Robustness of interferometric complementarity under decoherence

Interferometric complementarity is known to be one of the most nonclassical manifestations of the quantum formalism. It is commonly known as wave-particle duality and has been studied presently from the perspective of quantum information theory where wave and particle nature of a quantum system, called quanton, are characterised by coherence and path distinguishability respectively. We here consider the effect of noisy detectors on the complementarity relation. We report that by suitably choosing the initial quanton and the detector states along with the proper interactions between the quanton and the detectors, one can reduce the influence of noisy environment on complementarity, thereby pushing it towards saturation. To demonstrate this, three kinds of noise on detectors and their roles on the saturation of the complementarity relation are extensively studied. We also observe that for fixed values of parameters involved in the process, asymmetric quanton state posses low value of coherence while it can have a higher amount of distinguishability, and hence it has the potential to enhance the duality relation.     

相干与信息守恒及其在Mach-Zehnder干涉中的应用

自量子力学诞生以来,相干性和互补性一直是被广泛而深入研究的两个重要课题.随着量子信息近年来的发展,人们引入了若干度量来定量地刻画相干性和互补性.本文建立两个信息守恒关系式,分别基于"Bures距离-保真度"和"对称-非对称",并且利用它们来刻画相干性和互补性.具体来说,首先从信息守恒的观点解释Bures距离和保真度的互补关系,并由此自然推导出Mach-Zehnder干涉仪中的Englert"干涉-路径"互补关系.其次在量子态和信道相互作用的一般框架中讨论"对称-非对称"信息守恒关系,并揭示其与Bohr互补性和量子相干性的内在联系.最后,在Mach-Zehnder干涉仪中探讨相干、退相干及互补性,刻画两个信息守恒关系之间的密切联系.     

Complementarity Relations for Multi-Qubit Systems

No Heading We derive two complementarity relations that constrain the individual and bipartite properties that may simultaneously exist in a multi-qubit system. The first expression, valid for an arbitrary pure state of n qubits, demonstrates that the degree to which single particle properties are possessed by an individual member of the system is limited by the bipartite entanglement that exists between that qubit and the remainder of the system. This result implies that the phenomenon of entanglement sharing is one specific consequence of complementarity. The second expression, which holds for an arbitrary state of two qubits, pure or mixed, quantifies a tradeoff between the amounts of entanglement, separable uncertainty, and single particle properties that are encoded in the quantum state. The separable uncertainty is a natural measure of our ignorance about the properties possessed by individual subsystems, and may be used to completely characterize the relationship between entanglement and mixedness in two-qubit systems. The two-qubit complementarity relation yields a useful geometric picture in which the root mean square values of local subsystem properties act like coordinates in the space of density matrices, and suggests possible insights into the problem of interpreting quantum mechanics.     

Simultaneous Measurement of Fringe Visibility and Path Predictability of Wave-Particle Duality

An experimental scheme to simultaneously obtain the information of fringe visibility and path predictability is designed. In a modified Young's double-slit experiment, two density filters rotating at different frequencies are placed before the two pineholes to encode path information. The spatial and temporal distributions of the output provide us with the wave and particle information of the single photons, respectively. The simultaneous measurement of the wave and particle information inevitably disturbs the system and thus causes some loss of the duality information, which is equal to the mixedness of the photonic state behind the density filters.     

Minimum-error state discrimination and quantitative wave particle duality

We establish the link between minimum-error discrimination of two pure states and wave particle duality in two-path interferometers. In particular, the upper bound of the probability of success discrimination is derived directly from the corresponding duality relation. It is already known that quantum state discrimination can produce wave particle duality relations, here we show the converse is also true: Wave particle duality can be used to obtain information about state discrimination.     

Wave-Particle Complementarity and Reciprocity of Gauss Sums on Talbot Effects

Berry and Klein [J. Mod. Opt. 43, 2139-2164 (1997)] showed that the Talbot effects in classical optics are naturally expressed by Gauss sums in number theory. Their result was obtained by a computation of Helmholtz equation. In this article, we calculate the effects using Fresnel integral and show that the result is also represented by Gauss sums. However function forms of these two computational results are apparently different. We show that the reciprocity law of Gauss sums connects these results and both completely agree with. The Helmholtz equation can be regarded as an equation based upon wavy nature in optics whereas the Fresnel integral is defined by a sum over the paths based upon a particle picture in optics. Thus the agreement of these two computational results could be interpreted in terms of the concept of the wave-particle complementarity, though the concept is for quantum mechanical phenomenon. This interpretation leads us to a relation between the reciprocity of Gauss sums in number theory and the wave-particle complementarity in wave physics. We discuss it in detail.     

Extending Dualities to Trialities Deepens the Foundations of Dynamics

Dualities are often supposed to be foundational, but they may come into conflict with a strong form of background independence, which is the principle that the dynamical equations of a theory not depend on arbitrary, fixed, non-dynamical structures. This is because a hidden fixed structures is needed to define the duality transformation. Examples include a fixed, absolute notion of time, a fixed non-dynamical background geometry, or the metric of Hilbert space. We show that this conflict can be eliminated by extending a duality to a triality. This renders that fixed structure dynamical, while unifying it with the dual variables. To illustrate this, we study matrix models with a cubic action, which have a natural triality symmetry. We show how breaking this triality symmetry by imposing different compactifications, which are expansions around fixed classical solutions, yields particle mechanics, string theory and Chern-Simons theory. These result from compactifying, respectively, one, two and three dimensions. This may explain the origin of Born’s duality between position and momenta operators in quantum theory, as well as some of the the dualities of string theory.     

Features and states of microscopic particles in nonlinear quantum-mechanics systems

In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schr?dinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc.      

Features and states of microscopic particles in nonlinear quantum-mechanics systems

In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy,momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc.     

Wave-particle duality of single-photon states

We review the present status of wave-particle duality of single-photon states in the context of some recent experiments. In particular, Bohr's complementarity principle is critically reexamined. It is explained in detail how this principle is confronted in these experiments and how a contradiction with the notion of mutual exclusiveness of classical wave and particle pictures emerges.     

Quantitative complementarity relations in bipartite systems: Entanglement as a physical reality

We introduce a complete set of complementary quantities in bipartite, two-dimensional systems. Complementarity then relates the quantitative entanglement measure concurrence which is a bipartite property to the single-particle quantum properties predictability and visibility, for the most general quantum state of two qubits. Consequently, from an interferometric point of view, the usual wave-particle duality relation must be extended to a “triality” relation containing, in addition, the quantitative entanglement measure concurrence, which has no classical counterpart and manifests a genuine quantum aspect of bipartite systems. A generalized duality relation, that also governs possible violations of the Bell’s inequality, arises between single- and bipartite properties.     

Fringe visibility and correlation in Mach-Zehnder interferometer with an asymmetric beam splitter

We study the wave-particle duality in a general Mach-Zehnder interferometer with an asymmetric beam splitter from the viewpoint of quantum information theory. The correlations (including the classical correlation and the quantum correlation) between the particle and the which-path detector are derived when they are in pure state or mixed state at the output of Mach-Zehnder interferometer. It is found that the fringe visibility and the correlations are effected by the asymmetric beam splitter and the input state of the particle. The complementary relations between the fringe visibility and the correlations are also presented.     

Development of ultrahigh-precision coherent control and its applications

Coherent control is based on optical manipulation of the amplitudes and phases of wave functions. It is expected to be a key technique to develop novel quantum technologies such as bond-selective chemistry and quantum computing, and to better understand the quantum worldview founded on wave-particle duality. We have developed high-precision coherent control by imprinting optical amplitudes and phases of ultrashort laser pulses on the quantum amplitudes and phases of molecular wave functions. The history and perspective of coherent control and our recent achievements are described.     

Dynamical Measurement's Uncertainty in the Curved Space‐Time

The dynamical characteristics of measurement's uncertainty are investigated under two modes of Dirac field in the Garfinkle–Horowitz–Strominger dilation space‐time. It shows that the Hawking effect induced by the thermal field would result in an expansion of the entropic uncertainty with increasing dilation‐parameter value, as the systemic quantum coherence reduces, reflecting that the Hawking effect could undermine the systemic coherence. Meanwhile, the intrinsic relationship between the uncertainty and quantum coherence is obtained, and it is revealed that the uncertainty's bound is anti‐correlated with the system's quantum coherence. Furthermore, it is illustrated that the systemic mixedness is correlated with the uncertainty to a large extent. Via the information flow theory, various correlations including quantum and classical aspects, which can be used to form a physical explanation on the relationship between the uncertainty and quantum coherence, are also analyzed. Additionally, this investigation is extended to the case of multi‐component measurement, and the applications of the entropic uncertainty relation are illustrated on entanglement criterion and quantum channel capacity. Lastly, it is declared that the measurement uncertainty can be quantitatively suppressed through optimal quantum weak measurement. These investigations might pave an avenue to understand the measurement's uncertainty in the curved space‐time.     

The two-prism experiment and wave-particle duality of light

A number of papers on wave-particle duality has appeared since the two-prism experiment was performed by Mizobuchi and Ohtake, based on a suggestion by Ghose, Home, and Agarwal. Against this backdrop, the present paper provides further clarification of the key issues involved in the analysis of the two-prism experiment. In the process, we present an overview of wave-particle duality vis-a vis Bohr's complementarity principle.     

Some Methodological Problems in Quantum Physics

A consistent application of probabilistic theory is able to resolve traditionally perplexing quantum-theoretical issues, such as those concerned with quantum measurement procedures, wave-corpuscle duality, the reality of particle motion, hidden variables, the proper choice of the energy operator, the energy-time uncertainty relation, conservation laws, and the notion of wave packets. Germane to this resolution is the consideration that quantum physics deals with abstract physical systems and not with single measurements performed on concrete systems. We examine the two-slit diffraction phenomenon and those hypothetical experiments which attempt the simultaneous measurement of any coordinate and its conjugate momentum; their customary interpretations are shown to be basically incorrect. A logical error is likewise found to underlie the usual assertion that the ordinary rule for the addition of probabilities breaks down in quantum physics. And the confusion of energy with the Hamiltonian function is identified as the cause for a number of prevailing wrong conclusions. The probabilistic approach furthermore invalidates PAULI'S proof that time is a socalled c-number. Our treatment also readily exposes the fallacy in the common assumption that Schrödinger's wave equation goes over into the Hamilton-Jacobi equation when the classical limit is approached.