Chang-shui Yu, X. X. Yi, He-shan Song
The bounds on concurrence of the superposition state in terms of those of the states being superposed are studied in this paper. The bounds on concurrence are quite different from those on the entanglement measure based on von Neumann entropy (Phys. Rev. Lett. 97, 100502 (2006)). In particular, a nonzero lower bound can be provided if the states being superposed are properly constrained.
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In this paper we use the \textit{concurrence vector}, as a measure of entanglement, and investigate lower and upper bounds on the concurrence of a superposition of bipartite states as a function of the concurrence of the superposed states. We show that the amount of entanglement quantified by the concurrence vector is exactly the same as that quantified by \textit{I-concurrence}, so that our results can be compared to those given in [Phys. Rev. A {\bf 76}, 042328 (2007)]. We obtain a tighter lower bound in the case that two superposed states are orthogonal. We also show that when the two super…
The entanglement content of superpositions of quantum states is investigated based on a measure called {\it concurrence}. Given a bipartite pure state in arbitrary dimension written as the quantum superposition of two other such states, we find simple inequalities relating the concurrence of the state to that of its components. We derive an exact expression for the concurrence when the component states are biorthogonal, and provide elegant upper and lower bounds in all other cases. For quantum bits, our upper bound is tighter than the previously derived bound in [Phys. Rev. Lett. 97, 100502 (2…
The entanglement quantified by negativity of pure bipartite superposed states is studied. We show that if the entanglement is quantified by the concurrence two pure states of high fidelity to one another still have nearly the same entanglement. Furthermore this conclusion can be guaranteed by our obtained inequality, and the concurrence is shown to be a continuous function even in infinite dimensions. The bounds on the negativity of superposed states in terms of those of the states being superposed are obtained. These bounds can find useful applications in estimating the amount of the entangle…
We investigate the utility of non classical states of simple harmonic oscillators, particularly a superposition of coherent states, for sensitive force detection. We find that like squeezed states a superposition of coherent states allows displacement measurements at the Heisenberg limit. Entangling many superpositions of coherent states offers a significant advantage over a single mode superposition states with the same mean photon number.
Given a bipartite quantum state (in arbitrary dimension) and a decomposition of it as a superposition of two others, we find bounds on the entanglement of the superposition state in terms of the entanglement of the states being superposed. In the case that the two states being superposed are bi-orthogonal, the answer is simple, and, for example, the entanglement of the superposition cannot be more than one e-bit more than the average of the entanglement of the two states being superposed. However for more general states, the situation is very different.
The standard deviation (SD) quantifies the spread of the observed values on a measurement of an observable. In this paper, we study the distribution of SD among the different components of a superposition state. It is found that the SD of an observable on a superposition state can be well bounded by the SDs of the superposed states. We also show that the bounds also serve as good bounds on coherence of a superposition state. As a further generalization, we give an alternative definition of incompatibility of two observables subject to a given state and show how the incompatibility subject to a…
Direct and Efficient Detection of Quantum Superposition
本文提出利用XOR游戏通过局部测量和独立粒子验证量子叠加，实现高效检测，以单光子实验展示99%置信度。
For a tripartite pure state superposed by two individual states, the bipartitely shared entanglement can always be achieved by local measurements of the third party. Consider the different aims of the third party, i.e. maximizing or minimizing the bipartitely shared entanglement, we find bounds on both the possible bipartitely shared entanglement of the superposition state in terms of the corresponding entanglement of the two states being superposed. In particular, by choosing the concurrence as bipartite entanglement measure, we obtain calculable bounds for tripartite $(2\otimes 2\otimes n)$ …
We show how to make quantum networks, both standard and entanglement-based, genuine quantum by providing them with the possibility of handling superposed tasks and superposed addressing. This extension of their functionality relies on a quantum control register, which specifies not only the task of the network, but also the corresponding weights in a coherently superposed fashion. Although adding coherent control to classical tasks, such as sending or measuring -or not doing so-, is in general impossible, we introduce protocols that are able to mimick this behavior under certain conditions. We…
In this paper we investigate the effect of superposition of states on local conversion of pure bipartite states under deterministic LOCC. We are able to form a bridge between comparable and incomparable classes of states through the linear superposition of states. For example, if we consider two pairs of incomparable states, then their superposition may result into a comparable pair of states. We investigate many such cases and provide some of the results in tabular form. We also investigate the entanglement behavior of such classes of states, specifically their monotone nature. Finally we pro…
A central open problem of quantum physics is to reconcile theory with experience. In this work I present a framework for studying distinct modes of experience in a superposed world. A modes of experience is characterized by how the world, experiences, and options relate to each other by the perceptions, decisions, and actions, as well as by probabilistic rules encoding probabilistic or deterministic correlations among first person experiences. In a toy model, the life expectancies of beings in different candidate modes of experience are compared. It is found that the quantum mode without macro…
Generation of quantum entanglement in superposed diamond spacetime
该研究提出因果钻石时空叠加框架，首次推导叠加时空中狄拉克场的Unruh-钻石真空态解析表达式，发现时空叠加可产生额外纠缠资源，为量子信息处理提供新途径。
Quantum correlation and origin of Hawking radiation for mass-superposed BTZ black holes
利用速度关联函数研究BTZ黑洞质量叠加，发现关联峰可揭示量子特征并区分相同质量比的不同叠加，且能定位Hawking辐射起源，支持量子大气概念。
Considering the concept of "{\it nonlinear coherent states}", we will study the interference effects by introducing the {\it "superposition of two classes of nonlinear coherent states"} which are $\fracπ{2}$ out of phase. The formalism has then been applied to a few physical systems as "harmonious states", "SU(1,1) coherent states" and "the center of mass motion of trapped ion". Finally, the nonclassical properties such as sub-Poissonian statistics, quadrature squeezing, amplitude-squared squeezing and Wigner distribution function of the superposed states have been investigated, numerically. E…
Entanglement characteristics of a pair coherent state is studied using entanglement of superposition. It is demonstrated only few states in the expansion of a pair coherent state, in a harmonic oscillator basis, contribute significantly to the entanglement. We also study a case of two superposed pair coherent states
We investigate how the genuine multipartite entanglement is distributed among the components of superposed states. Analytical lower and upper bounds for the usual multipartite negativity and the genuine multipartite entanglement negativity are derived. These bounds are shown to be tight by detailed examples.
How long single-photon detectors stay in quantum superpositions during detection according to the Diósi-Penrose criterion
研究了在检测过程中与环境隔离的单光子探测器如何保持光子被检测与未被检测态的叠加态，通过使用平板电容器而非传统电压源抑制环境相互作用，并讨论了Diósi-Penrose模型及质量分布空间平均化版本，证明间接单光子探测器可维持叠加态数秒，并提出利用压电作动器生成镜面叠加态的新方法。
Bounds on positive operator-valued measure based coherence of superposition
该研究将相干性资源理论推广至POVM测量，解析推导了叠加纯态相干性的上下界，并用示例验证，可用于估计叠加态相干性范围。
We discuss the generation of field-induced entanglement between two objects each in a superposition of two trajectories.The objects have currents coupled to local quantum fields, and the currents are evaluated around each trajectory of the objects.The fields have only dynamical degrees of freedom and satisfy the microcausality condition. We find that the superposed state of trajectories cannot be entangled when the objects are spacelike separated.This means that the quantum fields do not generate spacelike entanglement in the superposition of two trajectories of each object.
Superposed quantum evolutions across chaotic and regular regimes
研究量子演化叠加在混沌与规则经典极限间的干涉效应，通过Mach-Zehnder干涉仪对比量子叠加与经典混合，揭示经典混沌与量子干涉的非平凡相互作用。
Unruh-deWitt detectors have been utilised widely as probes for quantum particles, entanglement and spacetime curvature. Here, we extend the standard treatment of an Unruh-deWitt detector interacting with a massless, scalar field to include the detector travelling in a quantum superposition of classical trajectories. We derive perturbative expressions for the final state of the detector, and show that it depends on field correlation functions evaluated locally along the individual trajectories, as well as non-locally between the superposed trajectories. By applying our general approach to a det…
Lower- versus higher-order nonclassicalities for a coherent superposed quantum state
本文研究相干态上叠加湮灭与产生算符所得量子态的非经典性，发现高阶判据比低阶条件更能有效检测非经典性。
The quantum state of Schroedinger's cat is usually incorrectly described as a superposition of "dead" and "alive," despite an argument by Rinner and Werner that, locally, the cat should be considered to be in a mixture of non-superposed states. Here, it is rigorously proven that the cat is not in a superposition. This is central to the measurement problem. Nonlocal two-photon interferometry experiments throw further light on the measurement state by probing the effect of a variable phase factor inserted between its superposed terms. These experiments demonstrate that both subsystems really are…
Can the latent signatures of quantum superposition be detected through correlation harvesting?
本文研究了量子叠加中通过关联收获检测时空特征的方法，发现时空叠加能增强纠缠和互信息提取，且在特定条件下达到最大值。
Decoherence of spin superposition state caused by a quantum electromagnetic field
本研究分析相对论量子电磁场中空间叠加的自旋-1/2中性粒子退相干，将其分为源于单轨迹关联的局域退相干与双轨迹关联的非局域退相干，分别对应相位和振幅阻尼，且热态下退相干随温度单调上升。
A bipartite quantum state (for two systems in any dimensions) can be decomposed as a superposition of many components. For a superposition of more than two components we prove that there is a bound of the entanglement of the superposition state which can be expressed according to entanglements of its component states. Especially, if the component states are mutually bi-orthogonal, the entanglement of the superposition state can be exactly given in terms of the entanglements of the states being superposed.
The entanglement of superpositions [Phys. Rev. Lett. 97, 100502 (2006)] is generalized to the multipartite scenario: an upper bound to the multipartite entanglement of a superposition is given in terms of the entanglement of the superposed states and the superposition coefficients. This bound is proven to be tight for a class of states composed by an arbitrary number of qubits. We also extend the result to a large family of quantifiers which includes the negativity, the robustness of entanglement, and the best separable approximation measure.
We derive the lower and upper bounds on the entanglement of a given multipartite superposition state in terms of the entanglement of the states being superposed. The first entanglement measure we use is the geometric measure, and the second is the q-squashed entanglement. These bounds allow us to estimate the amount of the multipartite entanglement of superpositions. We also show that two states of high fidelity to one another do not necessarily have nearly the same q-squashed entanglement.
Entanglement harvesting in quantum superposed spacetime
本文研究了量子叠加时空中的纠缠收割现象，通过两个 Unruh-DeWitt 探测器与标量场相互作用，发现时空叠加引发的干涉效应能显著增强纠缠，且在特定条件下达到最大值。
We consider the magnetic flux in a quantum mechanical superposition of two values and find that the Aharonov-Bohm effect interference pattern contains information about the nature of the superposition, allowing information about the state of the flux to be extracted without disturbance. The information is obtained without transfer of energy or momentum and by accumulated nonlocal interactions of the vector potential $\vec{A}$ with many charged particles forming the interference pattern, rather than with a single particle. We suggest an experimental test using already experimentally realized su…
We propose a method for protecting fragile quantum superpositions in many-particle systems from dephasing by external classical noise. We call superpositions "fragile" if dephasing occurs particularly fast, because the noise couples very differently to the superposed states. The method consists of letting a quantum superposition evolve under the internal thermalization dynamics of the system, followed by a time reversal manipulation known as Loschmidt echo. The thermalization dynamics makes the superposed states almost indistinguishable during most of the above procedure. We validate the metho…
Signatures of Rotating Black Holes in Quantum Superposition
本研究将量子叠加时空效应分析方法扩展到质量叠加的旋转BTZ黑洞，发现探测器响应在特定外视界半径比值处出现共振，支持贝肯斯坦关于黑洞离散视界谱的猜想，为量子引力研究提供新途径。
Particle detector in a position-superposed black hole spacetime
研究在位置叠加的黑洞时空中的粒子探测器响应，通过量子参考系变换分析其与标量场的相互作用，并与先前研究对比，揭示奇异性的差异。
We consider an entanglement harvesting protocol between two Unruh-deWitt detectors in quantum superpositions of static trajectories in the static de Sitter and thermal Minkowski spacetimes. We demonstrate for the first time that the spatial superposition of each detector's path allows entanglement to be harvested from the quantum field in regimes where it would be otherwise impossible for detectors on classical trajectories. Surprisingly, for detectors on sufficiently delocalised trajectories in a thermal bath, the amount of harvested entanglement grows with the temperature of the field, viola…
Generating Fock-state superpositions from coherent states by selective measurement
本文提出一种无需精心驱动、仅通过谐振器与辅助量子比特的Jaynes-Cummings耦合演化及选择性投影测量，即可从相干态高效生成高保真Fock态及其叠加态和Bell类态的量子测量协议。
Manipulation of Superposed Vortex States of $γ$ Photon via Nonlinear Compton Scattering
本文提出通过多频率圆极化激光场驱动非线性康普顿散射生成可控涡旋γ光子叠加态，利用量子电动力学框架揭示机制并计算辐射概率，实现轨道角动量分离和模权重的调控。
We study criteria for and properties of boundary-to-boundary holography in a class of spin network states defined by analogy to projected entangled pair states (PEPS). In particular, we consider superpositions of states corresponding to well-defined, discrete geometries on a graph. By applying random tensor averaging techniques, we map entropy calculations to a random Ising model on the same graph, with distribution of couplings determined by the relative sizes of the involved geometries. The superposition of tensor network states with variable bond dimension used here presents a picture of a …
Accelerated detector in a superposed spacetime
本文研究柱面认同 Rindler 时空叠加中的持续加速二能级探测器，发现紧致长度有理比处的响应共振及加速诱导的细致平衡。
In the absence of a fully-fledged theory of quantum gravity, we propose a "bottom-up" framework for exploring quantum-gravitational physics by pairing two of the most fundamental concepts of quantum theory and general relativity, namely quantum superposition and spacetime. We show how to describe such "spacetime superpositions" and explore effects they induce upon quantum matter. Our approach capitalizes on standard tools of quantum field theory in curved space, and allows us to calculate physical observables like transition probabilities for a particle detector residing in curvature-superpose…
The influence of gravitational field on entanglement of bipartite states is investigated based on the recent idea of superposition states of gravitational field. Different from earlier considerations, we study the case where the gravitational field cannot be separated unitarily from the bipartite system in the final stage of the interaction. When the different gravitational field states are orthogonal, entanglement cannot be generated for an initial product state. If the different gravitational field states are non-orthogonal, entanglement can be generated and the amount of generated entanglem…
Quantum uncertainty of gravitational field and entanglement in superposed massive particles
本研究探讨了电磁/引力势引起的粒子状态纠缠与量子不确定性、因果性及互补性的关系，数值分析表明场的量子不确定性引发的真空涨落会在满足因果性时禁止粒子纠缠，从而保证互补性成立。
Superposed circular motion Unruh effect in (3+1) dimensions
利用新的量子控制模型，研究(3 + 1)维中沿叠加圆周轨迹的探测器与无质量标量量子场相互作用的响应，给出四种场景下探测器跃迁概率和有效温度的数值结果。
The concept of a superposition is a revolutionary novelty introduced by Quantum Mechanics. If a system may be in any one of two pure states x and y, we must consider that it may also be in any one of many superpositions of x and y. An in-depth analysis of superpositions is proposed, in which states are represented by one-dimensional subspaces, not by unit vectors as in Dirac's notation. Superpositions must be considered when one cannot distinguish between possible paths, i.e., histories, leading to the current state of the system. In such a case the resulting state is some compound of the stat…
Existence of self-similar, superposed pulse-train solutions of the nonlinear, coupled Maxwell-Schrödinger equations, with the frequencies controlled by the oscillator strengths of the transitions, is established. Some of these excitations are specific to the resonant media, with energy levels in the configurations of $Λ$ and $N$ and arise because of the interference effects of cnoidal waves, as evidenced from some recently discovered identities involving the Jacobian elliptic functions. Interestingly, these excitations also admit a dual interpretation as single pulse-trains, with widely differ…
Within any anticipated unifying theory of quantum gravity, it should be meaningful to combine the fundamental notions of quantum superposition and spacetime to obtain so-called "spacetime superpositions": that is, quantum superpositions of different spacetimes not related by a global coordinate transformation. Here we consider the quantum-gravitational effects produced by superpositions of periodically identified Minkowski spacetime (i.e.\ Minkowski spacetime with a periodic boundary condition) with different characteristic lengths. By coupling relativistic quantum matter to fields on such a s…
Holographic properties of superposed quantum geometries
本文研究叠加离散几何数据的量子几何态的全息性质，利用代数化量子信息信道定义和随机张量网络技术分析体到边界及边界到边界的映射，得到面积算子主导熵贡献，并证明体区域只能等距映射到固定总面积的边界，为张量网络全息的量子引力实现提供新进展。
In modern physics only relative quantities are considered to have physical significance. For example, position assigned to a system depends on the choice of coordinates, and only relative distances between different systems have physical relevance. On the other hand, in quantum theory the scenario where one system, A, is localised around certain position while another system B is in a spatial superposition is considered to be physically different from the scenario where A is in a superposition, while B is localised. Different physical effects are anticipated in the two scenarios especially whe…
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