skew information. Generalizing the uncertainty relations for quantum observables to quantum channels, we introduce a new quantity with better quantum mechanical nature to describe the uncertainty relations for quantum channels. We derive several uncertainty relations for quantum channels via variances and the Wigner–Yanase skew information. [ABSTRACT FROM AUTHOR]

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 some analytical formulas of concurrence and elegant relations between the N-partite concurrence and the (N - 1) -partite concurrence for arbitrary N-partite W-class states. Applying these relations, we present better lower bounds of concurrence for some multipartite mixed states. An example is given to demonstrate that our lower bounds can detect more entanglements. [ABSTRACT FROM AUTHOR]

Quantum coherence, quantum entanglement and quantum nonlocality are important resources in quantum information processing. However, decoherence happens when a quantum system interacts with the external environments. We study the dynamical evolution of the three-qubit GHZ-like states in noninertial frame when one and/or two qubits undergo decoherence. Under the amplitude damping channel, we show that the quantum decoherence and the Unruh effect may have quite different influences on the initial state. Moreover, the genuine tripartite entanglement and the quantum coherence may suffer sudden death during the evolution. The quantum coherence is most resistant to the quantum decoherence and the Unruh effect and then comes the quantum entanglement and the quantum nonlocality which is most fragile among the three. The results provide a new research perspective for relativistic quantum informatics. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present protocols to generate quantum entanglement on nonlocal magnons in hybrid systems composed of yttrium iron garnet (YIG) spheres, microwave cavities and a superconducting (SC) qubit. In the schemes, the YIGs are coupled to respective microwave cavities in resonant way, and the SC qubit is placed at the center of the cavities, which interacts with the cavities simultaneously. By exchanging the virtual photon, the cavities can indirectly interact in the far-detuning regime. Detailed protocols are presented to establish entanglement for two, three and arbitrary N magnons with reasonable fidelities. [ABSTRACT FROM AUTHOR]

In spite of enormous theoretical and experimental progress in quantum uncertainty relations, the experimental investigation of the most current, and universal formalism of uncertainty relations, namely majorization uncertainty relations (MURs), has not been implemented yet. A major problem is that previous studies of majorization uncertainty relations mainly focus on their mathematical expressions, leaving the physical interpretation of these different forms unexplored. To address this problem, we employ a guessing game formalism to reveal physical differences between diverse forms of majorization uncertainty relations. Furthermore, we tighter the bounds of MURs by using flatness processes. Finally, we experimentally verify strong MURs in the photonic system to benchmark our theoretical results. [ABSTRACT FROM AUTHOR]

We explore the acceleration effect on the genuine tripartite nonlocality (GTN) for one or two accelerated detector(s) coupled to the vacuum field with initial mixed tripartite states. We show that the Hawking radiation degrades the physically accessible GTN, which suffers from "sudden death" at certain critical Hawking temperature. An novel phenomenon has been observed first time that the Hawking effect can generate the physically inaccessible GTN for fermion fields in curved spacetime, the "sudden birth" of the physically inaccessible GTN. This result shows that the GTN can pass through the event horizon of black hole for certain mixed initial states. We also derived analytically the tradeoff relations of genuine tripartite entanglement (GTE) and quantum coherence under the influence of Hawking effect. [ABSTRACT FROM AUTHOR]

The Bell nonlocality is closely related to the foundations of quantum physics and has significant applications to security questions in quantum key distributions. In recent years, the sharing ability of the Bell nonlocality has been extensively studied. The nonlocality of quantum network states is more complex. We first discuss the sharing ability of the simplest bilocality under unilateral or bilateral POVM measurements, and show that the nonlocality sharing ability of network quantum states under unilateral measurements is similar to the Bell nonlocality sharing ability, but different under bilateral measurements. For the star network scenarios, we present for the first time comprehensive results on the nonlocality sharing properties of quantum network states, for which the quantum nonlocality of the network quantum states has a stronger sharing ability than the Bell nonlocality. [ABSTRACT FROM AUTHOR]

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 → ∞ ), 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. [ABSTRACT FROM AUTHOR]

We study the separability of bipartite quantum systems in arbitrary dimensions based on the Bloch representation of density matrices. We present two separability criteria for quantum states in terms of the matrices T α β (ρ) and W a b , α β (ρ) constructed from the correlation tensors in the Bloch representation. These separability criteria can be simplified and detect more entanglement than the previous separability criteria. Detailed examples are given to illustrate the advantages of results. [ABSTRACT FROM AUTHOR]

We study detection of genuine multipartite entanglement based on one-particle loss operator. We obtain a criterion on detecting genuine pure tripartite entanglement. The results are then generalized to arbitrary pure multipartite states. For mixed states by using the correlation tensors of the Bloch representation of density matrices, we obtain an effective criterion of arbitrary dimensional genuine tripartite entanglement. Detailed examples are given to show that our criterion is able to detect more genuine tripartite entanglement states than some existing criteria. [ABSTRACT FROM AUTHOR]

The uncertainty principle is one of the fundamental features of quantum mechanics and plays an essential role in quantum information theory. We study uncertainty relations based on variance for arbitrary finite N quantum observables. We establish a series of parameterized uncertainty relations in terms of the parameterized norm inequalities, which improve the exiting variance-based uncertainty relations. The lower bounds of our uncertainty inequalities are non-zero unless the measured state is a common eigenvector of all the observables. Detailed examples are provided to illustrate the tightness of our uncertainty relations. [ABSTRACT FROM AUTHOR]

The quantum orthogonal arrays define remarkable classes of multipartite entangled states called k-uniform states whose every reductions to k parties are maximally mixed. We present constructions of quantum orthogonal arrays of strength 2 with levels of prime power, as well as some constructions of strength 3. As a consequence, we give infinite classes of 2-uniform states of N systems with dimension of prime power d ≥ 2 for arbitrary N ≥ 5; 3-uniform states of N-qubit systems for arbitrary N ≥ 6 and N≠ 7,8,9,11; 3-uniform states of N systems with dimension of prime power d ≥ 7 for arbitrary N ≥ 7. [ABSTRACT FROM AUTHOR]

The uncertainty principle is one of the fundamental features of quantum mechanics and plays a vital role in quantum information processing. We study uncertainty relations based on metric-adjusted skew information for finite quantum observables. Motivated by the paper [Physical Review A 104, 052414 (2021)], we establish tighter uncertainty relations in terms of different norm inequalities. Naturally, we generalize the method to uncertainty relations of metric-adjusted skew information for quantum channels and unitary operators. As both the Wigner–Yanase–Dyson skew information and the quantum Fisher information are the special cases of the metric-adjusted skew information corresponding to different Morozova–Chentsov functions, our results generalize some existing uncertainty relations. Detailed examples are given to illustrate the advantages of our methods. [ABSTRACT FROM AUTHOR]

We introduce Λ -moments with respect to any positive map Λ . We show that these Λ -moments can effectively characterize the entanglement of unknown quantum states without theirs prior reconstructions. Based on Λ -moments necessary and sufficient separability criteria, as well as necessary optimized criteria are presented, which include the ones in Yu et al. (Phys Rev Lett 127:060504, 2021) as special cases. Detailed example is given to show that our criteria can detect bound entanglement that cannot be identified by positive partial transpose criterion, with the explicit measurement operators to experimentally measure the corresponding Λ -moments. [ABSTRACT FROM AUTHOR]

We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in C d ⊗ C d ⊗ C d based on mutually orthogonal Latin squares. Then we generalize the approach to the case of C d 1 ⊗ C d 2 ⊗ C d 1 d 2 by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably presented with generality. Detailed examples in C 3 ⊗ C 3 ⊗ C 3 , C 2 ⊗ C 2 ⊗ C 4 and C 2 ⊗ C 5 ⊗ C 10 are provided to illustrate the advantages of our approach. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Quantum entanglement is the core resource in quantum information processing and quantum computing. It is a significant challenge to effectively characterize the entanglement of quantum states. Recently, elegant separability criterion is presented by Elben et al. (Phys Rev Lett 125:200501, 2020) based on the first three partially transposed (PT) moments of density matrices. Then, Yu et al. (Phys Rev Lett 127:060504, 2021) proposed two general powerful criteria based on the PT moments. In this paper, based on the realignment operations of matrices we propose entanglement detection criteria in terms of such realignment moments. We show by detailed example that the realignment moments can also be used to identify quantum entanglement. [ABSTRACT FROM AUTHOR]

We study the ability of a quantum channel to generate quantum coherence when it applies to incoherent states. We define the measure of coherence generating power (CGP) for a generic quantum channel to be the average coherence generated by the quantum channel acting on a uniform ensemble of incoherent states based on the skew information-based coherence measure. We present explicitly the analytical formulae of the CGP for any arbitrary finite dimensional unitary channels. We derive the mean value of the CGP over the unitary groups and investigate the typicality of the normalized CGP. Furthermore, we give an upper bound of the CGP for the convex combinations of unitary channels. Detailed examples are provided to calculate exactly the values of the CGP for the unitary channels related to specific quantum gates and for some qubit channels. [ABSTRACT FROM AUTHOR]

Radhakrishnan et al. (Phys. Rev. Lett. 124:110401, 2020) proposed quantum discord to multipartite systems and derived explicit formulae for any states. These results are significant in capturing quantum correlations for multiqubit systems. In this paper, we evaluate the geometric measure of multipartite quantum discord and obtain the results for a large family of multiqubit states. Furthermore, we investigated the dynamic behavior of geometric discord for the family of two-, three- and four-qubit states under phase noise acting on the first qubit. And we discover that sudden change of multipartite geometric discord can appear when phase noise act only on one part of the two-, three- and four-qubit states. [ABSTRACT FROM AUTHOR]

The original version of this article unfortunately contained two mistakes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Random unitary dynamical evolutions play an important role in characterizing quantum Markovianity. By exploiting the maximally entangled state under the representation of a set of generalized unitary Weyl operators, we present a necessary and sufficient condition for quantum Markovianity in d-level systems from the perspective of quantum mutual information. Moreover, we analyze three quantum Markovianity criteria among divisibility, BLP and LFS 0 to establish their connections and differences. It is shown that they coincide in many special cases, but different in general, and Markovianity in the sense of LFS 0 is less restrictive than Markovianities in the sense of divisibility and BLP by detailed examples. [ABSTRACT FROM AUTHOR]

Iteration method is commonly used in solving linear systems of equations. We present quantum algorithms for the relaxed row and column iteration methods by constructing unitary matrices in the iterative processes, which generalize row and column iteration methods to solve linear systems on a quantum computer. Comparing with the conventional row and column iteration methods, the convergence accelerates when appropriate parameters are chosen. Once the quantum states are efficiently prepared, the complexity of our relaxed row and column methods is improved exponentially and is linear with the number of the iteration steps. In addition, phase estimations and Hamiltonian simulations are not required in these algorithms. [ABSTRACT FROM AUTHOR]

The parameterized entanglement monotone, the q-concurrence, is also a reasonable parameterized entanglement measure. By exploring the properties of the q-concurrence with respect to the positive partial transposition and realignment of density matrices, we present tight lower bounds of the q-concurrence for arbitrary q ≥ 2 . Detailed examples are given to show that the bounds are better than the previous ones. [ABSTRACT FROM AUTHOR]

The Gram matrix of a set of quantum pure states plays key roles in quantum information theory. It has been highlighted that the Gram matrix of a pure-state ensemble can be viewed as a quantum state, and the quantumness of a pure-state ensemble can thus be quantified by the coherence of the Gram matrix [Europhys. Lett. 134, 30003]. Instead of the l1-norm of coherence and the relative entropy of coherence, we utilize the generalized α-z-relative Rényi entropy of coherence of the Gram matrix to quantify the quantumness of a pure-state ensemble and explore its properties. We show the usefulness of this quantifier by calculating the quantumness of six important pure-state ensembles. Furthermore, we compare our quantumness with other existing ones and show their features as well as orderings. [ABSTRACT FROM AUTHOR]

Quantum nonlocality is a kind of significant quantum correlation that is stronger than quantum entanglement and EPR steering. The standard tripartite nonlocality can be detected by the violation of the Mermin inequality. By using local filtering operations, we give a tight upper bound on the maximal expected value of the Mermin operators. By detailed examples we show that the hidden standard nonlocality can be revealed by local filtering which can enhance the robustness of the noised entangled states. [ABSTRACT FROM AUTHOR]

The gradient descent approach is the key ingredient in variational quantum algorithms and machine learning tasks, which is an optimization algorithm for finding a local minimum of an objective function. The quantum versions of gradient descent have been investigated and implemented in calculating molecular ground states and optimizing polynomial functions. Based on the quantum gradient descent algorithm and Choi-Jamiolkowski isomorphism, we present approaches to simulate efficiently the nonequilibrium steady states of Markovian open quantum many-body systems. Two strategies are developed to evaluate the expectation values of physical observables on the nonequilibrium steady states. Moreover, we adapt the quantum gradient descent algorithm to solve linear algebra problems including linear systems of equations and matrix-vector multiplications, by converting these algebraic problems into the simulations of closed quantum systems with well-defined Hamiltonians. Detailed examples are given to test numerically the effectiveness of the proposed algorithms for the dissipative quantum transverse Ising models and matrix-vector multiplications. [ABSTRACT FROM AUTHOR]

We study entanglement and genuine entanglement of tripartite and four-partite quantum states by using Heisenberg-Weyl (HW) representation of density matrices. Based on the correlation tensors in HW representation, we present criteria to detect entanglement and genuine tripartite and four-partite entanglement. Detailed examples show that our method can detect more entangled states than previous criteria. [ABSTRACT FROM AUTHOR]

We present an alternative framework for quantifying the coherence of quantum channels, which contains three conditions: the faithfulness, nonincreasing under sets of all the incoherent superchannels and the additivity. Based on the characteristics of the coherence of quantum channels and the additivity of independent channels, our framework provides an easier way to certify whether a function is a bona fide coherence measure of quantum channels. Detailed example is given to illustrate the effectiveness and advantages of our framework. [ABSTRACT FROM AUTHOR]

Establishing quantum correlations between two remote parties by sending an information carrier is an essential step of many protocols in quantum information processing. We obtain trade-off relations between discords and coherence within a bipartite system. Then we study the distribution of coherence in a bipartite quantum state by using the relations of relative entropy and mutual information. We show that the increase of the relative entropy of discord between two remote parties is bounded by the nonclassical correlations quantified by the relative entropy of coherence between the carrier and two remote parties, providing an optimal protocol for discord distribution and showing that quantum correlations are the essential resource for such tasks. [ABSTRACT FROM AUTHOR]

We study the genuine multipartite entanglement in tripartite quantum systems. By using the Schmidt decomposition and local unitary transformation, we convert the general states to simpler forms and consider certain matrices from correlation tensors in the Bloch representation of the simplified density matrices. Using these special matrices, we obtain new criteria for genuine multipartite entanglement. Detail examples show that our criteria are able to detect more tripartite entangled and genuine tripartite entangled states than some existing criteria. [ABSTRACT FROM AUTHOR]

The conventional coherence is defined with respect to a fixed orthonormal basis, i.e., to a von Neumann measurement. Recently, generalized quantum coherence with respect to general positive operator-valued measurements has been presented. Several well-defined coherence measures, such as the relative entropy of coherence C r , the l 1 norm of coherence C l 1 and the coherence C T , α based on Tsallis relative entropy with respect to general POVMs have been obtained. In this work, we investigate the properties of C r , C l 1 and C T , α . We estimate the upper bounds of C l 1 ; we show that the minimal error probability of the least square measurement state discrimination is given by C T , 1 / 2 ; we derive the uncertainty relations given by C r , and calculate the average values of C r , C T , α and C l 1 over random pure quantum states. All these results include the corresponding results of the conventional coherence as special cases. [ABSTRACT FROM AUTHOR]

The generalized eigenvalue (GE) problems are of particular importance in various areas of science engineering and machine learning. We present a variational quantum algorithm for finding the desired generalized eigenvalue of the GE problem, A | ψ ⟩ = λ B | ψ ⟩ , by choosing suitable loss functions. Our approach imposes the superposition of the trial state and the obtained eigenvectors with respect to the weighting matrix B on the Rayleigh quotient. Furthermore, both the values and derivatives of the loss functions can be calculated on near-term quantum devices with shallow quantum circuit. Finally, we propose a full quantum generalized eigensolver (FQGE) to calculate the minimal generalized eigenvalue with quantum gradient descent algorithm. As a demonstration of the principle, we numerically implement our algorithms to conduct a 2-qubit simulation and successfully find the generalized eigenvalues of the matrix pencil (A , B) . The numerically experimental result indicates that FQGE is robust under Gaussian noise. [ABSTRACT FROM AUTHOR]

The Holevo quantity and the SU(2)-invariant states have particular importance in quantum information processing. We calculate analytically the Holevo quantity for bipartite systems composed of spin-j and spin- 1 2 subsystems with SU(2) symmetry, when the projective measurements are performed on the spin- 1 2 subsystem. The relations among the Holevo quantity, the maximal values of the Holevo quantity and the states are analyzed in detail. In particular, we show that the Holevo quantity increases in the parameter region F < Fd and decreases in region F > Fd when j increases, where F is function of temperature in thermal equilibrium and Fd = j/(2j + 1), and the maximum value of the Holevo quantity is attained at F = 1 for all j. Moreover, when the dimension of system increases, the maximal value of the Holevo quantity decreases. [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]

We study the sum uncertainty relations based on variance and skew information for arbitrary finite N quantum mechanical observables. We derive new uncertainty inequalities which improve the exiting results about the related uncertainty relations. Detailed examples are provided to illustrate the advantages of our uncertainty inequalities. [ABSTRACT FROM AUTHOR]

We study the constructions of nonlocal orthogonal product states in multipartite systems that cannot be distinguished by local operations and classical communication. We first present two constructions of nonlocal orthogonal product states in tripartite systems C d ⊗ C d ⊗ C d (d ≥ 3) and C d ⊗ C d + 1 ⊗ C d + 2 (d ≥ 3) . Then for general tripartite quantum system C n 1 ⊗ C n 2 ⊗ C n 3 (3 ≤ n 1 ≤ n 2 ≤ n 3) , we obtain 2 (n 2 + n 3 - 1) - n 1 nonlocal orthogonal product states. Finally, we put forward a new construction approach in C d 1 ⊗ C d 2 ⊗ ⋯ ⊗ C d n (d 1 , d 2 , ⋯ d n ≥ 3 , n > 6) multipartite systems. Remarkably, our indistinguishable sets contain less nonlocal product states than the existing ones, which improves the recent results and highlights their related applications in quantum information processing. [ABSTRACT FROM AUTHOR]

We investigate the monogamy relations related to the concurrence, the entanglement of formation, convex-roof extended negativity, Tsallis-q entanglement and Rényi-α entanglement, the polygamy relations related to the entanglement of formation, Tsallis-q entanglement and Rényi-α entanglement. Monogamy and polygamy inequalities are obtained for arbitrary multipartite qubit systems, which are proved to be tighter than the existing ones. Detailed examples are presented. [ABSTRACT FROM AUTHOR]

The optimal state-independent lower bounds for the sum of variances or deviations of observables are of significance for the growing number of experiments that reach the uncertainty limited regime. We present a framework for computing the tight uncertainty relations of variance or deviation via determining the uncertainty regions, which are formed by the tuples of two or more of quantum observables in random quantum states induced from the uniform Haar measure on the purified states. From the analytical formulae of these uncertainty regions, we present state-independent uncertainty inequalities satisfied by the sum of variances or deviations of two, three and arbitrary many observables, from which experimentally friend entanglement detection criteria are derived for bipartite and tripartite systems. [ABSTRACT FROM AUTHOR]

Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the bounds on the catalytic states. We present the necessary conditions of catalytic states based on a set of points given by the Schmidt coefficients of the entangled source and target states. The lower bounds on the dimensions of the catalytic states are also investigated. Moreover, we give a detailed protocol of quantum mixed state transformation under entanglement-assisted LOCC. [ABSTRACT FROM AUTHOR]

We study quantum information masking of arbitrary dimensional states. Given a set of fixed reducing pure states, we study the linear combinations of them, such that they all have the same marginal states with the given ones. We define the so-called Hadamard set of quantum states whose Gram–Schmidt matrix can be diagonalized by Hadamard unitary matrices. We show that any Hadamard set can be deterministically masked by a unitary operation. We analyze the states which can be masked together with the given Hadamard set using the result about the linear combinations of fixed reducing states. Detailed examples are given to illustrate our results. [ABSTRACT FROM AUTHOR]

Based on the resource theory for quantifying the coherence of quantum channels, we introduce a new coherence quantifier for quantum channels via maximum relative entropy. We prove that the maximum relative entropy for coherence of quantum channels is directly related to the maximally coherent channels under a particular class of superoperations, which results in an operational interpretation of the maximum relative entropy for coherence of quantum channels. We also introduce the conception of sub-superchannels and sub-superchannel discrimination. For any quantum channels, we show that the advantage of quantum channels in sub-superchannel discrimination can be exactly characterized by the maximum relative entropy of coherence for quantum channels. Similar to the maximum relative entropy of coherence for channels, the robustness of coherence for quantum channels has also been investigated. We show that the maximum relative entropy of coherence for channels provides new operational interpretations of robustness of coherence for quantum channels and illustrates the equivalence of the dephasing-covariant superchannels, incoherent superchannels, and strictly incoherent superchannels in these two operational tasks. [ABSTRACT FROM AUTHOR]