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<jats:p>Bohr’s principle of complementarity has a long history and it is an important topic in quantum theory, among which the famous example is the duality relation. The relation between visibility <jats:italic>C</jats:italic> and distinguishability <jats:italic>D</jats:italic>, <jats:inline-formula> <jats:tex-math> <?CDATA ${C}^{2}+{D}^{2}\le 1$?> </jats:tex-math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>+</mml:mo> <mml:msup> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msup> <mml:mo>≤</mml:mo> <mml:mn>1</mml:mn> </mml:math> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="cpb_29_5_050307_ieqn1.gif" xlink:type="simple" /> </jats:inline-formula>, has long been recognized as the only representative of the duality relation. However, recent researches have shown that this inequality is not good enough because it is not tight for multipath interferometers. Meanwhile, a tight bound for the multipath interferometer has been put forward. Here we design and experimentally implement a three-path interferometer coupling with path indicator states. The wave property of photons is characterized by <jats:italic>l</jats:italic> <jats:sub>1</jats:sub>-norm coherence measure, and the particle property is based on distinguishability of the indicator states. The new duality relation of the three-path interferometer is demonstrated in our experiment, which bounds the union of a right triangle and a part of elliptical area inside the quadrant of a unit circle. Data analysis confirms that the new bound is tight for photons in three-path interferometers.</jats:p>

<jats:p>The phase-modulated quadrature squeezing in the system that composed of two coupled cavities interacting with a two-level atom is investigated. The variances of the amplitude and phase quadrature of the output field are calculated. It turns out that the squeezing behaviors of the output field can be obviously modified due to the phase difference of the coupling strengths between the atom and the two cavities. The squeezing in one quadrature (<jats:italic>i.e.</jats:italic>, phase quadrature) can be transferred into another (<jats:italic>i.e.</jats:italic>, amplitude quadrature), or the quadrature squeezing located at the low-frequency region can be transferred into the high-frequency region by modulating the relative phase of the coupling strengths. Furthermore, the effects of the decay mismatch between the two cavities and the coupling mismatch between the atom and the cavities on the quadrature squeezing have been discussed. The results show that both the decay mismatch and the coupling mismatch play a positive role in generating better quadrature squeezing.</jats:p>

<jats:p>Continuous-variable quantum key distribution (CVQKD) can be integrated with thermal states for short-distance wireless quantum communications. However, its performance is usually restricted with the practical thermal noise. We propose a method to improve the security threshold of thermal-state (TS) CVQKD by employing a heralded hybrid linear amplifier (HLA) at the receiver. We find the effect of thermal noise on the HLA-involved scheme in near-and-mid infrared band or terahertz band for direct and reverse reconciliation. Numerical simulations show that the HLA-involved scheme can compensate for the detriment of thermal noise and hence increase the security threshold of TS-CVQKD. In near-and-mid infrared band, security threshold can be extended by 2.1 dB in channel loss for direct reconciliation and 1.6 dB for reverse reconciliation, whereas in terahertz band, security threshold can be slightly enhanced for the gain parameter less than 1 due to the rise in thermal noise.</jats:p>

<jats:p>Treating the cosmological constant as a dynamical variable, we investigate the thermodynamics and weak cosmic censorship conjecture (WCCC) of a charged AdS black hole (BH) in the Rastall gravity. We determine the energy momentum relation of charged fermion at the horizon of the BH using the Dirac equation. Based on this relation, it is shown that the first law of thermodynamics still holds as a fermion is absorbed by the BH. However, the entropy of both the extremal and near-extremal BH decreases in the irreversible process, which means that the second law of thermodynamics is violated. Furthermore, we verify the validity of the WCCC by the minimum values of the metric function <jats:italic>h</jats:italic>(<jats:italic>r</jats:italic>) at its final state. For the extremal charged AdS BH in the Rastall gravity, we find that the WCCC is always valid since the BH is extreme. While for the case of near-extremal BH, we find that the WCCC could be violable in the extended phase space (EPS), depending on the value of the parameters of the BH and their variations.</jats:p>

<jats:p>It is well known that the quantum fluctuation of entanglement (QFE) between Unruh–De Witt detector (modeled by a two-level atom) is always investigated in a relativistic setting. However, both of the Unruh radiation and quantum fluctuation effects play an important role in precise measurements of quantum entanglement. In this paper, we have quantitatively analyzed how the relativistic motion affects the QFE for two entangled Unruh–De Witt detectors, one of which is accelerated and interacting with the neighbor external scalar field. Our results show that the QFE, which initially increases by the Unruh thermal noise, will suddenly decay when the acceleration reaches to a considerably large value. Therefore, the relativistic effect will lead to non-negligible QFE effect. We also find that the initial QFE (without acceleration effect) reaches its minimum value at the maximally entangled state and the separable state. More importantly, our analysis demonstrates that although the QFE has a huge decay when the acceleration is greater than ∼0.96, the ratio of Δ<jats:italic>E</jats:italic>/<jats:italic>C</jats:italic> is still very large, due to the simultaneous decay of concurrence to a very low value. Finally, enlightened by the well-known equivalence principle, we discuss the possibility of applying the above findings to the dynamics of QFE under the influence of gravitation field.</jats:p>

<jats:p>Based on adiabatic approximation theory, in this paper we study the asymmetric stochastic resonance system with time-delayed feedback driven by non-Gaussian colored noise. The analytical expressions of the mean first-passage time (MFPT) and output signal-to-noise ratio (SNR) are derived by using a path integral approach, unified colored-noise approximation (UCNA), and small delay approximation. The effects of time-delayed feedback and non-Gaussian colored noise on the output SNR are analyzed. Moreover, three types of asymmetric potential function characteristics are thoroughly discussed. And they are well-depth asymmetry (DASR), well-width asymmetry (WASR), and synchronous action of well-depth and well-width asymmetry (DWASR), respectively. The conclusion of this paper is that the time-delayed feedback can suppress SR, however, the non-Gaussian noise deviation parameter has the opposite effect. Moreover, the correlation time plays a significant role in improving SNR, and the SNR of asymmetric stochastic resonance is higher than that of symmetric stochastic resonance. Our experiments demonstrate that the appropriate parameters can make the asymmetric stochastic resonance perform better to detect weak signals than the symmetric stochastic resonance, in which no matter whether these signals have low frequency or high frequency, accompanied by strong or weak noise.</jats:p>

<jats:p>We study the disorder-induced phase transition in two-dimensional non-Hermitian systems. First, the applicability of the noncommutative geometric method (NGM) in non-Hermitian systems is examined. By calculating the Chern number of two different systems (a square sample and a cylindrical one), the numerical results calculated by NGM are compared with the analytical one, and the phase boundary obtained by NGM is found to be in good agreement with the theoretical prediction. Then, we use NGM to investigate the evolution of the Chern number in non-Hermitian samples with the disorder effect. For the square sample, the stability of the non-Hermitian Chern insulator under disorder is confirmed. Significantly, we obtain a nontrivial topological phase induced by disorder. This phase is understood as the topological Anderson insulator in non-Hermitian systems. Finally, the disordered phase transition in the cylindrical sample is also investigated. The clean non-Hermitian cylindrical sample has three phases, and such samples show more phase transitions by varying the disorder strength: (1) the normal insulator phase to the gapless phase, (2) the normal insulator phase to the topological Anderson insulator phase, and (3) the gapless phase to the topological Anderson insulator phase.</jats:p>

<jats:p>Significant and persistent trajectory-to-trajectory variance are commonly observed in particle tracking experiments, which have become a major challenge for the experimental data analysis. In this theoretical paper we investigate the ergodicity recovery behavior, which helps clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media. The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis. The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations. The strange ergodicity recovery behavior is reported in the quenched disordered case, which arises from a localization mechanism. The first-passage approach is introduced to the ergodicity analysis for this case, of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.</jats:p>

<jats:p>This paper studies the dynamics of a new fractional-order discrete system based on the Caputo-like difference operator. This is the first study to explore a three-dimensional fractional-order discrete chaotic system without equilibrium. Through phase portrait, bifurcation diagrams, and largest Lyapunov exponents, it is shown that the proposed fractional-order discrete system exhibits a range of different dynamical behaviors. Also, different tests are used to confirm the existence of chaos, such as 0–1 test and <jats:italic>C</jats:italic> <jats:sub>0</jats:sub> complexity. In addition, the quantification of the level of chaos in the new fractional-order discrete system is measured by the approximate entropy technique. Furthermore, based on the fractional linearization method, a one-dimensional controller to stabilize the new system is proposed. Numerical results are presented to validate the findings of the paper.</jats:p>

<jats:p>We study two-lane totally asymmetric simple exclusion processes (TASEPs) with an intersection. Monte Carlo simulations show that only symmetric phases exist in the system. To verify the existence of asymmetric phases, we carry out a cluster mean-field analysis. Analytical results show that the densities of the two upstream segments of the intersection site are always equal, which indicates that the system is not in asymmetric phases. It demonstrates that the spontaneous symmetry breaking does not exist in the system. The density profiles and the boundaries of the symmetric phases are also investigated. We find that the cluster mean-field analysis shows better agreement with simulations than the simple mean-field analysis where the correlation of sites is ignored.</jats:p>