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Einstein–Podolsky–Rosen (EPR) paradox highlights the absence of a local realistic explanation for quantum mechanics, and shows the incompatibility of the local-hidden-state models with quantum theory. For N-qubit states, or more importantly, the N-qubit mixed states, we present the EPR steering paradox in the form of the contradictory equality " 2 = 1 ". We show that the contradiction holds for any N-qubit state as long as both "the pure state requirement" and "the measurement requirement" are satisfied. This also indicates that the EPR steering paradox exists in more general cases. Finally, we give specific examples to demonstrate and analyze our arguments. [ABSTRACT FROM AUTHOR]

The N -qubit Greenberger–Horne–Zeilinger (GHZ) states are the maximally entangled states of N qubits, which have had many important applications in quantum information processing, such as quantum key distribution and quantum secret sharing. Thus how to distinguish the GHZ states from other quantum states becomes a significant problem. In this work, by presenting a family of the generalized Clauser–Horne–Shimony–Holt (CHSH) inequality, we show that the N -qubit GHZ states can be indeed identified by the maximal violations of the generalized CHSH inequality under some specific measurement settings. The generalized CHSH inequality is simple and contains only four correlation functions for any N -qubit system, thus has the merit of facilitating experimental verification. Furthermore, we present a quantum phenomenon of robust violations of the generalized CHSH inequality in which the maximal violation of Bell's inequality can be robust under some specific noises adding to the N -qubit GHZ states. [ABSTRACT FROM AUTHOR]

The no-masking theories show that it is impossible to mask the set of all qubit states into the quantum correlation of bipartite qubit system or tripartite qubit system. In this paper, we give a new proof of the no-masking situation of the tripartite qubit system. Recent work has shown that there exists a universal masker which can mask an arbitrary set of qubit states in four-qubit systems perfectly by means of the maximum entangled states. Here we show that there exist more than one masking scheme even for the same multipartite qubit system. Basing on the maximum entangled states we give the deterministic masking scenario for N-qubit system. In practice, decoherence hinders us from obtaining the maximum entangled states. From this viewpoint, the masking scenario based on non-maximum entangled states becomes more universal. Furthermore, we provide an approximate quantum masking scenario and investigate the relation between approximate masking and quantum entanglement. [ABSTRACT FROM AUTHOR]

Quantum contextuality, a more general quantum correlation, is an important resource for quantum computing and quantum information processing. Meanwhile, quantum contextuality plays an important role in fundamental quantum physics. Yu and Oh (YO) proposed a proof of the Kochen–Specker theorem for a qutrit with only 13 rays. Here, we further study quantum contextuality of YO-13 rays using the inequality approach. The maximum quantum violation value of the optimal noncontextuality inequality constructed by YO-13 rays is increased to 11.9776 in the four-dimensional system, which is larger than 11.6667 in the qutrit system. The result shows that the set of YO-13 rays has stronger quantum contextuality in the four-dimensional system. Moreover, we provide an all-versus-nothing proof (i.e. Hardy-like proof) to study YO-13 rays without using any inequality, which is easily applied to experimental tests. Our results will further deepen the understanding of YO-13 rays. [ABSTRACT FROM AUTHOR]

The Greenberger–Horne–Zeilinger (GHZ) paradox is an exquisite no-go theorem that shows the sharp contradiction between classical theory and quantum mechanics by ruling out any local realistic description of quantum theory. The investigation of GHZ-type paradoxes has been carried out in a variety of systems and led to fruitful discoveries. However, its range of applicability still remains unknown and a unified construction is yet to be discovered. In this work, we present a unified construction of GHZ-type paradoxes for graph states, and show that the existence of GHZ-type paradox is not limited to graph states. The results have important applications in quantum state verification for graph states, entanglement detection, and construction of GHZ-type steering paradox for mixed states. We perform a photonic experiment to test the GHZ-type paradoxes via measuring the success probability of their corresponding perfect Hardy-type paradoxes, and demonstrate the proposed applications. Our work deepens the comprehension of quantum paradoxes in quantum foundations, and may have applications in a broad spectrum of quantum information tasks. [ABSTRACT FROM AUTHOR]

We propose a scenario to increase the probability of probabilistic quantum deletion and to enhance the fidelity of approximate quantum deletion for two non-orthogonal states via weak measurement. More interestingly, by pretreating the given non-orthogonal states, the probability of probabilistic quantum deletion and fidelity of approximate quantum deletion can reach 1. Since outcomes of the weak measurement that we required are probabilistic, we perform the subsequent deleting process only when the outcome of weak measurement is "yes". Remarkably, we find that our scenario has better performance in quantum information process; for example, it costs less quantum resources and time. [ABSTRACT FROM AUTHOR]

We introduce a quantity of contextuality, i.e. the maximum contextuality of a two-qubit state in 4-cycle measurement scenarios, to study quantum contextuality of two-qubit states for the 4-cycle noncontextual inequalities. Subsequently, we prove several appealing features of this quantity of contextuality, including the faithfulness, the boundedness, the invariance under unitary operations and the convexity. Remarkably, for arbitrary two-qubit state, we reformulate this quantity of contextuality analytically by eigenvalues of the state. Therefore, in 4-cycle measurement scenarios, we establish an efficient way to distinguish two-qubit states that can reveal contextuality from ones that cannot. [ABSTRACT FROM AUTHOR]

It is known that the linear n-setting steering inequalities introduced in [D. J. Saunders, S. J. Jones, H. M. Wiseman and G. J. Pryde, Nat. Phys.6 (2010) 845.] are very efficient inequalities in detecting steerability of the Werner states by using optimal measurement axes. Here, we construct chained steering inequalities that have improved visibility for the Werner states under a finite number of settings. Specifically, the threshold values of quantum violation of our inequalities for the n=4,6,10 settings are lower than those of the linear steering inequalities. Furthermore, for almost all generalized Werner states, the chained steering inequalities always have improved visibility in comparison with the linear steering inequalities. [ABSTRACT FROM AUTHOR]

For the Abner Shimony (AS) inequalities, the simplest unified forms of directions attaining the maximum quantum violation are investigated. Based on these directions, a family of Einstein-Podolsky-Rosen (EPR) steering inequalities is derived from the AS inequalities in a systematic manner. For these inequalities, the local hidden state (LHS) bounds are strictly less than the local hidden variable (LHV) bounds. This means that the EPR steering is a form of quantum nonlocality strictly weaker than Bell nonlocality. [ABSTRACT FROM AUTHOR]

Based on the fact that both nonlocality and contextuality are resource theories, it is natural to ask how to amplify them more efficiently. In this paper, we present a contextuality distillation protocol which produces an n-cycle box B ∗ B′ from two given n-cycle boxes B and B′. It works efficiently for a class of contextual n-cycle (n ≥ 4) boxes which we termed as “the generalized correlated contextual n-cycle boxes”. For any two generalized correlated contextual n-cycle boxes B and B′, B ∗ B′ is more contextual than both B and B′. Moreover, they can be distilled toward to the maximally contextual box CHn as the times of iteration goes to infinity. Among the known protocols, our protocol has the strongest approximate ability and is optimal in terms of its distillation rate. What is worth noting is that our protocol can witness a larger set of nonlocal boxes that make communication complexity trivial than the protocol in Brunner and Skrzypczyk (Phys. Rev. Lett. 102, 160403 2009), this might be helpful for exploring the problem that why quantum nonlocality is limited. [ABSTRACT FROM AUTHOR]

In order to quantify contextuality of empirical models, the quantity of contextuality (QoC) of empirical models is introduced in terms of the trace-distance. Let Q C( e) denote the QoC of an empirical model e. The following conclusions are proved. (i) An empirical model e is non-contextual if and only if Q C( e)=0, and then it is contextual if and only if Q C( e)>0; (ii) the QoC function QC is convex, contractive and continuous. Finally, the QoC of some famous models is computed, including PM-isotropic boxes P M , M-isotropic boxes M , C H -isotropic boxes $CH_{n}^{\alpha }$ as well as K box, where α∈[0,1]. Moreover, P M is non-contextual if and only if $\alpha \in [\frac {1}{6},\frac {5}{6}]$ ; M is non-contextual if and only if $\alpha \in [0,\frac {4}{5}]$ ; when n is even, $CH_{n}^{\alpha }$ is non-contextual if and only if $\alpha \in [\frac {1}{n},\frac {n-1}{n}]$ , and when n is odd, $CH_{n}^{\alpha }$ is non-contextual if and only if $\alpha \in [0,\frac {n-1}{n}]$ . The most important thing is that it is very easy to compare the QoC of any two isotropic boxes discussed in the above. [ABSTRACT FROM AUTHOR]

The uncertainty principle in quantum mechanics is a fundamental relation with different forms, including Heisenberg's uncertainty relation and Schrödinger's uncertainty relation. In this paper, we prove a Schrödinger-type uncertainty relation in terms of generalized metric adjusted skew information and correlation measure by using operator monotone functions, which reads, for some operator monotone functions f and g, all n-dimensional observables A, B and a non-singular density matrix $$\rho $$ . As applications, we derive some new uncertainty relations for Wigner-Yanase skew information and Wigner-Yanase-Dyson skew information. [ABSTRACT FROM AUTHOR]

A generalized duality quantum computer acting on mixed states (GDQC-MS) is established, which is a device consisting of a generalized quantum wave divider, a finite number of generalized quantum operations, and a generalized quantum wave combiner. Some of the interesting properties of a GDQC are explored. For example, it is proved that the divider and the combiner of a GDQC-MS are mutually dual contractions, and when the generalized quantum operations used in a GDQC-MS are contractions, the GDQC-MS is also a contraction. In that case, the loss of an input state passing through a GDQC-MS is measured and the corresponding operator of a GDQC-MS is a generalized quantum operation. [ABSTRACT FROM AUTHOR]

By introducing the relative robustness of Λ -entanglement of a multipartite state related to a Λ -separable state, the robustness of Λ -entanglement of a multipartite state is defined as the minimum of the relative robustness of Λ -entanglement of a state related to all Λ -separable states. It is proved that, as a function on the set of all quantum states of an n-partite system, robustness of Λ -entanglement is nonnegative, lower semi-continuous, and convex, and it is zero if and only if the state is Λ -separable. Thus, robustness of Λ -entanglement not only quantifies the endurance of Λ -entanglement of a state against linear noise, but also can be used to distinguish Λ -separable states from Λ -entangled states. Furthermore, influences of a quantum channel on robustness of Λ -entanglement are discussed. [ABSTRACT FROM AUTHOR]