Bell Theorem without Inequality for Some Generalized GHZ and W States

Bell＇s theorem without inequalities is applied for some general Greenberger-Horn-Zeilinger （GHZ） states and W states and a wide range of such states can exhibit all-versus-nothing conflict between local realism and quantum theory. The case of standard GHZ state is contained in our proposal. For some generalized GHZ states more intensive violation on local realism is manifested.     

Qubit portrait of qudit states and Bell inequalities

A linear map of qudit tomogram onto qubit tomogram (qubit portrait) is proposed as a characteristics of the qudit state. In view of the qubit-portrait method, the Bell inequalities for two qubits and two qutrits are discussed within the framework of the probability-representation of quantum mechanics. A semigroup of stochastic matrices is associated with tomographic-probability distributions of qubit and qutrit states. Bell-like inequalities are studied using the semigroup of stochastic matrices. The qudit-qubit map of tomographic probability distributions is discussed as an ansatz to provide a necessary condition for the separability of quantum states.     

One-Step Generation of Multi-Qubit GHZ and W States in Superconducting Transmon Qubit System

We propose a one-step method to prepare multi-qubit GHZ and W states with transmon qubits capacitively coupled to a superconducting transmission line resonator(TLR).Compared with the scheme firstly introduced by Wang et al.[Phys.Rev.B 81(2010) 104524],our schemes have longer dephasing time and much shorter operation time because the transmon qubits we used are not only more robust to the decoherence and the unavoidable parameter variations,but also have much stronger coupling constant with TLR.Based on the favourable properties of transmons and TLR,our method is more feasible in experiment.     

A Complete Set of Invariant for Bell State and GHZ State

Fano statistical tensor parameters is a well known aspect for expression the density matrix of spin-j states. Enumeration SU(2) invariants for the most general symmetric states were constructed with making use of Multiaxial representation of spin- j density matrix into j(2j+1) axes and 2j real scalars (Sirsi and Adiga J. Russ. Laser Res. 32, 495, 2011). In this paper we will enumerate a complete set of invariants for Bell state and three qubit GHZ state using Multiaxial representation of the density matrix.     

Spin Squeezing of Superposition of Biaxial State and Two Qubit Bell State

In this study we investigate the spin squeezing in superposition of a Biaxial state (Mallesh et al. in J. Phys. A, Math. Gen. 33:779–789, 2000 and Sirsi in Theoretical studies on spin distributions in external electric and magnetic fields, 1995) and Bell state. Numerical and analytical solutions for the length of mean spin, mean spin direction and spin squeezing are given. It is shown that both the mean spin direction and spin squeezing parameter are determined by the coefficients of superposition and the relative phase.     

Correlations and efficiency: Testing the Bell inequalities

This paper examines the efficiency problem involved in experimental tests of so-called local hidden variables. It separates the phenomenological locality at issue in the Bell case from Einstein's different conception of locality, and shows how phenomenological locality also differs from the factorizability needed to derive the Bell inequalities in the stochastic case. It then pursues the question of whether factorizable, local models (or, equivalently, deterministic ones) exist for the experiments designed to test the Bell inequalities, thus rendering the experimental argument against them incomplete. This leads to an investigation of the so-called prism models and to new inequalities for a significant class of such models, inequalities that are testable even at the low efficiencies of the photon correlation experiments.Dedicated to David Bohm on the occasion of his 70th birthday, December 20, 1987.     

Generalized Qubit Portrait of the Qutrit-State Density Matrix

We obtain new inequalities for tomographic probability distributions and density matrices of qutrit states by generalization of the qubit-portrait method. We propose an approach based on the quditportrait method of obtaining new entropic inequalities. Our approach can be applied to the case of arbitrary nonnegative hermitian matrices, including the density matrices of multipartite qudit states.     

Bell Inequalities as Constraints on Unmeasurable Correlations

The interpretation of the violation of Bell-Clauser-Horne inequalities is revisited, in relation with the notion of extension of QM predictions to unmeasurable correlations. Such extensions are compatible with QM predictions in many cases, in particular for observables with compatibility relations described by tree graphs. This implies classical representability of any set of correlations 〈A _i 〉, 〈B〉, 〈A _i B〉, and the equivalence of the Bell-Clauser-Horne inequalities to a non void intersection between the ranges of values for the unmeasurable correlation 〈A ₁ A ₂〉 associated to different choices for B. The same analysis applies to the Hardy model and to the “perfect correlations” discussed by Greenberger, Horne, Shimony and Zeilinger. In all the cases, the dependence of an unmeasurable correlation on a set of variables allowing for a classical representation is the only basis for arguments about violations of locality and causality.     

Effects of Phase Damping on Controlled Teleportation of a Qubit by a GHZ State

We investigate controlled teleportation ofa qubit via a GHZ state with the influence of phase damping in the Bloch sphere representation. We use the average trace distance to describe how close the output state is to the input state to be teleported. Our results show that the average trace distance is a function of decoherence rates and angles of the analyzer performed by the controller in the single-particle projective measurement. Moreover, for a fixed value of the decoherence rate, one can adjust the analyzer angle to achieve the optimal average trace distance.     

Joint Remote State Preparation of a Single-Atom Qubit State via a GHZ Entangled State

We proposed a physical protocol for the joint remote preparation of a single-atom qubit state via a three-atom entangled GHZ-type state previously shared by the two senders and one receiver. Only rotation operations of single-atom, which can be achieved though the resonant interaction between the two-level atom and the classical field, are required in the scheme. It shows that the splitting way of the classical information of the secret qubit not only determines the success of reconstruction of the secret qubit, but also influences the operations of the senders.     

Investigating Three Qubit Entanglement with Local Measurements

In this paper we describe how three qubit entanglement can be analyzed with local measurements. For this purpose we decompose entanglement witnesses into operators that can be measured locally. Our decompositions are optimized in the number of measurement settings needed for the measurement of one witness. Our method allows to detect true threepartite entanglement and especially GHZ-states with only four measurement settings.     

Frame Independent Nonlocality for Three Qubit State

Bell’s inequality is investigated for the three qubit GHZ state in relativistic regime. Two different relativistic spin operator are considered. One of them is defined by Lee and Ee (New J. Phys. 6:67, 2004). and the other which is the Pauli-Lubanski pseudovector used by Kim and Son (Phys. Rev. A 71:014102, 2005). It is shown that for both spin operator Bell’s inequality is still maximally violated in a Lorentz-boosted frame.     

Probing Bell Diagonal State without Disturbing Its Correlations

In this paper, we propose a very simple scheme to probe the quantum and classical correlation including quantum entanglement of Bell diagonal state. In the probing process, the correlation of Bell diagonal state, even the state itself, is not disturbed, which means a non-destructive probing. In addition, our scheme can be performed even though the two qubits of the Bell diagonal state are separate in space.     

Probing Bell Diagonal State without Disturbing Its Correlations

In this paper, we propose a very simple scheme to probe the quantum and classical correlation including quantum entanglement of Bell diagonal state. In the probing process, the correlation of Bell diagonal state, even the state itself, is not disturbed, which means a non-destructive probing. In addition, our scheme can be performed even though the two qubits of the Bell diagonal state are separate in space.     

Correlations for a new Bell’s inequality experiment

Proofs of Bell’s theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell’s inequality holds identically for cross correlations of three or four lists of ±l’s, independently of statistical assumptions. When data consistent with its derivation are analyzed without imposition of the stationarity assumption, the resulting correlations satisfy the Bell inequality.     

Tripartite Entanglement Measures of Generalized GHZ State in Uniform Acceleration

Using the single-mode approximation,we study entanglement measures including two independent quantities;i.e.,negativity and von Neumann entropy for a tripartite generalized Greenberger-Horne-Zeilinger(GHZ)state in noninertial frames.Based on the calculated negativity,we study the whole entanglement measures named as the algebraic average π3-tangle and geometric average Π3-tangle.We find that the difference between them is very small or disappears with the increase of the number of accelerated qubits.The entanglement properties are discussed from one accelerated observer and others remaining stationary to all three accelerated observers.The results show that there will always exist entanglement,even if acceleration r arrives to infinity.The degree of entanglement for all 1-1 tangles are alwa.ys equal to zero,but 1-2 tangles always decrease with the acceleration parameter r.We notice that the von Neumann entropy increases with the number of the accelerated observers and Sκ_Ιζ_Ι(κ,ζ∈(A,B,C)) first increases and then decreases with the acceleration parameter r.This implies that the subsystem ρκΙζΙ is first more disorder and then the disorder will be reduced as the acceleration parameter r increases.Moreover,it is found that the von Neumann entropies SABCI,SABICI and SAIBICI always decrease with the controllable angle θ,while the entropies of the bipartite subsystems S2-2_(non)(two accelerated qubits),S2-1_(non)(one accelerated qubit) and S2-0_(non)(without accelerated qubit) first increase with the angle θ and then decrease with it.     

Analysis of Assumptions in BIG Bell Test Experiments

Recently, a group of experiments tested local realism with random choices prepared by humans. These various tests were subject to additional assumptions, which lead to loopholes in the interpretations of almost all of the experiments. Among these assumptions are fair sampling, no signaling, and faithful reproduction of a Bell-type quantum model. The data from 9 of 13 experiments were examined and occurring anomalies were analyzed in view of the above assumptions. It is concluded that further tests of local realism need better setup calibration to avoid apparent signaling or necessity of the complicated underlying quantum model.     

Binary Bell Polynomials Approach to Generalized Nizhnik-Novikov-Veselov Equation

The elementary and systematic binary Bell polynomials method is applied to the generalized Nizhnik-Novikov-Veselov (GNNV) equation. The bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite conservation laws of the GNNV equation are obtained directly, without too much trick like Hirota's bilinear method.