Bell(<Emphasis Type="Italic">δ</Emphasis>) Inequalities Derived from Separate Common Causal Explanation of Almost Perfect EPR Anticorrelations

It is a well known fact that a common common causal explanation of the EPR scenario which consists in providing a local, non-conspiratorial common common cause system for a set of EPR correlations is excluded by various Bell inequalities. But what if we replace the assumption of a common common cause system by the requirement that each correlation of the set has a local, non-conspiratorial separate common cause system? In the paper we show that this move does not yield a solution by providing a general recipe how to derive any Bell(δ) inequality—that is an inequality differing from some Bell inequality in a term of order of δ—from the assumption that an appropriate set of almost perfect anticorrelations has a separate common causal explanation.     

Degree of Entanglement and Violation of Bell Inequality by Two-Spin-1/2 States

Bell inequality is violated by the quantum mechanical predictions made from an entangled state of the composite system. In this paper we examine this inequality and entanglement measures in the construction of the coherent states for two-qubit pure and mixed states. we find a link to some entanglement measures through some new parameters (amplitudes of coherent states). Conditions for maximal entanglement and separability are then established for both pure and mixed states. Finally, we analyze and compare the violation of Bell inequality for a class of mixed states with the degree of
entanglement by applying the formalism of Horodecki et al.     

Large Violation of Bell Inequalities with Low Entanglement

In this paper we obtain violations of general bipartite Bell inequalities of order \({\frac{\sqrt{n}}{\log n}}\) with n inputs, n outputs and n-dimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor.     

基于量子相干性的四体贝尔不等式构建

贝尔不等式在定域性和实在性的双重假设下,对于被分隔的粒子同时被测量时其结果的可能关联程度建立了一个严格的限制,违反贝尔不等式确保量子态存在纠缠.本文利用量子相干性的l1和相对熵测度构建了四体量子贝尔不等式,发现一般实系数Greenberger-Horne-Zeilinger纯态和簇纯态总是违反四体相对熵相干性测度贝尔不等式,因此违反四体相对熵相干性测度贝尔不等式的这些态是纠缠态.     

Generation of a two-photon KLM quantum channel

As demonstrated by E. Knill et al. [Nature 409, 46 (2001)], quantum teleportation and quantum logic gates with a success probability close to one can be implemented using only linear optical elements, additional photons, and post-selection. To do this, it is desirable to have special quantum channels in sight before quantum teleportation performance. Here, we propose an experimental arrangement to generate a two-photon KLM state different from the well-known Bell states. This two-photon KLM state can be used to enhance the success probability of the quantum teleportation of a one-mode quantum qubit from 0.5 up to 2/3.     

Multihop Teleportation via the Composite of Asymmetric W State and Bell State

In this article, quantum teleportation schemes of a single qubit, two-qubit and N-qubit state are presented in a multihop communication network. All the schemes can be completed deterministicly. The shared entanglement resource between two adjacent nodes is the composition of the asymmetric W state and Bell state. It is not equivalent to the composite of GHZ state and Bell state used by Zou et al. (Phys. Lett. A 381, 76–81 2017).     

Semi-Quantum Private Comparison Using Single Photons

Recently, by using the BB84 quantum key distribution (QKD) protocol, Sun et al. put forward two quantum private comparison (QPC) protocols with a semi-honest third party (TP) and a malicious TP, respectively (Sun et al., Quantum Inf. Process. 14, 2125–2133, 2015). In this paper, we absorb the concept of semi-quantumness suggested by Boyer et al. (Phys. Rev. Lett. 99(14), 140501, 2007 and Phys. Rev. A 79(3), 032341, 2009) into Sun et al.’s QPC protocols and construct two corresponding SQPC protocols. The common interesting feature of the proposed SQPC protocols is that apart from the establishment of shared keys between different participants, the rest parts of the protocols are completely classical. The output correctness and the security of the proposed SQPC protocols are validated. Compared with the present SQPC protocols, the advantages of the proposed SQPC protocols lies in the following aspects: on the aspect of quantum resource, they employ single photons rather than Bell entangled states; with respect to quantum measurement for TP, they need single-photon measurements rather than Bell state measurements; as for quantum entanglement swapping, they do not need it at all; and the second proposed SQPC protocol takes effect under a malicious TP and makes TP know neither the genuine contents of secret inputs nor the comparison result.     

New Probabilistic Quantum Key Distribution Protocol

On the basis of entanglement swapping of Bell states, Hwang et al. proposed a probabilistic quantum key distribution (PQKD) protocol Quantum Inf. Comput. 11(7-8), 615–637 (2011). Recently, Lin et al. Quantum Inf. Comput. 14(9-10), 757–762 (2014) proposed a unitary operation attack on Hwang et al.’s PQKD. However, unlike the unitary operation attack, this work points out that a malicious participant in Hwang et al.’s PQKD protocol can manipulate the secret key. As a result, the security requirements of a PQKD protocol, i.e., fairness, cannot be satisfied in their protocol. Moreover, the same attack can also crack the fairness requirement of the existing quantum key agreement (QKA) protocols. To overcome both problems, this paper proposes a new PQKD protocol based on the order rearrangement of the transmitted photons. Furthermore, the rearrangement method can also solve the key manipulation attack in QKA protocols.     

Bell Inequalities and Group Symmetry

Recently the method based on irreducible representations of finite groups has been proposed as a tool for investigating the more sophisticated versions of Bell inequalities (V. Ugǔr G?ney, M. Hillery, Phys. Rev. A90, 062121 ([2014]) and Phys. Rev. A91, 052110 ([2015])). In the present paper an example based on the symmetry group S ₄ is considered. The Bell inequality violation due to the symmetry properties of regular tetrahedron is described. A nonlocal game based on the inequalities derived is described and it is shown that the violation of Bell inequality implies that the quantum strategies outperform their classical counterparts.     

Entanglement of three qubits

For the formulation of Bell inequalities, it is important to include not just N-site correlation functions, but also (N-n)-site correlation functions. In this article, we focus on a three-qubit Bell inequality, which has been shown to be a good candidate for generalizing Gisin’s theorem to three qubits. The three-qubit Bell inequality can be used to detect the W-type entanglement in a proposed experiment.     

All bipartite entangled States display some hidden nonlocality

One of the most significant and well-known properties of entangled states is that they may lead to violations of Bell inequalities and are thus inconsistent with any local-realistic theory. However, there are entangled states that cannot violate any Bell inequality, and in general the precise relationship between entanglement and observable nonlocality is not well understood. We demonstrate that a violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality can be demonstrated in a certain kind of Bell experiment for all entangled states. Our proof of the result consists of two main steps. We first provide a simple characterization of the set of states that do not violate the CHSH inequality even after general local operations and classical communication. Second, we prove that for each entangled state sigma, there exists another state rho not violating the CHSH inequality, such that rhomultiply sign in circlesigma violates the CHSH inequality.     

Extended Rearrangement Inequalities and Applications to Some Quantitative Stability Results

In this paper, we prove a new functional inequality of Hardy–Littlewood type for generalized rearrangements of functions. We then show how this inequality provides quantitative stability results of steady states to evolution systems that essentially preserve the rearrangements and some suitable energy functional, under minimal regularity assumptions on the perturbations. In particular, this inequality yields a quantitative stability result of a large class of steady state solutions to the Vlasov–Poisson systems, and more precisely we derive a quantitative control of the L¹ norm of the perturbation by the relative Hamiltonian (the energy functional) and rearrangements. A general non linear stability result has been obtained by Lemou et al. (Invent Math 187:145–194, 2012) in the gravitational context, however the proof relied in a crucial way on compactness arguments which by construction provides no quantitative control of the perturbation. Our functional inequality is also applied to the context of 2D-Euler systems and also provides quantitative stability results of a large class of steady-states to this system in a natural energy space.     

An Efficient and Secure Arbitrary <Emphasis Type="Italic">N</Emphasis>-Party Quantum Key Agreement Protocol Using Bell States

Two quantum key agreement protocols using Bell states and Bell measurement were recently proposed by Shukla et al. (Quantum Inf. Process. 13(11), 2391–2405, 2014). However, Zhu et al. pointed out that there are some security flaws and proposed an improved version (Quantum Inf. Process. 14(11), 4245–4254, 2015). In this study, we will show Zhu et al.’s improvement still exists some security problems, and its efficiency is not high enough. For solving these problems, we utilize four Pauli operations {I, Z, X, Y} to encode two bits instead of the original two operations {I, X} to encode one bit, and then propose an efficient and secure arbitrary N-party quantum key agreement protocol. In the protocol, the channel checking with decoy single photons is introduced to avoid the eavesdropper’s flip attack, and a post-measurement mechanism is used to prevent against the collusion attack. The security analysis shows the present protocol can guarantee the correctness, security, privacy and fairness of quantum key agreement.     

Asymptotic violation of Bell inequalities and distillability

A multipartite quantum state violates a Bell inequality asymptotically if, after jointly processing by general local operations an arbitrarily large number of copies of it, the result violates the inequality. In the bipartite case we show that asymptotic violation of the Clauser-Horne-Shimony-Holt inequality is equivalent to distillability. Hence, bound entangled states do not violate it. In the multipartite case we consider the complete set of full-correlation Bell inequalities with two dichotomic observables per site. We show that asymptotic violation of any of these inequalities by a multipartite state implies that pure-state entanglement can be distilled from it, although the corresponding distillation protocol may require that some of the parties join into several groups. We also obtain the extreme points of the set of distributions generated by measuring N quantum systems with two dichotomic observables per site.     

First principles electronic structure investigation of order of singlet and triplet states of oxyhemoglobin and analysis of possible influence of muon trapping

Interest in the possibility of magnetic character for oxyhemoglobin (OxyHb) has been recently stimulated by the observations of muon spin-lattice relaxation effects studied (Nagamine et al., Proc Jpn Acad Ser B Phys Biol Sci 83:120–126, 2007) with the muon-spin rotation (μSR) technique. In view of this, we have carried out first-principles electronic structure investigations involving Hartree–Fock theory combined with many body perturbation effects for the singlet and triplet states of OxyHb. Our results indicate that using two recent x-ray structural data (Paoli et al., J Mol Biol 256:775, 1996; Park et al., J Mol Biol 360:690, 2006) for OxyHb, for only Hartree–Fock theory without many-body effects included, the singlet state lies above the triplet state by energies of about 0.08 and 0.13 a.u. for the two structures in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). Incorporation of many-body effects by the perturbation method reverses the order, with the triplet state located 0.18 and 0.14 a.u. above the singlet state for the structures in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). Physical reasons for these relative orderings of the singlet and triplet states will be discussed. It is clear that OxyHb by itself would be in a singlet state at room temperature or below, since from our calculation, the triplet state lies about KT above the singlet state with T having the value of 44,098 K and 56,449 K for the two structural data in Paoli et al. (J Mol Biol 256:775, 1996) and Park et al. (J Mol Biol 360:690, 2006). As regards the muon spin-lattice relaxation effects obtained by recent μSR measurements (by Nagamine et al., Proc Jpn Acad Ser B Phys Biol Sci 83:120–126, 2007) at room temperature, the sensitive dependence of the singlet-triplet separation on many-body effects in our investigation suggests that it is possible that the singlet-triplet separation could be reversed or reduced significantly when a muon is trapped near an oxygen atom of the oxygen molecule, allowing the triplet to be occupied at room temperature and lead to significant muon spin-lattice relaxation.     

Bell’s Theorem Without Inequalities and Only Two Distant Observers

A proof of Bell's theorem without inequalities and involving only two observers is given by suitably extending a proof of the Bell-Kochen-Specker theorem due to Mermin. This proof is generalized to obtain an inequality-free proof of Bell's theorem for a set of n Bell states (with n odd) shared between two distant observers. A generalized CHSH inequality is formulated for n Bell states shared symmetrically between two observers and it is shown that quantum mechanics violates this inequality by an amount that grows exponentially with increasing n.     

Comment on the “Quantum Private Comparison Protocol Based on Bell Entangled States”

Recently, Liu et al. proposed a quantum private comparison (QPC) based on Bell entangled states (Liu et al. in Commun. Theor. Phys. 57(4): 583, 2012). This paper points out a security loophole in Liu et al.’s protocol, in which the third party can disclose the private information of both users. In addition, an improvement is proposed to avoid the loophole.     

13-Moment System with Global Hyperbolicity for Quantum Gas

We point out that the quantum Grad’s 13-moment system (Yano in Physica A 416:231–241, 2014) is lack of global hyperbolicity, and even worse, the thermodynamic equilibrium is not an interior point of the hyperbolicity region of the system. To remedy this problem, by fully considering Grad’s expansion, we split the expansion into the equilibrium part and the non-equilibrium part, and propose a regularization for the system with the help of the new hyperbolic regularization theory developed in Cai et al. (SIAM J Appl Math 75(5):2001–2023, 2015) and Fan et al. (J Stat Phys 162(2):457–486, 2016). This provides us a new model which is hyperbolic for all admissible thermodynamic states, and meanwhile preserves the approximate accuracy of the original system. It should be noted that this procedure is not a trivial application of the hyperbolic regularization theory.     

Improvement of Efficient Multiparty Quantum Secret Sharing Based on Bell States and Continuous Variable Operations

Yuan et al. (Int. J. Theor. Phys. 51:3443, 2012) proposed a multiparty quantum secret sharing protocol using Bell states and continuous variable operations. Zhang and Qin (Int. J. Theor. Phys. 52:3953, 2013) showed that their protocol is not secure. In this paper, we will give an improvement of Yuan et al. protocol. Our improved protocol can stand against not only Zhang et al. attack strategies, but also the other ones efficiently.