Bell type inequalities are used to test local realism against quantum theory. In this paper, we consider a two party system with two settings and two possible outcomes on each side, and derive equalities in local theories which are violated by quantum theory by a factor of 1.522 tolerating 0.586 fraction of white noise admixture which is twice that of the previous results.November 8, 2018 I. INTRODUCTIONThe idea of local realism opened its way into quantum theory by the work of Einstein, Podolsky and Rosen which is well known as EPR paradox [1], though it is not really a paradox, because it has been argued recently that the assumptions of EPR were wrong [2]. However it was left to John S. Bell who derived an inequality based on local theories and proved that it was violated by statistical predictions of quantum theory [3,4]. Since then many attempts have been made to derive Bell type inequalities which are violated by a stronger factor, so that it can be tested in the real experiments in which errors are inevitable. Among these are Clauser, Horne, Shimony and Holt inequality, the so called CHSH inequality [5,6].Nowadays, with the growing power of computers, the numerical methods have attracted attentions for constructing these inequalities as much as possible [7-9] though analytical approaches are in progress too [10]; with the hope that some of which could be violated by a stronger factor.In this paper we first introduce a simple but general method for constructing Bell expressions which can be applied to two party experiments each measuring two observables with different outputs. Generalization to more parties and/or more observables is straightforward. Then in a special case of a two party system with two settings and two possible outcomes on each side, we use these expressions and show that according to local theories there exist equalities which are violated by quantum theory by a stronger factor than Bell type inequalities. Meanwhile we derive an inequality in this case which is violated by a factor of 1.621 tolerating 0.293 fraction of white noise admixture. Although in this case the tolerance is the same as those derived previously in the literature the range of violation is greater. II. DERIVATION OF BELL TYPE EXPRESSIONSLet's consider a two party system with no known interaction between its parts. Suppose the left party, say A performs two possible measurements a with outcomes i ∈ {0, · · · , m − 1} and a ′ with outcomes i ′ ∈ {0, · · · , m ′ − 1}. Similarly the right party, say B, performs two possible measurements b with outcomes j ∈ {0, · · · , n − 1} and b ′ with outcomes j ′ ∈ {0, · · · , n ′ − 1}. For simplicity, from now on we use unprimed/primed variables and indexes for the first/second measurement for each party whenever applicable and label such a system as mn ⊗ m ′ n ′ . As a consequence of locality, for measurements which are not simultaneous, there exists a probability q ii ′ jj ′ aa ′ bb ′ defined as the probability that measurements of a results i, a ′ results i ′ , b results j and b ′ r...

In the present work, initially a mixed-three-spin (1/2,1,1/2) cell of a mixed-N -spin chain with Ising-XY model is introduced, for which pair spins (1,1/2) have Ising-type interaction and pair spins (1/2,1/2) have both XY-type and Dzyaloshinskii-Moriya(DM) interactions together. An external homogeneous magnetic field B is considered for the system in thermal equilibrium. Integer-spins have a single-ion anisotropy property with coefficient ζ. Then, we investigate the quantum entanglement between half-spins (1/2,1/2), by means of the concurrence. Classical correlation(CC) for this pair of spins is investigated as well as the concurrence and some interesting the temperature, the magnetic field and the DM interaction properties are expressed. Moreover, single-ion anisotropy effects on the correlation between half-spins is verified. According to the verifications based on the communication channels category by D. Rossini, V. Giovannetti and R. Fazio 63 , we theoretically consider such tripartite spin model as an ideal quantum channel, then calculate its information transmission rate and express some differences in behaviour between this suggested model and introduced simple models in the previous works(chains without spin integer and DM interaction) from information transferring protocol point of view. March 15, 2018 0:19 WSPC/INSTRUCTION FILE ws-ijmpb 2 H. ARIAN ZAD AND H. MOVAHHEDIAN the concurrence 16,17,18 , negativity 22,23,24 , quantum discord 25,26,27,28,29,30 , quantum disorder 31 , correlation functions 3,28 and von Neumann entropies 11,32,33,34 . Somewhere, spin models have been studied with the DM interaction 4,35,36,37,38,39 , that such interaction arises naturally in the perturbation theory due to the spinorbit coupling in magnetic systems.Straightforward researches have been caried out to investigate interaction between the next-nearest-neighbour sites of a Heisenberg spin model in Refs. 40,41,42,43 . Such interaction may has an essential role to generate a Heisenberg model with diamond chain topology by organizing mixture of particles that have different spins. Motivated by this issue, several studies have been done on the mixture of different spins with various models and many interesting results have been reported 44,45,46 . Diamond chains as attractive structures among these spin models were exactly investigated from quantum entanglement, quantum correlation, phase transitions etc. view points 47,48,49,50,51,52 .The motivation for the study of a diamond chain with the Ising-XXZ model is that it can describes real materials such as natural mineral azurite Cu 3 (CO 3 ) 2 (OH) 2 , where according to experimental results, theoretical calculations are interestingly reasonable in this case 53 (another polymeric coordination compounds such as M 3 (OH) 2 with spin-1 Heisenberg diamond chain were investigated in the literature 54 ). Another quantum spin models consisting of diamond-shaped cells can be theoretically suggested and solved. In this regard, we here are interested to introduce a few body diamond c...

We have recently shown that for the special case of a bipartite system with binary inputs and outputs there exist equalities in local theories which are violated by quantum theory. The amount of white noise tolerated by these equalities are twice that of inequalities. In this paper we will first introduce an inequality in bipartite qutrits systems which, if non-maximally entangled state is used instead of maximally entangled state, is violated more strongly by quantum theory. Hence reproducing the results obtained in the literature. We will then prove that our equalities in this case are violated by quantum theory too, and they tolerate much more white noise than inequalities.

We initially introduce one-dimensional mixed-five-spin chain with Ising-XY model which includes mixture of spins-1/2 and spins-1. Here, it is considered that nearest spins (1, 1/2) have Ising-type interaction and nearest spins (1/2, 1/2) have both XY -type and Dzyaloshinskii-Moriya (DM) interactions together. Nearest spins (1, 1) have XX Heisenberg interaction. This system is in the vicinity of an external homogeneous magnetic field B in thermal equilibrium state. We promote the quantum information transmitting protocol verified for a normal spin chain with simple model (refer to Rossini D, Giovannetti V and Fazio R 2007 Int. J. Quantum Infor. 5 439) (widely in reference: Giovannetti V and Fazio R 2005 Phys. Rev. A 71 032314) by means of considering the suggested mixed-five-spin chain as a quantum communication channel for transmitting both qubits and qutrits ideally. Hence, we investigate some useful quantities such as quantum capacity and quantum information transmission rate for the system. Finally, we conclude that, when the DM interaction between spins (1/2, 1/2) increases the system is a more ideal channel for transmitting information.

Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant [Formula: see text] and spins (1/2,1/2) have coupling constant [Formula: see text]. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants [Formula: see text] and [Formula: see text]. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.