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In Monras et al. (Phys. Rev. A, 2011, 84(1):012301 2011), the authors presented an entanglement measure for bipartite pure states based on local unitary operations. In this paper, motivated by this idea, we obtained an entanglement measure for multipartite quantum states with respect to k-partitions, which is called mirror entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-MEM. We show that this measure is well-defined, i.e., it satisfies some necessary conditions of entanglement measure including vanishes iff the multipartite quantum states are k-separable, invariance under local unitary operation and monotonicity under local quantum operation and classical communication.

We look into multipartite quantum states on which quantum cryptographic protocols including quantum key distribution and quantum secret sharing can be perfectly performed, and define the quantum cryptographic resource distillable rate as the asymptotic rate at which such multipartite state can be distilled from a given multipartite state. Investigating several relations between entanglement and the rate, we show that there exists a multipartite bound entangled state whose quantum cryptographic resource distillable rate is strictly positive, that is, there exists a multipartite entangled state which is not distillable, but can be useful for quantum cryptography such as quantum key distribution and quantum secret sharing., 9 pages, 2 figures

It is well known that the quantum mutual information and its conditional version do not increase under local channels. I this paper we show that the recently established lower semicontinuity of the quantum conditional mutual information implies (in fact, is equivalent to) the lower semicontinuity of the loss of the quantum (conditional) mutual information under local channels considered as a function on the Cartesian product of the set of all states of a composite system and the sets of all local channels (equipped with the strong convergence). Some applications of this property are considered. New continuity conditions for the quantum mutual information and for the squashed entanglement in both bipartite and multipartite infinite-dimensional systems are obtained. It is proved, in particular, that the multipartite squashed entanglement of any countably-non-decomposable separable state with finite marginal entropies is equal to zero. Special continuity properties of the information gain of a quantum measurement with and without quantum side information are established that can be treated as robustness (stability) of these quantities w.r.t. perturbation of the measurement and the measured state., Comment: 32 pages, preliminary version, any comments and references are welcome

We present a new quantum-memory-assisted entropic uncertainty relation for multipartite systems which shows the uncertainty principle of quantum mechanics. Notably, our results recover some well-known entropic uncertainty relations for two arbitrary incompatible observables that demonstrate the uncertainties about the results of two measurements. This uncertainty relation might play a critical role in the foundations of quantum theory.

The exploration of quantum entanglement in multipartite quantum systems is of great significance to the study of quantum entanglement, maximally multi-qubit entangled state is one of the research objects. Recently, Che et al. presented a recurrence relation of multi-qubit state. According to this inspiration, we present the recurrence relation of maximally multi-qubit pure states of N-qubits for N = 6, 7, 8. Further, some new forms of the seven- and eight-qubit maximally entangled states are found with the recurrence relation.

The Seidel energy of a simple graph G is the sum of the absolute values of the eigenvalues of the Seidel matrix of G. In this paper we study the Seidel eigenvalues of complete multipartite graphs and find the exact value of the Seidel energy of the complete multipartite graphs.

Bell nonlocality of quantum states is an important resource in quantum information and then has various applications. It is usually detected by the violation of some Bell’s inequalities and the all-versus-nothing test. In the present paper, we aim to establish some mathematical methods for proving Bell nonlocality without inequalities, inspired by the work [Phys. Rev. Lett., 89, 080402 (2002)] regarding the GHZ paradox. For self-containedness, we recall the mathematical definition of Bell nonlocality proposed in [Sci. China-Phys. Mech. Astron. 62, 030311 (2019)] and then give some basic properties on it. Then we derive some necessary conditions for a multipartite state to be Bell local and obtain some sufficient conditions for a state to be Bell nonlocal in terms of “expectations” of local observables without invoking Bell inequalities. Unlike the standard approach to nonlocality detection based on violation of Bell inequalities, the obtained criteria are formulated in terms of certain relations for expectation values of local observables that are constructed from the well-known GHZ paradoxes.

We calculate spin correlation functions using IBM quantum processors, accessed online. We demonstrate the rotational invariance of the singlet state, interesting properties of the triplet states, and surprising features of a state of three entangled qubits. This exercise is ideal for remote learning and generates data with real quantum mechanical systems that are impractical to investigate in the local laboratory. Students learn a wide variety of skills, including calculation of multipartite spin correlation functions, design and analysis of quantum circuits, and remote measurement with real quantum processors.

Descrying all aspects of the quantum entanglement of multipartite quantum systems is an essential part when researching the quantum entanglement. Maximally multi-qubit entangled state is one of the research objects. Recently, attracted by a criterion for maximally entangled nine-qubit state and construct a nine-qubit maximally entangled state, we construct a new genuine maximally nine-qubit entangled state via the recurrence relation. Further, nine-qubit entangled state is found which can be seen as a new form maximally nine-qubit entangled state. There are 108 of purity equal to 1/16, 18 of purity equal to 1/8 in observation. We believe the result could provide a new idea for constructing more new maximally multi-qubit states.

We consider the Bell experiment for a system described by multipartite states in the case where n dichotomic observables are measured per site. If n is two, we consider a two-setting Bell experiment. If n is M, we consider a M-setting Bell experiment. Two-setting model is an explicit local realistic model for the values of a correlation function, given in a two-setting Bell experiment. M-setting model is an explicit local realistic model for the values of a correlation function, given in a M-setting Bell experiment. Surprisingly we can discuss incompleteness in the Bell theorem. Also, we show a loophole problem of all the Bell-CHSH experimental claims. We discuss every Bell-CHSH experiment admits a local realistic theory if we rule out probability and statistics from the analysis of the experiment. We cannot obtain a violation of a Bell-CHSH inequality when we use only number theory and we do not use probability and statistics.

This article presents the basis of a theory of entanglement. We begin with a classical theory of entangled discrete measures in Section~1. Section~2 treats quantum mechanics and discusses the statistics of bounded operators on a Hilbert space in terms of context coefficients. In Section~3 we combine the work of the first two sections to develop a general theory of entanglement for quantum states. A measure of entanglement called the entanglement number is introduced. Although this number is related to entanglement robustness, its motivation is not the same and there are some differences. The present article only involves bipartite systems and we leave the study of multipartite systems for later work., Comment: 20 pages

Quantum nonlocality can be shown by measuring a quantum system containing multipartite entangled state. A key to quantum measurement is to find out what kinds of measurement settings are optimal. We design programable quantum circuit to demonstrate quantum nonlocality for multi-qubit systems based on quantum programming. A series of multiple quantum measurements are performed via cycle structure. As a result, we reveal quantum nonlocality of multipartite quantum systems as well as verify optimizing of measurement settings.

The nonlocality research of quantum entanglement plays an important role in the development of quantum mechanics theory and quantum information technology. As multipartite entangled state is a rare quantum resource, its nonlocality research has always been an important subject in the study of quantum theory. In this paper, we focus on N entangled states composed of N copies of an entangled state. First, a new Bell test with respect to N entangled states is presented, and lifting Bell inequalities are applied to certify nonlocality. Second, we obtain the nonlocality certification standard of N entangled states by parity binning lifting Bell inequality. Third, we prove the conjecture that N + 2 entangled states must be local if N entangled states are local certified by parity binning lifting Bell inequality. The research will promote the theoretical research progress of quantum coherence, and provide theoretical basis and technical support for the multipartite entangled states application in quantum cryptographic protocols.

We construct randomized entangled mixed states by using the formalism of phase states for d-dimensional systems (qudits). The randomized entangled mixed states are a special kind of mixed states that exhibit genuine multipartite correlation. Such states are obtained by the application of randomized entangling operators to an arbitrary pair of qudits of a multiqudit system. The study of the entanglement of randomized mixed states is of great importance in quantum computation since any experimental implementation of entangled states in a realistic environment can be made by imperfect entangling gates. We give a brief review of some necessary background about unitary phase operators and phase states of a multi-qudit system. Evolved density matrices arise when qudits of the multi-qudit system interact via a Hamiltonian of Heisenberg type. The randomized entangled states associated with evolved density matrices are derived via the action of an entangling operator on a pair of two qudits {i, j} of the multi-qudit system with some probability p. The randomized entangled mixed states for bipartite, tripartite and multipartite systems are explicitly expressed and their Kraus decomposition properties are discussed.

In this paper, an entanglement measure for multipartite quantum states with respect to k-partition was introduced, which is called Schmidt number entanglement measure for multipartite k-nonseparable states, it is simply denoted by k-ME SN. We show that this measure is well-defined, i.e., it satisfies some basic properties as an entanglement measure. In addition, we give a super bound and lower bound of k-ME SN for multipartite pure states according to the definition of joint k-Schmidt number with respect to k-partition. Furthermore, we give some examples to show that Schmidt number entanglement measure can quantify the strength of entanglement for multipartite quantum states.

One of the fundamental traits of quantum entanglement is the restricted shareability among multipartite quantum systems, namely monogamy of entanglement, while it is well known that monogamy inequalities are always satisfied by entanglement measures with convexity. Here we present a measure of entanglement, logarithmic convex-roof extended negativity (LCREN) satisfying important characteristics of an entanglement measure, and investigate the monogamy relation for logarithmic negativity and LCREN both without convexity. We show exactly that the α th power of logarithmic negativity, and a newly defined good measure of entanglement, LCREN, obey a class of general monogamy inequalities in multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems for α ≥ 4 ln 2 . We provide a class of general polygamy inequalities of multiqubit systems in terms of logarithmic convex-roof extended negativity of assistance (LCRENoA) for 0 ≤ β ≤ 2 . Given that the logarithmic negativity and LCREN are not convex, these results are surprising. Using the power of the logarithmic negativity and LCREN, we further establish a class of tight monogamy inequalities of multiqubit systems, 2 ⊗ 2 ⊗ 3 systems and 2 ⊗ 2 ⊗ 2 n systems in terms of the α th power of logarithmic negativity and LCREN for α ≥ 4 ln 2 . We also show that the β th power of LCRENoA obeys a class of tight polygamy inequalities of multiqubit systems for 0 ≤ β ≤ 2 .

Continuous variables multipartite entanglement is a key resource for quantum technologies. This works considers the multipartite entanglement generated in separated spatial modes of the same light beam by three different parametric sources: a standard $\chi^{(2)}$ medium pumped by two pumps, a single-pump nonlinear photonic crystal, and a doubly pumped nonlinear photonic crystal. These sources have in common the coexistence of several concurrent nonlinear processes in the same medium, which allows the generation of non-standard 3 and 4-mode couplings. We test the genuine nature of the multipartite entangled states thereby generated in a common framework, using both criteria based on proper bounds for the variances of nonlocal observables and on the positive partial transpose criterion. The relative simplicity of these states allows a (hopefully) useful comparison of the different inseparability tests., Comment: Accepted for publication in Phys. Rev. A

Bipartite and multipartite entangled states are basic ingredients for constructing quantum networks and their accurate verification is crucial to the functioning of the networks, especially for untrusted networks. Here we propose a simple approach for verifying the Bell state in an untrusted quantum network in which one party is not honest. Only local projective measurements are required for the honest party. It turns out each verification protocol is tied to a probability distribution on the Bloch sphere and its performance has an intuitive geometric meaning. This geometric picture enables us to construct the optimal and simplest verification protocols, which are also very useful to detecting entanglement in the untrusted network. Moreover, we show that our verification protocols can achieve almost the same sample efficiencies as protocols tailored to standard quantum state verification. Furthermore, we establish an intimate connection between the verification of Greenberger-Horne-Zeilinger states and the verification of the Bell state. By virtue of this connection we construct the optimal protocol for verifying Greenberger-Horne-Zeilinger states and for detecting genuine multipartite entanglement., 8+21 pages, 4+2 figures, and 1 table; published in npj Quantum Information

Detecting multipartite quantum coherence usually requires quantum state reconstruction, which is quite inefficient for large-scale quantum systems. Along this line of research, several efficient procedures have been proposed to detect multipartite quantum coherence without quantum state reconstruction, among which the spectrum-estimation-based method is suitable for various coherence measures. Here, we first generalize the spectrum-estimation-based method for the geometric measure of coherence. Then, we investigate the tightness of the estimated lower bound of various coherence measures, including the geometric measure of coherence, $l_1$-norm of coherence, the robustness of coherence, and some convex roof quantifiers of coherence multiqubit GHZ states and linear cluster states. Finally, we demonstrate the spectrum-estimation-based method as well as the other two efficient methods by using the same experimental data [Ding et al. Phys. Rev. Research 3, 023228 (2021)]. We observe that the spectrum-estimation-based method outperforms other methods in various coherence measures, which significantly enhances the accuracy of estimation., 7 pages, 1 figure

In the holographic framework, we argue that the partial entanglement entropy (PEE) can be explicitly interpreted as the component flow flux in a locking bit thread configuration. By applying the locking theorem of bit threads, and constructing a concrete locking scheme, we obtain a set of uniquely determined component flow fluxes from this viewpoint, and successfully derive the PEE proposal and its generalized version in the multipartite cases. Moreover, from this perspective of bit threads, we also present a coherent explanation for the coincidence between the BPE (balanced partial entanglement)/EWCS (entanglement wedge cross section) duality proposed recently and the EoP (entanglement of purification)/EWCS duality. We also discuss the issues implied by this coincident between the idea of the PEE and the picture of locking thread configuration., Comment: 35 pages, 7 figures, accepted by jhep

Quantum steering, a type of quantum correlation with unique asymmetry, has important applications in asymmetric quantum information tasks. We consider a new quantum steering scenario in which one half of a two-qubit Werner state is sequentially measured by multiple Alices and the other half by multiple Bobs. We find that the maximum number of Alices who can share steering with a single Bob increases from 2 to 5 when the number of measurement settings $N$ increases from 2 to 16. Furthermore, we find a counterintuitive phenomenon that for a fixed $N$, at most 2 Alices can share steering with 2 Bobs, while 4 or more Alices are allowed to share steering with a single Bob. We further analyze the robustness of the steering sharing by calculating the required purity of the initial Werner state, the lower bound of which varies from 0.503(1) to 0.979(5). Finally, we show that our both-sides sequential steering sharing scheme can be applied to control the steering ability, even the steering direction, if an initial asymmetric state or asymmetric measurement is adopted. Our work gives insights into the diversity of steering sharing and can be extended to study the problems such as genuine multipartite quantum steering when the sequential unsharp measurement is applied., 15 pages, 4 figures, 1 table

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively analyse entanglement, as it induces a partial order in the Hilbert space. However, it has been shown that, for systems with fixed local dimensions, this order is generically trivial, which prevents relating multipartite states to each other with respect to any entanglement measure. In order to obtain a non-trivial partial ordering, we study a physically motivated extension of LOCC: multi-state LOCC. Here, one considers simultaneous LOCC transformations acting on a finite number of entangled pure states. We study both multipartite and bipartite multi-state transformations. In the multipartite case, we demonstrate that one can change the stochastic LOCC (SLOCC) class of the individual initial states by only applying Local Unitaries (LUs). We show that, by transferring entanglement from one state to the other, one can perform state conversions not possible in the single copy case; provide examples of multipartite entanglement catalysis; and demonstrate improved probabilistic protocols. In the bipartite case, we identify numerous non-trivial LU transformations and show that the source entanglement is not additive. These results demonstrate that multi-state LOCC has a much richer landscape than single-state LOCC., 28 pages, 8 figures

Quantum coherence is the most fundamental of all quantum quantifiers, underlying other well-known quantities such as entanglement, quantum discord, and Bell correlations. It can be distributed in a multipartite system in various ways -- for example, in a bipartite system it can exist within subsystems (local coherence) or collectively between the subsystems (global coherence) and exhibits a trade-off relation. In quantum systems with more than two subsystems, there are more trade-off relations, due to the various decomposition ways of the coherence. In this paper, we experimentally verify these coherence trade-off relations in adiabatically evolved quantum systems using a spin system by changing the state from a product state to a tripartite entangled state. We study the full set of coherence trade-off relations between the original state, the bipartite product state, the tripartite product state, and the decohered product state. We also experimentally verify the monogamy inequality and show that both the quantum systems are polygamous except for the initial product state. We find that despite the different types of states involved, the properties of the state in terms of coherence and monogamy are equivalent. This illustrates the utility of using coherence as a characterization tool for quantum states., Comment: 12 pages, 7 figures

Recently, Halder et al. (in Phys Rev Lett 122:040403, 2019) present two sets of strong nonlocality of orthogonal product states based on the local irreducibility. However, for a set of locally indistinguishable orthogonal entangled states, the remaining question is whether the states can reveal strong quantum nonlocality. Here we present a general definition of strong quantum nonlocality based on the local indistinguishability. Then, in $$2 \otimes 2 \otimes 2$$ quantum system, we show that a set of orthogonal entangled states is locally reducible but locally indistinguishable in all bipartitions, which means the states have strong nonlocality. Furthermore, we generalize the result in N-qubit quantum system with $$N\geqslant 3$$ . Finally, we also construct a class of strong nonlocality of orthogonal entangled states in $$d\otimes d\otimes \cdots \otimes d, d\geqslant 3$$ . Our results extend the concept of strong nonlocality for entangled states.

We investigate the entanglement and nonlocality dynamics of a two-qubit Bell state and the three-qubit Greenberger–Home–Zeilinger (GHZ) state in a noisy environment by solving analytically a master equation in the Lindblad form. In the case of the Bell state, we obtain the analytic expressions of the concurrence and the maximal violation of the Clauser–Horne–Shimony–Holt inequality of the evolution state. In the case of the three-qubit GHZ state, we obtain the analytic formula of the genuinely multipartite concurrence of the evolution state. Usually, it is difficult to give the analytic expression of the maximum violation of the Svetlichny inequality for a general three-qubit state, but we find the analytic expression for a class of three-qubit states whose correlation matrices are of a special form. We use this result to obtain the analytic expression of the maximum violation of the Svetlichny inequality of the evolution state when parameters in the master equation meet certain conditions.

Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the R\'enyi-$\alpha$ entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer characterization of entanglement distributions., Comment: 17 pages, 4 figures

We study a class of multipartite open quantum dynamics for systems of arbitrary number of qubits. The non-Markovian quantum master equation can involve arbitrary single or multipartite and time-dependent dissipative coupling mechanisms, expressed in terms of strings of Pauli operators. We formulate the general constraints that guarantee the complete positivity of this dynamics. We characterize in detail underlying mechanisms that lead to memory effects, together with properties of the dynamics encoded in the associated system rates. We specifically derive multipartite "eternal" non-Markovian master equations that we term hyperbolic and trigonometric due to the time dependence of their rates. For these models we identify a transition between positive and periodically divergent rates. We also study non-Markovian effects through an operational (measurement-based) memory witness approach., Comment: 12 pages, 2 figures

The ability to precisely discriminate multiple quantum channels is fundamental to achieving quantum enhancements in data-readout, target detection, pattern recognition, and more. Optimal discrimination protocols often rely on entanglement shared between an incident probe and a protected idler-mode. While these protocols can be highly advantageous over classical ones, the storage of idler-modes is extremely challenging in practice. In this work, we investigate idler-free block protocols based on the use of multipartite entangled probe states. In particular, we focus on a class of idler-free protocol which uses non-disjoint distributions of multipartite probe states irradiated over multi-channels, known as dynamic discrimination protocols. We derive new, analytical bounds for the average error probability of such protocols in a bosonic Gaussian channel setting, revealing idler-free strategies that display performance close to idler-assistance for powerful, near-term quantum sensing applications., 22 pages, 5 figures. Close to accepted version

We study three independent pairs of Jaynes–Cummings systems such that two atoms might be correlated with each other but the third atom is uncorrelated with rest. We investigate the conditions under which these uncorrelated three atoms may become genuinely entangled. We find that this task is impossible if the cavity interacting with uncorrelated atom share classical correlations with any other cavity. We observe that atomic state can become genuine multipartite entangled, at least if the cavity with uncorrelated atom, is highly entangled with any other cavity. This is an interesting and non-trivial observation and may serve as another technique to generate multipartite entangled atoms via JC-interactions.

We introduce a generalized concept of quantum teleportation in the framework of quantum measurement and reversing operation. Our framework makes it possible to find an optimal protocol for quantum teleportation enabling a faithful transfer of unknown quantum states with maximum success probability up to the fundamental limit of the no-cloning theorem. Moreover, an optimized protocol in this generalized approach allows us to overcome noise in quantum channel beyond the reach of existing teleportation protocols without requiring extra qubit resources. Our proposed framework is applicable to multipartite quantum communications and primitive functionalities in scalable quantum architectures., Comment: 17 pages, 6 figures

We generalize the constructions for the multipartite reflected entropy in order to construct spacetimes capable of representing multipartite entanglement wedge cross sections of differing party number as Ryu-Takayanagi surfaces on a single replicated geometry. We devise a general algorithm for such constructions for arbitrary party number and demonstrate how such methods can be used to derive novel inequalities constraining mulipartite entanglement wedge cross sections., Comment: 23 pages, 9 figures

We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the $d$--level Dicke states., title slightly changed, appendix B fixed; journal ref. added

We report on the realization of a three-node entanglement-based quantum network. We combine remote quantum nodes based on diamond communication qubits into a scalable phase-stabilized architecture, supplemented with a robust memory qubit and local quantum logic. Also, we achieve real-time communication and feed-forward gate operations across the network. We demonstrate two key quantum network protocols without post-selection: the distribution of genuine multipartite entangled states across the three nodes and entanglement swapping through an intermediary node. Finally, we will discuss the most recent experiments using the network as a platform for exploring, testing, and developing multi-node quantum network protocols and a quantum network control stack.

We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability and the optimal trade-off between the type-I and type-II errors, thus establishing the associated Chernoff, Stein, Hoeffding, and the strong converse exponents. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB., Comments are welcome

We discuss two methods that, through a combination of cyclically gluing copies of a given $n$-party boundary state in AdS/CFT and a canonical purification, creates a bulk geometry that contains a boundary homologous minimal surface with area equal to 2 or 4 times the $n$-party entanglement wedge cross-section, depending on the parity of the party number and choice of method. The areas of the minimal surfaces are each dual to entanglement entropies that we define to be candidates for the $n$-party reflected entropy. In the context of AdS$_3$/CFT$_2$, we provide a boundary interpretation of our construction as a multiboundary wormhole, and conjecture that this interpretation generalizes to higher dimensions., 20 pages, 7 figures; added references, one figure, and expanded discussion on black holes and the boundary state

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., 12 pages, 3 figures

Continuous variable entangled states and especially entangled coherent states have attracted increasing interest in the Geld of quantum information processing. The characteristic features of the superposition of quantum states can be found in the literature. Because of these significant findings, we introduce and investigate a special superposition of multipartite entangled coherent states. We prove that the free-traveling optical field scheme can generate such a superposed state. Using a geometric measure of entanglement, we then investigate the correlation behavior of the superposed state.

We present the results of our study of correlations in noncomposite systems like qudits (N-level atom or spin-j system). We show that they correspond to correlations in composite systems like bipartite or multipartite systems. We establish the correspondence between correlations in noncomposite systems and composite ones using the map of indices labeling the random variables in classical probability theory or matrix elements of density matrices in quantum mechanics. We obtain new information-entropic inequalities for density matrices of noncomposite systems. Also we present Bayes’ formula for noncomposite classical system with one random variable. Finally we discuss the possibility to use hidden correlations and entanglement of a single-qudit state.

We investigate genuine multipartite entanglement in general multipartite systems. Based on the norms of the correlation tensors of a multipartite state under various partitions, we present an analytical sufficient criterion for detecting the genuine four-partite entanglement. The results are generalized to arbitrary multipartite systems.

The Kochen-Specker theorem is investigated for n spin-1/2 systems by using an inequality proposed in Nagata (J. Math. Phys. 46, 102101, 2005) on the basis on binary logic. A measurement theory based on the truth values (binary logic), i.e., the truth T (1) for true and the falsity F (0) for false is used. The values of measurement outcome are either + 1 or 0 (in $\hbar /2$ unit). The quantum predictions by n-multipartite states violate the inequality by an amount that grows exponentially with n. The measurement theory based on the binary logic provides an exponentially stronger refutation of the existence of hidden-variable when the number of parties of the state increases more. It turns out that the Kochen-Specker theorem becomes a quite strong theorem when the dimension of the multipartite state highly increases, regardless of entanglement properties.

In this paper we use a 11-particle entangled state as quantum channel for the mutual transfer of two three-qubit generalized W-state between two parties in the presence of a supervisor. The protocol we present is a perfect controlled bidirectional teleportation protocol. The research is in the line of exploring the possibilities for use of multi-particle entanglement in quantum multitasking.

It is desirable to evaluate the maximal violation of Bell inequalities as the violation of constraints indicates the quantum effect of correlation in composite quantum system. In this paper, we propose a new approach to compute the maximal violation of Bell inequalities for multipartite qubit via partially symmetric tensor. For a class of well known Bell inequalities, we find that their maximal violation values derived by partially symmetric tensors cover the previous results as a special case. This sheds new light on the applications of tensor in the quantum multipartite system.

Characterization of the multipartite mixed state entanglement is still a challenging problem. This is due to the fact that the entanglement for the mixed states, in general, is defined by a convex-roof extension. That is the entanglement measure of a mixed state ρ of a quantum system can be defined as the minimum average entanglement of an ensemble of pure states. In this paper, we show that polynomial entanglement measures of degree 2 of even-N qubits X states is in the full agreement with the genuine multipartite (GM) concurrence. Then, we plot the hierarchy of entanglement classification for four qubit pure states and then using new invariants, we classify the four qubit pure states. We focus on the convex combination of the classes whose at most the one of the invariants is non-zero and find the relationship between entanglement measures consist of non-zero-invariant, GM concurrence and one-tangle. We show that in many entanglement classes of four qubit states, GM concurrence is equal to the square root of one-tangle.

Quantum entanglement is one of important resources for quantum communication. Entanglement criteria help us detect entangled states. One of important criteria is the local uncertainty relation (LUR) entanglement criteria, which is studied extensively. However, all existent LUR criteria are dependent on the chosen observables. In the paper, applying the uncertainty principle, we improve the LUR criteria to obtain entanglement criteria for multipartite Gaussian states, which are independent on observalbes.

Quantum coherence and quantum correlations lie in the center of quantum information science, since they both are considered as fundamental reasons for significant features of quantum mechanics different from classical mechanics. We present a group of complementary relations for quantum coherence and quantum correlations; specifically, we focus on thermal discord and conditional information in scenarios of multiple measurements. We show that the summation of quantum coherence quantified in different bases has a lower bound, resulting from entropic uncertainty relations with multiple measurements. Similar results are also obtained for thermal discord and for post-measurement conditional information with multiple measurements in a multipartite system. These results indicate the general applications of the uncertainty principle to various concepts of quantum information., Comment: 7 pages

Beyond future applications, quantum networks open interesting fundamental perspectives, notably novel forms of quantum correlations. In this work we discuss quantum correlations in networks from the perspective of the underlying quantum states and their entanglement. We address the questions of which states can be prepared in the so-called triangle network, consisting of three nodes connected pairwise by three sources. We derive necessary criteria for a state to be preparable in such a network, considering both the cases where the sources are statistically independent and classically correlated. This shows that the network structure imposes strong and non-trivial constraints on the set of preparable states, fundamentally different from the standard characterization of multipartite quantum entanglement., 7 pages, 1 figure, see related work from Navascues et al.: arXiv:2002.02773, comments are welcome!

A multipartite state that is not the convex sum of bipartite product states is said to be a genuine multipartite entangled (GME) state, which offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy n-partite W state when $$n = 3, 4, 5$$ and 6 and find that the criterion can detect more noisy W states when n ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of 3-qutrit states. The result is stronger than that based on GME concurrence and Fisher information.

Nonlocality without entanglement(NLWE) is a nonlocal phenomenon that occurs in quantum state discrimination of multipartite separable states. In the discrimination of orthogonal separable states, the term NLWE is used when the quantum states cannot be discriminated perfectly by local operations and classical communication. In this case, the occurrence of NLWE is independent of nonzero prior probabilities of quantum states being prepared. Recently, it has been found that the occurrence of NLWE can depend on nonzero prior probabilities in minimum-error discrimination of nonorthogonal separable states. Here, we show that even in optimal unambiguous discrimination, the occurrence of NLWE can depend on nonzero prior probabilities. We further show that NLWE can occur regardless of nonzero prior probabilities, even if only one state can be locally discriminated without error. Our results provide new insights into classifying sets of multipartite quantum states in terms of quantum state discrimination., 10 pages, 1 figure, published version

We analyze decoherence and objectivization processes in spin-spin models for arbitrary spins. We first derive the most general analytic form of the decoherence factor in the measurement limit, where the interaction Hamiltonian dominates the rest. We then analyze thermal environments and derive exact, analytic formulas for both the decoherence factor and the state fidelity of post-interaction environment states. This allows to analyze the objectivization process of the state of the central spin during the interaction. We do so using, so called, Spectrum Broadcast Structures (SBS), which are specific multipartite quantum states encoding a certain operation notion of objectivity. We analyze analytically (for short times) and numerically how higher spin influences the efficiency of decoherence and objectivization processes. As expected, the higher the spin of the environment, the more efficient decoherence and objectivization become. This work is a generalization of previous studies, limited to spin-$1/2$ systems only, and we hope will be useful in future objectivity experiments., 8 pages, 1 figure

We propose a reliable scheme for one-step synthesizing of a quantum fan-out gate in a system of neutral atoms. By introducing the off-resonant driving fields with Gaussian temporal modulation, the dynamics of the system is strictly restricted to the ground-state subspace on the basis of unconventional Rydberg pumping, which exhibits more robustness than the constant driving method against the fluctuation of system parameters, such as operating time and environment noise. As a direct application of this quantum fan-out gate, we discuss in detail the preparation of multipartite Greenberger–Horne–Zeilinger (GHZ) state for neutral atoms. The result shows that a high fidelity better than 99% can be obtained within the state-of-the-art experiments.