Measurement Theory Based on the Truth Values Violates Local Realism

We investigate the violation factor of the Bell-Mermin inequality. Until now, we use an assumption that the results of measurement are ±1. In this case, the maximum violation factor is 2^(n?1)/2. The quantum predictions by n-partite Greenberger-Horne-Zeilinger (GHZ) state violate the Bell-Mermin inequality by an amount that grows exponentially with n. Recently, a new measurement theory based on the truth values is proposed (Nagata and Nakamura, Int. J. Theor. Phys. 55:3616, 2016). The values of measurement outcome are either +1 or 0. Here we use the new measurement theory. We consider multipartite GHZ state. It turns out that the Bell-Mermin inequality is violated by the amount of 2^(n?1)/2. The measurement theory based on the truth values provides the maximum violation of the Bell-Mermin inequality.     

Tighter Weighted Polygamy Inequalities of Multipartite Entanglement in Arbitrary-Dimensional Quantum Systems

We investigate polygamy relations of multipartite entanglement in arbitrary-dimensional quantum systems. By improving an inequality and using the βth (0 ≤ β ≤ 1) power of entanglement of assistance, we provide a new class of weighted polygamy inequalities of multipartite entanglement in arbitrary-dimensional quantum systems. We show that these new polygamy relations are tighter than the ones given in Kim (Phys. Rev. A 97, 042332 2018).

     

Central Limit Theorem for the Free Energy of the Random Field Ising Model

A central limit theorem is proved for the free energy of the random field Ising model with all plus or all minus boundary condition, at any temperature (including zero temperature) and any dimension. This solves a problem posed by Wehr and Aizenman (J Stat Phys 60:287–306, 1990). The proof uses a variant of Stein’s method.

     

Incompatibility of New Symmetry Reductions in U(1) × U(2) × U(3) Gauge Group with Higgs Mechanism

Noncommutative (NC) space-time leads to some strong constraints on the possible choices of gauge groups and allowed representations of matter and gauge fields. The standard model based on U(3) × U(2) × U(1) can be transcribed to NC space-time consistently with these constraints (Chaichian et al., Eur. Phys. J. C29:413, 1). In fact, through two new symmetry reduction mechanisms, this gauge group is reduced to the usual standard model one. In this paper, we show that, on the contrary to the usual standard model, the Goldestone boson equivalence theorem is violated due to the incompatibility of the new symmetry reduction mechanisms with the electroweak Higgs mechanism.

     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

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.     

Thermal Entanglement Properties in Two Qubits One-Axis Spin Squeezing Model with an External Magnetic Field

In a recent article in this journal Guo-Hui (Int. J. Theor. Phys. 56, 600, 2017) has investigated the quantum correlation properties in the two qubits one-axis spin squeezing model with an external magnetic field by means of concurrence (C) and quantum discord (QD) criteria. We are to reveal numerically and analytically that in the limiting case T→ 0 (ground state) the sudden disappearance phenomenon (SDP) does not occur in the behavior of C and the values obtained for C are incorrect.

     

Uncertainty Inequality for the Entanglement of Both Two-rebits and Two-qubits States

We assume that both the concurrence C_r of a two-rebits state and the concurrence C_q of the usual two-qubits states are represented by hermitian operators (observables). We calculate the respective uncertainty ΔC_r and the uncertainty ΔC_q measured both as the standard deviation . We make the strictly mathematical assumption that there exists a canonical conjugate variable (called ξ) to the concurrence (C) such that both quantities satisfy a Robertson’s [1] uncertainty inequality of the form \( {\left(\Delta A\right)}^2{\left(\Delta B\right)}^2>{\left|\frac{1}{2}\left\langle \right[A,B\left]\right\rangle \right|}^2 \). From such inequality we impose bounds for both uncertainties Δξ_r and Δξ_q.

     

Superadiabatic Shortcuts for Fast Generating Two-Atom Four-Dimensional Entanglement

We propose a scheme for rapidly generating two-atom four-dimensional entanglement based on superadiabatic shortcuts. In the scheme, the counterdiabatic Hamiltonian has the same form as that of the effective Hamiltonian, and the scheme avoids the disadvantage of the invariants-based scheme Dong et al. (Int. J. Theor. Phys. 57, 3149–3162, 2018), so the scheme is more feasible in experiment. In addition, numerical simulation results show that the scheme is robust against decoherence and variations in various parameters, and the two atoms four-dimensional entanglement can be generated with high fidelity.

     

Cryptanalysis and Improvement of Ye et al’s Quantum Private Comparison Protocol

Recently, Ye et al. (Int. J. Theor. Phys. 56, 1517–1529, 2017) proposed a quantum private comparison (QPC) protocol based on five-qubit entanglement state. Two parties can verify that their secret information is equal or not with the help of the semi-honest third party (TP). However, in this paper we will point out the Ye et al.’s initial protocol is not safe under a special participant attack. That is a malicious participant can get the other party’s secret input information illegally under the forgery attack. Furthermore, we give two possible improvement protocols, which can perform this protocol secure against this kind of attack.

     

Cryptanalysis and Improvement of a Multiparty Quantum Direct Secret Sharing of Classical Messages with Bell States and Bell Measurements

Recently, a multiparty quantum direct secret sharing protocol with Bell states was presented (Song et al., Int. J Theor. Phys. 57, 1559, 2018). In this protocol, the secret message of the dealer is directly encoding into the transmitted particles. All agents obtain their pieces of secret by making Bell state measurement on their receiving particles, then cooperate to recover the dealer’s secret. However, as we show, this protocol is insecure, because an outside attacker or two special dishonest agents can eavesdrop the secret fully. Furthermore, an improved version of this protocol is proposed, which can stand against the presented attacks.

     

Multipartite Generalized Bell Inequality with an Arbitrary Number of Settings

We derive a generalized Bell inequality for N qubits which involves an arbitrary number of settings for each of the local measuring apparatuses. The inequality forms a necessary condition for the existence of a local realistic model for the values of a correlation function, given in a n-setting Bell experiment. We show that a local realistic model for the values of a correlation function, given in a two-setting Bell experiment, cannot construct a local realistic model for the values of a correlation function, given in an arbitrary number of n-setting Bell experiment, even though there exist two-setting models for the n measurement directions chosen in the given n-setting experiment. Therefore, the property of two-setting model is different from the property of n-setting model. We discuss classification of local realistic theories in further detail more than the result presented in (J. Phys. A: Math. Theor. 41:155308, 2008). The generalized Bell inequality covers the previous results correctly.     

Kochen-Specker Theorem in Krein Space

The well known Kochen-Specker’s theorem (Kochen and Specker J. Math. Mech. 17:59–87, 1967) is devoted to the problem of hidden variables in quantum mechanics. In the paper we present a geometric proof for an indefinite analogy of Kochen-Specker’s theorem. On the real three-dimensional Krein space there exists unique two-valued probability measure.     

Improvement of Gao et al.’s semi-quantum secret sharing protocol

Recently, Yin and Fu (Int. J. Theor. Phys. 55(9), 4027–4035 (2016)) pointed out that Xie et al.’s semi-quantum secret sharing (SQSS) protocol (Int. J. Theor. Phys. 54(10), 3819–3824 (2015)) suffers from the intercept-resend attack from a dishonest party, and suggested an improved protocol accordingly. Later, Gao et al. (Int. J. Theor. Phys. 56(8), 2512–2520 (2017)) pointed out that Yin and Fu’s analysis on the intercept-resend attack from a dishonest party is incorrect. Moreover, they also pointed out that Yin and Fu’s improved protocol does not satisfy the condition of semi-quantum, and proposed an improved protocol. This paper is devoted to putting forward an improved version for Gao et al.’s protocol. Compared with Gao et al.’s protocol, the improved version has higher quantum efficiency and less classical communication cost.

     

Quantum contextuality for rational vectors

The Kochen-Specker theorem states that noncontextual hidden variable models are inconsistent with the quantum predictions for every yes-no question on a qutrit, corresponding to every projector in three dimensions. It has been suggested [D.A. Meyer, Phys. Rev. Lett. 83 (1999) 3751] that the inconsistency would disappear when restricting to projectors on unit vectors with rational components; that noncontextual hidden variables could reproduce the quantum predictions for rational vectors. Here we show that a qutrit state with rational components violates an inequality valid for noncontextual hidden-variable models [A.A. Klyachko et al., Phys. Rev. Lett. 101 (2008) 020403] using rational projectors. This shows that the inconsistency remains even when using only rational vectors.     

Homogenization for a Class of Generalized Langevin Equations with an Application to Thermophoresis

We study a class of systems whose dynamics are described by generalized Langevin equations with state-dependent coefficients. We find that in the limit, in which all the characteristic time scales vanish at the same rate, the position variable of the system converges to a homogenized process, described by an equation containing additional drift terms induced by the noise. The convergence results are obtained using the main result in Hottovy et al. (Commun Math Phys 336(3):1259–1283, 2015), whose version is proven here under a weaker spectral assumption on the damping matrix. We apply our results to study thermophoresis of a Brownian particle in a non-equilibrium heat bath.

     

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.     

Kochen-Specker theorem for finite precision spin-one measurements

Unsharp spin-one observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth values in a noncontextual way.     

Mermin's n-particle Bell inequality and operators' noncommutativity

The relationship between the noncommutativity of operators and the violation of the Bell inequality is exhibited in the light of the n-particle Bell-type inequality discovered by Mermin (Phys. Rev. Lett. 65 (1990) 1838). It is shown, in particular, that the maximal amount of violation of Mermin's inequality predicted by quantum mechanics decreases exponentially by a factor of 2^−m/2 whenever any m among the n single-particle commutators happen to vanish.     

Towards a Resolution of Dilemma: Nonlocality or Nonobjectivity?

This paper discusses a possible resolution of the nonobjectivity-nonlocality dilemma in quantum mechanics in the light of experimental tests of the Bell inequality for two entangled photons and a Bell-like inequality for a single neutron. My conclusion is that these experiments show that quantum mechanics is nonobjective: that is, the values of physical observables cannot be assigned to a system before measurement. Bell’s assumption of nonlocality has to be rejected as having no direct experimental confirmation, at least thus far. I also consider the relationships between nonobjectivity and contextuality. Specifically, I analyze the impact of the Kochen-Specker theorem on the problem of contextuality of quantum observables. I argue that, just as von Neumann’s “no-go” theorem, the Kochen-Specker theorem is based on assumptions that do not correspond to the real physical situation. Finally, I present a theory of measurement based on a classical, purely wave model (pre-quantum classical statistical field theory), a model that reproduces quantum probabilities. In this model continuous fields are transformed into discrete clicks of detectors. While this model is classical, it is nonobjective. In this case, nonobjectivity is the result of the dependence of experimental outcomes on the context of measurement, in accordance with Bohr’s view.