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We investigate the complementarity relation among the l1 norm of imaginarity, linear entropy and the Brukner–Zeilinger invariant information in the presence of conjugate symmetry. By using an equality derived from the complementarity relation, we define a quantity named index of imaginarity distribution with respect to the imaginarity, linear entropy and invariant information in finite dimensional quantum systems. We show that the index of imaginarity distribution is nonnegative and upper bounded by the square of the l1 norm of imaginarity, and serves as an invaluable tool in characterizing effectively the imaginarity distribution. Detailed examples are presented to illustrate our theoretical analysis.

We study the steerability for arbitrary dimensional bipartite systems based on the correlation matrices given by local special unitary groups. We present families of steering criteria for bipartite quantum states in terms of parameterized correlation matrices. We show that these steering criteria may detect more steerable states than the existing steering criteria. The results are illustrated by detailed examples.

The quantum network correlations play significant roles in long distance quantum communication, quantum cryptography and distributed quantum computing. Generally it is very difficult to characterize the multipartite quantum network correlations such as nonlocality, entanglement and steering. In this paper, we propose the network and the genuine network quantum steering models from the aspect of probabilities in the star network configurations. Linear and nonlinear inequalities are derived to detect the network and genuine network quantum steering when the central party performs one fixed measurement. We show that our criteria can detect more quantum network steering than that from the violation of the n-locality quantum networks. Moreover, it is shown that biseparable assemblages can demonstrate genuine network steering in the star network configurations.

Abstract 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.

We study genuine multipartite entanglement (GME) and multipartite k-entanglement based on q-concurrence. Well-defined parameterized GME measures and measures of multipartite k-entanglement are presented for arbitrary dimensional n-partite quantum systems. Our GME measures show that the GHZ state is more entangled than the W state. Moreover, our measures are shown to be inequivalent to the existing measures according to entanglement ordering. Detailed examples show that our measures characterize the multipartite entanglement finer than some existing measures, in the sense that our measures identify the difference of two different states while the latter fail.

In this paper, we investigate steered quantum coherence, i.e., the l1 norm of steered coherence and the relative entropy of steered coherence, and the quantum Fisher information in the Gibbs state of two-qubit XXZ systems. Their variations with respect to the temperature, external magnetic field, and interaction intensities are analyzed both analytically and numerically in detail. The similar behaviors among these three quantum measures in the XXZ model are presented.

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

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

Generally quantum processes tend to mix the pure input states and degrade the original coherence. Such processes display exactly the trade-offs between the coherence and the mixedness. In this paper, we present trade-offs between the coherence measures (l2 norm of coherence, coherence via skew information, geometric measure of coherence) and the mixedness (normalized linear entropy mixedness, geometric measure of mixedness, mixedness via skew information). The evolution of these trade-offs are also investigated under four quantum noise channels: the bit flip, phase flip, depolarizing and amplitude damping channels.

We study the genuine multipartite entanglement of arbitrary n-partite quantum states by representing the density matrices in terms of the generalized Pauli operators. We introduce a general framework for detecting genuine multipartite entanglement and non full-separability of multipartite quantum states with arbitrary dimensions based on correlation tensors. Effective criterion is derived to verify the genuine multipartite entanglement. Detailed examples are given to show that the criterion detects more genuine multipartite entanglement than the existing criteria.

Quantifying coherence is an essential endeavor for both quantum mechanical foundations and quantum technologies. We present a bona fide measure of quantum coherence by utilizing the Tsallis relative operator (α,β)-entropy. We first prove that the proposed coherence measure fulfills all the criteria of a well defined coherence measure, including the strong monotonicity in the resource theories of quantum coherence. We then study the ordering of the Tsallis relative operator (α,β)-entropy of coherence, Tsallis relative α-entropies of coherence, Rényi α-entropy of coherence and l1 norm of coherence for both pure and mixed qubit states. This provides a new method for defining new coherence measure and entanglement measure, and also provides a new idea for further study of quantum coherence.

The superposition of states is one of the most fundamental issues in the quantum world. Generally there do not exist physical operations to superpose two unknown random states with nonzero probability. We investigate the superposition problem of unknown qubit states with respect to a known qubit state. It is shown that under trace-nonincreasing completely positive operations the superposable state sets are located in some circles on the Bloch sphere. Meanwhile, we prove that the quantum states in a circle on the Bloch sphere are superposable with respect to a known state. Finally, for the high-dimensional case, we illustrate that any superposition transformation protocols will violate the no-cloning principle for almost all the states. Our results also promote the understanding and applications of the superposition principle in view of quantum no-go theorems.

We study the quantification of genuine multipartite entanglement (GME) for general multipartite states. A set of inequalities satisfied by the entanglement of N-partite pure states is derived by exploiting the restrictions on entanglement distributions, showing that the bipartite entanglement between each part and its remaining ones cannot exceed the sum of the other partners with their remaining ones. Then a series of triangles, named concurrence triangles, are established corresponding to these inequalities. Proper genuine multipartite entanglement measures are thus constructed by using the geometric mean area of these concurrence triangles, which are non-increasing under local operation and classical communication. The GME measures classify which parts are separable or entangled with the rest ones for non genuine entangled pure states. The GME measures for mixed states are given via the convex roof construction, and a witness to detect the GME of multipartite mixed states is presented by an approach based on state purifications. Detailed examples are given to illustrate the effectiveness of our GME measures.

Abstract 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.

The quantum instruction set (QIS) is defined as the quantum gates that are physically realizable by controlling the qubits in quantum hardware. Compiling quantum circuits into the product of the gates in a properly defined QIS is a fundamental step in quantum computing. We here propose the quantum variational instruction set (QuVIS) formed by flexibly designed multiqubit gates for higher speed and accuracy of quantum computing. The controlling of qubits for realizing the gates in a QuVIS is variationally achieved using the fine-grained time optimization algorithm. Significant reductions in both the error accumulation and time cost are demonstrated in realizing the swaps of multiple qubits and quantum Fourier transformations, compared with the compiling by a standard QIS such as the quantum microinstruction set (QuMIS, formed by several one- and two-qubit gates including one-qubit rotations and controlled-not gates). With the same requirement on quantum hardware, the time cost for QuVIS is reduced to less than one-half of that for QuMIS. Simultaneously, the error is suppressed algebraically as the depth of the compiled circuit is reduced. As a general compiling approach with high flexibility and efficiency, QuVIS can be defined for different quantum circuits and be adapted to the quantum hardware with different interactions.

Learning physical properties of a quantum system is essential for the developments of quantum technologies. However, Heisenberg’s uncertainty principle constrains the potential knowledge one can simultaneously have about a system in quantum theory. Aside from its fundamental significance, the mathematical characterization of this restriction, known as ‘uncertainty relation’, plays important roles in a wide range of applications, stimulating the formation of tighter uncertainty relations. In this work, we investigate the fundamental limitations of variance-based uncertainty relations, and introduce several ‘near optimal’ bounds for incompatible observables. Our results consist of two morphologically distinct phases: lower bounds that illustrate the uncertainties about measurement outcomes, and the upper bound that indicates the potential knowledge we can gain. Combining them together leads to an uncertainty interval, which captures the essence of uncertainties in quantum theory. Finally, we have detailed how to formulate lower bounds for product-form variance-based uncertainty relations by employing entropic uncertainty relations, and hence built a link between different forms of uncertainty relations.

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 [...]

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.

Summary: Quantum entanglement has shown distinguished features beyond any classical state. Many methods have been presented to verify unknown entanglement with the complete information about the density matrices by quantum state tomography. In this work, we aim to identify unknown entanglement with only partial information of the state space. The witness consists of a generalized Greenberger-Horne-Zeilinger-like paradox expressed by Pauli observables, and a nonlinear entanglement witness expressed by density matrix elements. First, we verify unknown bipartite entanglement and study the robustness of entanglement witnesses against the white noise. Second, we generalize such verification to partially unknown multipartite entangled states, including the Greenberger-Horne-Zeilinger-type and W-type states. Third, we give a quantum-information application related to the quantum zero-knowledge proof. It further provides a useful method in blindly verifying universal quantum computation resources. These results may be interesting in entanglement theories, quantum communication, and quantum networks.

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.

As already known by Rana’s result, all eigenvalues of any partial-transposed bipartite state fall within the closed interval [−12,1]. In this note, we study a family of bipartite quantum states where the minimal eigenvalues of partial-transposed states are −12. For a two-qubit system, we find that the minimal eigenvalue of its partial-transposed state is −12 if and only if such a two-qubit state is maximally entangled. However this result does not hold in general for a two-qudit system when the dimensions of the underlying space are larger than two.

We investigate the discrimination of pure-mixed (quantum filtering) and mixed-mixed states and compare their optimal success probability with the one for discriminating other pairs of pure states superposed by the vectors included in the mixed states. We prove that under the equal-fidelity condition, the pure-pure state discrimination scheme is superior to the pure-mixed (mixed-mixed) one. With respect to quantum filtering, the coherence exists only in one pure state and is detrimental to the state discrimination for lower dimensional systems; while it is the opposite for the mixed-mixed case with symmetrically distributed coherence. Making an extension to infinite-dimensional systems, we find that the coherence which is detrimental to state discrimination may become helpful and vice versa.

Entangled systems in experiments may be lost or off-line in distributed quantum information processing. This inspires a general problem to characterize quantum operations, which result in breaking of entanglement or not. Our goal in this paper is to solve this problem both in single entanglement and network scenarios. We firstly propose a local model for characterizing all entangled states that are breaking for losing particles. This implies a simple criterion for witnessing single entanglement such as generalized GHZ states and Dicke states. It further provides an efficient witness for entangled quantum networks depending on its connectivity such as k-independent quantum networks, completely connected quantum networks, and k-connected quantum networks. These networks are universal resources for measurement-based quantum computations. The strong nonlocality can be finally verified by using nonlinear inequalities. These results show distinctive features of both single entangled systems and entangled quantum networks.

We show the properties and characterization of coherence witnesses. We show methods for constructing coherence witnesses for an arbitrary coherent state. We investigate the problem of finding common coherence witnesses for certain class of states. We show that finitely many different witnesses W1,W2,⋯,Wn can detect some common coherent states if and only if ∑i=1ntiWi is still a witnesses for any nonnegative numbers ti(i=1,2,⋯,n). We show coherent states play the role of high-level witnesses. Thus, the common state problem is changed into the question of when different high-level witnesses (coherent states) can detect the same coherence witnesses. Moreover, we show a coherent state and its robust state have no common coherence witness and give a general way to construct optimal coherence witnesses for any comparable states.

We propose the tensor-network compressed sensing (TNCS) by incorporating the ideas of compressed sensing, tensor network (TN), and machine learning. The primary idea is to compress and communicate the real-life information through the generative TN state and by making projective measurements in a designed way. First, the state |Ψ〉 is obtained by the unsupervised learning of TN, and then the data to be communicated are encoded in the separable state with the minimal distance to the projected state |Φ〉, where |Φ〉 can be acquired by partially projecting |Ψ〉. A protocol analogous to the compressed sensing assisted by neural-network machine learning is thus suggested, where the projections are designed to rapidly minimize the uncertainty of information in |Φ〉. To characterize the efficiency of TNCS, we propose a quantity named as q sparsity to describe the sparsity of quantum states, which is analogous to the sparsity of the signals required in the standard compressed sensing. The need of the q sparsity in TNCS is essentially due to the fact that the TN states obey the area law of entanglement entropy. The tests on the real-life data (handwritten digits and fashion images) show that the TNCS has competitive efficiency and accuracy.

The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets. By using the approach of adding noises to measurement operators, we present a complete classification of the incompatibility of a given measurement assemblage with n members. Detailed examples are given for the incompatibility of unbiased qubit measurements based on a semidefinite program.

We present uncertainty relations based on Wigner–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.