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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]

Quantum technology can break through the bottleneck of traditional information technology by ensuring information security, speeding up computation, improving measurement accuracy, and providing revolutionary solutions to some issues of economic and social development. Quantum entanglement swapping is a highly significant technology in quantum entanglement repeaters, which are generally employed to realize long-distance quantum entanglements in many quantum information processing tasks. This Special Issue is intended to investigate some basic features and applications of quantum information, including but not limited to complementarity, quantum algorithms, quantum coherence, quantum correlations, quantum measurement, quantum metrology, quantum uncertainties, and quantum information processing. The Belavkin-Staszewski (BS) relative entropy is an enticing and crucial entropy used to process quantum information tasks, which can be used to describe the effects of possible noncommutativity of the quantum states (the quantum relative entropy does not work well for this case). [Extracted from the article]

Extracting work from quantum system is one of the important areas in quantum thermodynamics. As a significant thermodynamic quantity, the ergotropy gap characterizes the difference between the global and local maximum extractable works. We derive an analytical upper bound of the ergotropic gap with respect to d × d × d tripartite separable states. This bound also provides a necessary criterion for the separability of tripartite states. Detailed examples are presented to illustrate the efficiency of this separability criterion. [ABSTRACT FROM AUTHOR]

Einstein-Podolsky-Rosen steering is a kind of powerful nonlocal quantum resource in quantum information processing such as quantum cryptography and quantum communication. Many criteria have been proposed in the past few years to detect steerability, both analytically and numerically, for bipartite quantum systems. We propose effective criteria for tripartite steerability and genuine tripartite steerability of three-qubit quantum states by establishing connections between the tripartite steerability (resp. genuine tripartite steerability) and the tripartite entanglement (resp. genuine tripartite entanglement) of certain corresponding quantum states. From these connections, tripartite steerability and genuine tripartite steerability can be detected without using any steering inequalities. The "complex cost" of determining tripartite steering and genuine tripartite steering can be reduced by detecting the entanglement of the newly constructed states in the experiment. Detailed examples are given to illustrate the power of our criteria in detecting the (genuine) tripartite steerability of tripartite states. [ABSTRACT FROM AUTHOR]

We propose a novel parameterized entanglement measure α -concurrence for bipartite systems. By employing positive partial transposition and realignment criteria, we derive analytical lower bounds for the α -concurrence. Moreover, we calculate explicitly the analytic expressions of the α -concurrence for isotropic states and Werner states. [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 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]

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 investigate complementary measurement-induced quantum uncertainty based on metric adjusted skew information, and propose two new measures of quantum uncertainty associated with mutually unbiased measurements and general symmetric informationally complete measurements, respectively. Based on these measures of quantum uncertainty, we present two entanglement criteria and show that they detect better entanglement than the existing corresponding criteria by detailed examples. [ABSTRACT FROM AUTHOR]

We study the minimum time to implement an arbitrary two-qubit gate in two heteronuclear spins systems. We give a systematic characterization of two-qubit gates based on the invariants of local equivalence. The quantum gates are classified into four classes, and for each class the analytical formula of the minimum time to implement the quantum gates is explicitly presented. For given quantum gates, by calculating the corresponding invariants one easily obtains the classes to which the quantum gates belong. In particular, we analyze the effect of global phases on the minimum time to implement the gate. Our results present complete solutions to the optimal time problem in implementing an arbitrary two-qubit gate in two heteronuclear spins systems. Detailed examples are given to typical two-qubit gates with or without global phases. [ABSTRACT FROM AUTHOR]

We study the monogamy and polygamy relations related to quantum correlations for 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. These monogamy and polygamy inequalities are complementary to the existing ones with different parameter regions of α and β . Applying these results to specific quantum correlations, the corresponding new classes of monogamy and polygamy relations are obtained, which include the existing ones as special cases. Detailed examples are given. [ABSTRACT FROM AUTHOR]

Monogamy and polygamy are the most striking features of the quantum world. We investigate the monogamy and polygamy relations satisfied by all quantum correlation measures for arbitrary multipartite quantum states. By introducing residual quantum correlations, analytical polygamy inequalities are presented, which are shown to be tighter than the existing ones. Then, similar to polygamy relations, we obtain strong monogamy relations that are better than all the existing ones. Typical examples are presented for illustration. [ABSTRACT FROM AUTHOR]

We present a different kind of monogamy and polygamy relations based on concurrence and concurrence of assistance for multiqubit systems. By relabeling the subsystems associated with different weights, a smaller upper bound of the α th ( 0 ≤ α ≤ 2 ) power of concurrence for multiqubit states is obtained. We also present tighter monogamy relations satisfied by the α th ( 0 ≤ α ≤ 2 ) power of concurrence for N-qubit pure states under the partition AB and C 1 ⋯ C N - 2 , as well as under the partition A B C 1 and C 2 ⋯ C N - 2 . These inequalities give rise to the restrictions on entanglement distribution and the trade-off of entanglement among the subsystems. Similar results are also derived for negativity. [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]

Information transfer in generalized probabilistic theories (GPT) is an important problem. We have dealt with the problem based on repeatability postulate, which generalizes Zurek's result to the GPT framework (Wu et al., Phys. Lett. A 379, 2694, 2015). A natural question arises: can we deduce the information transfer result under weaker assumptions? In this paper, we generalize Zurek's result to the framework of GPT using weak repeatability postulate. We show that if distinguishable information can be transferred from a physical system to a series of apparatuses under the weak repeatability postulate in GPT, then the initial states of the physical system must be completely distinguishable. Moreover, after each step of invertible transformation, the composite states of the composite system composed of the physical systems and the apparatuses must also be completely distinguishable. [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]

We investigate the generalized monogamy and polygamy relations N-qubit systems. We give a general upper bound of the αth (0 ≤ α ≤ 2) power of concurrence for N-qubit states. The monogamy relations satisfied by the αth (0 ≤ α ≤ 2) power of concurrence are presented for N-qubit pure states under the partition AB and C1...CN− 2, as well as under the partition ABC1 and C2⋯CN− 2. These inequalities give rise to the restrictions on entanglement distribution and the trade off of entanglement among the subsystems. Similar results are also derived for negativity. [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 present uncertainty relations based onWigner-Yanase-Dyson skew information with quantum memory. Uncertainty inequalities both in product and summation forms are derived. It is shown that the lower bounds contain two terms: one characterizes the degree of compatibility of two measurements, and the other is the quantum correlation between the measured system and the quantum memory. Detailed examples are given for product, separable and entangled states. [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]

In this paper, we study the concurrence of arbitrary-dimensional tripartite quantum states. An explicit operational lower bound of concurrence is obtained in terms of the concurrence of substates. A given example shows 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 $$m\otimes n\otimes l$$ -dimensional tripartite quantum states. [ABSTRACT FROM AUTHOR]

We investigate one-way quantum deficit for 2 ⊗ d systems. Analytical expressions of one-way quantum deficit under both von Neumann measurement and weak measurement are presented. As an illustration, qubit-qutrit systems are studied in detail. It is shown that there exists non-zero one-way quantum deficit even quantum entanglement vanishes. Moreover, one-way quantum deficit via weak measurement turns out to be weaker than that via von Neumann measurement. The dynamics of entanglement and one-way quantum deficit under dephasing channels is also investigated. [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]

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]

We study sum uncertainty relations for arbitrary finite N quantum mechanical observables. Some uncertainty inequalities are presented by using skew information introduced by Wigner and Yanase. These uncertainty inequalities are nontrivial as long as the observables are mutually noncommutative. The relations among these new and existing uncertainty inequalities have been investigated. Detailed examples are presented. [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]

We revisit the quantum discord, quantum entanglement and local hidden variable models in quantum mechanics, and present a kind of understanding of quantum states from the view of correlations given by the probability distributions of local measurements outcomes. [ABSTRACT FROM AUTHOR]

We derive uncertainty relation inequalities according to the mutually unbiased measurements. Based on the calculation of the index of coincidence of probability distribution given by $$d+1$$ MUMs on any density operator $$\rho $$ in $${\mathbb {C}}^{d}$$ , both state-dependent and state-independent forms of lower entropic bounds are given. Furthermore, we formulate uncertainty relations for MUMs in terms of Rényi and Tsallis entropies. [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]

Based on the generators of SU(n) we present inequalities for detecting quantum entanglement for 2 ⊗ d and M ⊗ N systems. These inequalities provide a sufficient condition of entanglement for bipartite mixed states and give rise to an experimental way of entanglement detection. [ABSTRACT FROM AUTHOR]

We study the concurrence of four-qubit quantum states and provide analytical lower bounds of concurrence in terms of the monogamy inequality of concurrence for qubit systems. It is shown that these lower bounds are able to improve the existing bounds and detect entanglement better. The approach is generalized to arbitrary qubit systems. [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]

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]

We investigate the dynamics of two identical atoms resonantly coupled to independent single-mode cavity in zero detuning without rotating wave approximation (RWA). It is shown that for two atoms initially in the ground state, the entanglement (concurrence) and the normalized geometric measure of quantum discord (NGMQD) display similar behavior. There is no sudden death and sudden birth. And the entanglement is always larger than NGMQD in this case. For two atoms initially in excited state, one can see the novel entanglement sudden death (ESD) and sudden birth (ESB) phenomena. The entanglement is not always greater than the NGMQD in this case. Consequently, there is no simple dominance relation between the entanglement and the NGMQD. [ABSTRACT FROM AUTHOR]

A new form of zero-discord state via Petz's monotonicity condition on relative entropy with equality has been derived systematically. A generalization of symmetric zero-discord states is presented and the related physical implications are discussed. [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 introduce a new class of multipartite entangled mixed states with pure state decompositions of generalized W states, similar to Schmidt-correlated states having generalized GHZ states in the pure state decomposition. The entanglement and separability properties are studied according to PPT operations. Monogamy relations linked to these states are also investigated. [ABSTRACT FROM AUTHOR]

We study the entanglement of a multipartite quantum state. An inequality between the bipartite concurrence and the multipartite concurrence is obtained. More effective lower and upper bounds of the multipartite concurrence are obtained. By using the lower bound, the entanglement of more multipartite states is detected. [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]

• The system consists of two acoustic wave resonator, two ensembles of nitrogen-vacancy centers, and a superconducting resonator. • The interaction is nonlocal. • Generate the Bell state and construct the controlled-phase gate. We study the generation of entanglement and the realization of controlled quantum phase gates in hybrid quantum systems. Based on the researches on acoustic wave resonators (AWRs) in recent years, we propose a hybrid system which consists of two high quality-factor AWRs, two ensembles of nitrogen-vacancy-centers (NVEs), and a superconducting resonator used to interact two NVEs. Utilizing this hybrid system we present detailed schemes to produce entangled states and carry out controlled-phase gates on two distant AWRs. The numerical simulation shows that from our protocols the fidelities of the entangled states and the controlled-phase gates can reach 99.19 % and 98.56 %, respectively, by taking into account the dissipation and dephasing of the whole system. [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 study the quantum entanglement and separability of Hermitian and pseudo-Hermitian systems of identical bosonic or fermionic particles with point interactions. The separability conditions are investigated in detail. [ABSTRACT FROM AUTHOR]

Abstract: We construct a set of PPT (positive partial transpose) states and show that these PPT states are not separable, thus present a class of bound entangled quantum states. [Copyright &y& Elsevier]

Approximation of matrices to the sum of tensor products of Hermitian matrices is studied. A minimum decomposition of matrices on tensor space H 1 ⨂ H 2 in terms of the sum of tensor products of Hermitian matrices on H 1 and H 2 is presented. From this construction the separability of quantum states is discussed. [Copyright &y& Elsevier]

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]

Abstract: We investigate the equivalence of quantum states under local unitary transformations. A complete set of invariants under local unitary transformations is presented for a class of mixed states. It is shown that two states in this class are locally equivalent if and only if all these invariants have equal values for them. [Copyright &y& Elsevier]