Induced States from Coherent State via Photon-Addition Operations

Three classes of quantum states are induced from coherent state (CS) based on three operations associated with the photon creation operator. One class is the famous photon-added coherent state (PACS) introduced by Agarwal and Tara (Phys. Rev. A 43, 492–497, 1991). The other two classes are the orthogonal states of the CS (Here we abbreviate them as OCS1 and OCS2). Indeed, the OCS1 is just the displacement Fock state, and the OCS2 is constructed by orthogonalizer proposed by Kim group (Phys. Rev. Lett. 116, 110501, 2016). In contrast to the original CS, the three induced states can exhibit their respective nonclassical properties. We study and compare some properties for these four quantum states (CS, PACS, OCS1, OCS2). The studied properties include the mean number of photons, the sub-Poissonian character, the squeezing effect in the field quadrature, and the quasi-probability distributions including the Husimi Q function and the Wigner function. Besides, their fidelities between each two of them are also discussed.

     

Quantum Algorithms and Circuits for Linear Equations with Infinite or No Solutions

Linear equations with infinite or no solutions play key roles in machine learning and optimization. However, the existed quantum algorithms cannot be applied directly for these classes of equations. In this paper, based on the modification of algorithm (Wossnig et al., Phys. Rev. Lett. 120, 050502 2017), we describe a quantum algorithm to compute the minimal norm solution or minimum norm least-squares solution for equations with infinite or no solutions, respectively. It can be shown that the presented algorithm can achieve an exponential speedup over the best classical algorithm. Furthermore, the corresponding quantum circuit is designed on a quantum computer.

     

Second-order Nonlinearity Induced Unconventional Photon Blockade

In the recent publications (Gerace and Savona, Phys. Rev. A 89(R), 031803 2014; Zhou et al., Opt. Express 24, 17332 2016), the unconventional photon blockades are studied in a three-mode-second-order-nonlinearity system with linear coupling between the two low frequency modes. In this paper, the unconventional photon blockade is studied in a complementary case with linear coupling between the two high frequency modes. By solving the master equation in the steady-state limit and calculating the zerodelay- time second-order correlation function, a strong photon antibunching is found in this three-mode-second-order-nonlinearity system. The optimal antibunching conditions are derived and the numerical simulations confirm the optimal conditions. Our scheme can be used as a tunable single-photon source.

     

Damping in the Interaction of a Two-Photon Field and a Two-Level Atom Through Quantized Caldirola-Kanai Hamiltonian

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior.

     

Observable-Geometric Phases and Quantum Computation

This paper presents an alternative approach to geometric phases from the observable point of view. Precisely, we introduce the notion of observable-geometric phases, which is defined as a sequence of phases associated with a complete set of eigenstates of the observable. The observable-geometric phases are shown to be connected with the quantum geometry of the observable space evolving according to the Heisenberg equation. They are indeed distinct from Berry’s phase (Berry Proc. R. Soc. London Series A 392:45–57, 1984; Simon Phys. Rev. Lett. 51:2167–2170, 1983) as the system evolves adiabatically. It is shown that the observable-geometric phases can be used to realize a universal set of quantum gates in quantum computation. This scheme leads to the same gates as the Abelian geometric gates of Zhu and Wang (Phys. Rev. Lett. 89: 097902: 1–4, 2002, Phys. Rev. A 67: 022319: 1–9, 2003), but based on the quantum geometry of the observable space beyond the state space.

     

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.

     

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.

     

Trade-Off Relations of CHSH Violations Based on Norms of Bloch Vectors

By considering the norms of Bloch vectors, we present an improved trade-off relation of CHSH violations of pairwise qubits systems for any multi-qubit system, which leads to restrictions on the distribution of non-locality among the pairwise qubits systems. Detailed examples are computed to show that our result improves the trade-off relation in Qin et al. (Phys. Rev. A 92, 062339 2015). Our bounds are given by the norms of the Bloch vectors. Thus the bounds give experimentally feasible way in describing trade-off relation of maximal violations of CHSH inequalities for any multipartite-qubit state.

     

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).

     

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.

     

Using Inequalities as Tests for the Kochen-Specker Theorem for Multiparticle States

The Kochen-Specker theorem is investigated for n spin-1/2 systems by using an inequality proposed in Nagata (J. Math. Phys. 46, 102101, 2005) on the basis on binary logic. A measurement theory based on the truth values (binary logic), i.e., the truth T (1) for true and the falsity F (0) for false is used. The values of measurement outcome are either + 1 or 0 (in \(\hbar /2\) unit). The quantum predictions by n-multipartite states violate the inequality by an amount that grows exponentially with n. The measurement theory based on the binary logic provides an exponentially stronger refutation of the existence of hidden-variable when the number of parties of the state increases more. It turns out that the Kochen-Specker theorem becomes a quite strong theorem when the dimension of the multipartite state highly increases, regardless of entanglement properties.

     

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.

     

Geometry of Quantum Coherence for Two Qubit X States

The geometry of the structure of entanglement and discord for Bell-diagonal states is depicted by Lang and Caves (Phys. Rev. Lett. 105, 150501, 2010). In this paper, we investigate the geometry with respect to several distance-based quantifiers of coherence for Bell-diagonal states. We find that as both l₁ norm and relative entropy of coherence vary continuously from zero to one, their related geometric surfaces move from the region of separable states to the region of entangled states, a fact illustrating intuitively that quantum states with nonzero coherence can be used for entanglement creation. We find the necessary and sufficient conditions that quantum discord of Bell-diagonal states equals to its relative entropy of coherence, and depict the surfaces related to the equality. We give surfaces of relative entropy of coherence for X states. We show the surfaces of dynamics of relative entropy of coherence for Bell-diagonal states under local nondissipative channels and find that all coherences under local nondissipative channels decrease.

     

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.

     

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.

     

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.

     

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.

     

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.

     

Quantum Algorithms for the Resiliency of Vectorial Boolean Functions

Recently, Cui and Guo (Quantum Inform. Process. 18, 182, 2019) gave some quantum testing algorithms of multi-output Boolean functions, one of them was for resiliency testing. However, through the algorithm, we cannot get the probability distribution of a Boolean function. Improving the algorithm there, we present quantum algorithms for this problem. Under the condition of non-resiliency, we obtain not only the conclusion that the function F(x) is statistically dependent of which t variables but also the distance of the probability distribution from the uniform distribution.

     

Masking Quantum Information Encoded in Pure and Mixed States

Masking of quantum information means that information is hidden from a subsystem and spread over a composite system. Modi et al. proved in [Phys. Rev. Lett. 120, 230501 (2018)] that this is true for some restricted sets of nonorthogonal quantum states and it is not possible for arbitrary quantum states. In this paper, we discuss the problem of masking quantum information encoded in pure and mixed states, respectively. Based on an established necessary and sufficient condition for a set of pure states to be masked by an operator, we find that there exists a set of four states that can not be masked, which implies that to mask unknown pure states is impossible. We construct a masker S^? and obtain its maximal maskable set, leading to an affirmative answer to a conjecture proposed in Modi’s paper mentioned above. We also prove that an orthogonal (resp. linearly independent) subset of pure states can be masked by an isometry (resp. injection). Generalizing the case of pure states, we introduce the maskability of a set of mixed states and prove that a commuting subset of mixed states can be masked by an isometry S^◇ while it is impossible to mask all of mixed states by any operator. We also find the maximal maskable sets of mixed states of the isometries S^? and S^◇, respectively.