Tommaso Favalli, Augusto Smerzi
We consider a global quantum system (the "Universe") satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a model of 3+1 dimensional, non-relativistic, quantum spacetime emerging from entanglement among different subsystems in a globally "timeless" and "positionless" Universe.
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General Relativity and Quantum Jumps: The Existence of Nondiffeomorphic Solutions to the Cauchy Problem in Nonempty Spacetime and Quantum Jumps as a Provider of a Canonical Spacetime Structure
它表明，尽管一个普遍接受的概念，存在非空时空中的柯西问题的非纯解，这意味着正则互补条件的必要性。正是非定域量子跃迁提供了时空流形的正则整体结构，同样，也提供了正则互补条件。
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 Computing Spacetime
一个因果集C可以描述一个离散时空，但这个离散时空不是量子的，因为C被赋予了布尔逻辑，因为它不允许循环。在一个拟序集合Q中，允许有圈。本文考虑拟序集Q的一个子集QC，它的元素都是圈。在具有量子逻辑的量子控制中，节点中最大出度N的每个圈都与N个纠缠量子比特相关联。然后QC描述了一个量子计算时空。这种非定域和非偶然的结构可以被理解为一个原始时空。微观因果性和局域性可以在Q的子集U中恢复，其元素是未纠缠的量子比特，我们将其解释为量子时空的状态。量子时空到原时空的映射是通过异或门的作用给出的。此外，通过阿达玛门的作用，从布尔因果集到U的映射是可能的。特别地，定义在U的元素上的因果序导致自旋网络的因果演化。
We argue that the flat spacetime with inexact quantum mechanics in it is dual to the de Sitter spacetime with exact quantum mechanics in it, and the positive cosmological constant of this de Sitter spacetime is in the second order of the degree of the violation of the bulk quantum mechanics in the flat spacetime. The flat spacetime is holographic and has a dual time-contracted boundary conformal field theory with two redefined central charges at null infinity. The vanishing smallness of the observed positive cosmological constant suggests the extraordinary exactness of the bulk quantum mechani…
In classical spacetime null geodesics give information on where free massless particles travel. In quantum spacetime where quantum indefiniteness renders spacetime fuzzy null geodesics as sharp trajectories cannot be retained. We propose a "tendency postulate" that gives information on where free massless objects tend to travel based exclusively on meaningful notions in quantum spacetime. It says that free massless objects tend to trace large quantum causal fluctuations. We implement the tendency postulate in concrete models of quantum spacetime that describe causal fluctuation. The tendency p…
We experimentally simulate the spin networks -- a fundamental description of quantum spacetime at the Planck level. We achieve this by simulating quantum tetrahedra and their interactions. The tensor product of these quantum tetrahedra comprises spin networks. In this initial attempt to study quantum spacetime by quantum information processing, on a four-qubit nuclear magnetic resonance quantum simulator, we simulate the basic module -- comprising five quantum tetrahedra -- of the interactions of quantum spacetime. By measuring the geometric properties on the corresponding quantum tetrahedra a…
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…
Spatiotemporally-localized-stationary typical wave function satisfying Klein-Gordon equation with emergent mass
本文从相对论无质量的马德隆流体出发，在有限平均量子势的条件下，通过使Shannon熵最大化，导出了一类典型的波函数。我们表明，有一类解决方案，其中的波函数是时空本地化与有限的时空支持，均匀移动，因此固定。结果表明，量子振幅满足Klein-Gordon方程，其中突现质量项与平均量子势的平方根成正比。我们表明，有物理时间的不确定性，随着质量的增加而减少。我们还重新推导了经典的能量-动量关系提供的德布罗意-爱因斯坦关系成立。在这种情况下，时间不确定性与经典能量的倒数成正比。
Super quantum mechanics, spacetime and quantum information
本文以信息时空为超空间，说明时空与量子信息之间的联系。给出了量子信息与反对易变量的关系。此外，一个孤立子袋的信息被限制。
We study the notion of causal orders for the cases of (classical and quantum) circuits and spacetime events. We show that every circuit can be immersed into a classical spacetime, preserving the compatibility between the two causal structures. Using the process matrix formalism, we analyse the realisations of the quantum switch using 4 and 3 spacetime events in classical spacetimes with fixed causal orders, and the realisation of a gravitational switch with only 2 spacetime events that features superpositions of different gravitational field configurations and their respective causal orders. W…
Feynman's sum-over-histories formulation of quantum mechanics is reviewed as an independent statement of quantum theory in spacetime form. It is different from the usual Schrödinger-Heisenberg formulation that utilizes states on spacelike surfaces because it assigns probabilities to different sets of alternatives. Sum-over-histories quantum mechanics can be generalized to deal with spacetime alternatives that are not "at definite moments of time". An example in field theory is the set of alternative ranges of values of a field averaged over a spacetime region. An example in particle mechanics …
Generalizing Quantum Mechanics for Quantum Spacetime
熟悉的教科书量子力学假设一个固定的背景时空来定义类空表面上的态以及它们之间的幺正演化。量子理论随着我们对空间和时间概念的发展而改变。但对于时空几何起伏不定且无定值的量子引力，量子力学需要进一步推广。本文综述了宇宙时空几何的四维、历史求和、广义量子力学。这种推广是在广义量子理论的框架内构建的。这是从封闭系统的现代量子力学中抽象出来的量子理论的最小原则集，最常见的是宇宙。在这种推广中，类空表面上的场态及其幺正演化是适合于时空几何近似经典行为的涌现性质。广义量子理论的原理允许进一步的推广，如果时空不是基本的，这将是必要的。出现的时空现象进行了一般性的讨论，并说明了与大的类空表面，从“无边界”的宇宙波函数的经典时空几何的例子。它们必须是具有一个且只有一个时间方向的洛伦兹。文章最后提出了量子力学本身是否是突现的问题。
The evolution of expanding spacetime realizes approximate quantum cloning
本文研究膨胀时空中量子场信息的非幺正演化，并在 de Sitter 时空中导出对应量子信道，揭示其近似量子克隆特性及与时空曲率的联系。
The state-of-the-art physics consists of two irreconcilable branches, i.e., the quantum theory and the general relativity, which work well in their own territories, independently. However, what are quantum and spacetime after all? The key question was never addressed, satisfactorily. In this work, we describe a possibility to reformulate the quantum theory in the Minkowski spacetime from the viewpoint of classic physics in the Euclidean spacetime, i.e., classic mechanics and stochastic process theory. We show that quantum theory and Minkowski spacetime may connect with each other and emerge fr…
Quantum Mechanical Motion of Relativistic Particle in Non-Continuous Spacetime
研究了相对论性粒子在非连续时空中的量子力学运动。时空模型是二维闵可夫斯基时空的一个稠密、合理的子集。狄拉克方程的解是使用费曼棋盘模型的广义版本计算的。它们与连续统传播子密切相关。
Quantum coherence control is presented for wavelength convertible quantum memory in a double-lambda-type solid ensemble whose spin states are inhomogeneously broadened. Unlike typical atomic media whose spin decay is homogeneous, a spin inhomogeneously broadened solid ensemble requires a counter-intuitive access in the quantum coherence control to avoid spontaneous emission-caused quantum noises. Such quantum coherence control in a solid ensemble results in a near perfect retrieval efficiency and is applicable to ultralong photon storage up to the spin phase relaxation time. Here, the basic ph…
On the spacetime geometry of quantum nonlocality
我们提出了一种新的时空几何，其中事件可能是正维的。这种几何是通过将量子统计学的基本原理--不变量的恒等式应用于时间而得到的。量子非定域性是这种几何的自然结果。我们还研究了在这个框架中的波函数的本体。特别是，我们展示了如何在时空纠缠交换失效的PBR定理的准备假设。
The idea that spacetime geometry is built from quantum entanglement has been widely accepted in the last years. But how exactly the geometry is related with quantum states is still unclear. In this note, based on the idea of deep learning, we propose a mechanism for Susskind's QM=GR hypothesis, spacetime geometry as the optimal generative network of quantum states. We speculate that the space geometry stems as a geodesic tensor network which defines the quantum state complexity of a fundamental quantum state under a given metric. Spacetime corresponds to an evolving tensor network that generat…
Quantum Heat Baths satisfying the eigenstate thermalization hypothesis
提出了一类满足本征态热化假设（ETH）准则的自治量子热浴。我们表明，这样的系统预计将导致热松弛耦合到一个浴局部可观的小得多的量子系统。热化的过程中，检查通过剩余波动的局部可观的浴在其附近的ETH预测的热值。结果表明，这种涨落扰动小量子系统，导致其退相干的热态。作为一个例子，我们研究理论和数值热化的量子位耦合到一个现实的ETH量子热浴。
Spacetime-Free Approach to Quantum Theory and Effective Spacetime Structure
受时空结构的有效涌现性质的启发，我们为量子理论建立了一个时空自由的代数框架，其中不需要先验的背景几何结构。这样一个框架是必要的，以便以一致的方式研究有效时空结构的出现，而不必从一开始就假设背景几何。相反，背景几何被证明是作为一个有效的结构的代数和动力学之间的关系，是由系统的背景统计所施加的可观的。也就是说，我们认为量子参考态在一个扩展的可观测代数上，即由可观测量生成的自由代数上，可以产生有效的时空结构。因此，参考态的扰动导致诱导的有效时空几何的扰动。我们开始研究这些微扰，以及它们与引力现象的关系。
Nowadays, quantum simulation schemes come in two flavours. Either they are continuous-time discrete-space models (a.k.a Hamiltonian-based), pertaining to non-relativistic quantum mechanics. Or they are discrete-spacetime models (a.k.a Quantum Walks or Quantum Cellular Automata-based) enjoying a relativistic continuous spacetime limit. We provide a first example of a quantum simulation scheme that unifies both approaches. The proposed scheme supports both a continuous-time discrete-space limit, leading to lattice fermions, and a continuous-spacetime limit, leading to the Dirac equation. The tra…
We introduce superdensity operators as a tool for analyzing quantum information in spacetime. Superdensity operators encode spacetime correlation functions in an operator framework, and support a natural generalization of Hilbert space techniques and Dirac's transformation theory as traditionally applied to standard density operators. Superdensity operators can be measured experimentally, but accessing their full content requires novel procedures. We demonstrate these statements on several examples. The superdensity formalism suggests useful definitions of spacetime entropies and spacetime qua…
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