Roberto Casadio, Giovanni Venturi
An extended monopole detector at constant acceleration coupled to a massless scalar field is allowed to evolve quantum mechanically. It is found that while in the classical, followed by the point particle, limit the usual result Unruh effect is recovered, in the point particle (before the classical) limit the detector decouples from the scalar field and therefore the effect disappears.
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The dynamics of tripartite entanglement of fermionic system in noninertial frames through linear contraction criterion when one or two observers are accelerated is investigated. In one observer accelerated case the entanglement measurement is not invariant with respect to the partial realignment of different subsystems and for two observers accelerated case it is invariant. It is shown that the acceleration of the frame does not generate entanglement in any bipartite subsystems. Unlike the bipartite states, the genuine tripartite entanglement does not completely vanish in both one observer acc…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how…
The quantum mechanical evolution of an accelerated extended detector coupled to a massless scalar field is exhibited and the back-reaction due to emission or absorption processes computed at first order in the change of the detector's mass and acceleration. An analogy with black hole evaporation is found and illustrated.
Nonperturbative analysis of quantum entanglement and quantum teleportation protocol using oscillator variables carried by observers in relativistic motion under the continuous influence of the environment is given. The full time evolution of quantum entanglement among static and accelerated observers is studied. The environment plays a dual role. While it creates bipartite and tripartite entanglement among observers even when the initial state is separable, it suppresses the entanglement via decoherence. Motivated by the black hole information problem, we consider quantum teleportation between…
The sampled negative energy density seen by inertial observers, in arbitrary quantum states is limited by quantum inequalities, which take the form of an inverse relation between the magnitude and duration of the negative energy. The quantum inequalities severely limit the utilization of negative energy to produce gross macroscopic effects, such as violations of the second law of thermodynamics. The restrictions on the sampled energy density along the worldlines of accelerated observers are much weaker than for inertial observers. Here we will illustrate this with several explicit examples. We…
Entanglement of Dirac fields has been studied and it is known to decrease with increasing acceleration when a quantum state is shared between users in non-inertial frames. A new form of an entangled vacuum state observed by the accelerated observer is postulated in which it is assumed that entanglement is present between the modes of the quantum field with sharp and opposite momenta defined in two causally disconnected regions of space-time. We find that this assumption does not affect the entanglement of the system.
We calculate the quantum discord between two free modes of a scalar field which start in a maximally entangled state and then undergo a relative, constant acceleration. In a regime where there is no distillable entanglement due to the Unruh effect, we show that there is a finite amount of quantum discord, which is a measure of purely quantum correlations in a state, over and above quantum entanglement. Even in the limit of infinite acceleration of the observer detecting one of the modes, we provide evidence for a non-zero amount of purely quantum correlations, which might be exploited to gain …
We have studied entanglement between two Dirac modes respectively observed by two independently accelerated observers. Due to Unruh effect, the entanglement degrades, but residual nonzero entanglement remains even when the accelerations of both observers are infinite. We have also investigated quantum teleportation using entangled Dirac modes, and calculated the fidelities in various cases. In general, the fidelity depends on the single-qubit state $γ|0\rangle +δ|1\rangle$ to be teleported, as well as which Bell state to use. In the limit that both accelerations are infinite, the average fidel…
Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in non-inertial frames. In the high acceleration limit, our results can be applied to a non-accelerated observer falling into a black hole while the accelerated one barely esca…
A detector undergoing uniform acceleration $a$ in a vacuum field responds just as though it were immersed in thermal radiation of temperature $T=\hbar a/2πk c$. A simple, intuitive derivation of this result is given for the case of a scalar field in one spatial dimension. The approach is then extended to treat the case where the field seen by the accelerated observer is a spin-1/2 Dirac field.
Due to the Unruh effect, accelerated and inertial observers differ in their description of a given quantum state. The implications of this effect are explored for the entropy assigned by such observers to localized objects that may cross the associated Rindler horizon. It is shown that the assigned entropies differ radically in the limit where the number of internal states $n$ becomes large. In particular, the entropy assigned by the accelerated observer is a bounded function of $n$. General arguments are given along with explicit calculations for free fields. The implications for discussions …
Minkowski-Fock states in accelerated frames
针对非惯性观察者缺乏 Minkowski 粒子态显式 Wigner 表述的问题，本文提出计算加速系中 Minkowski-Fock 态特征函数的通用方法，并揭示可通过 Rindler 粒子分布及动量间关联检测加速度。
Localization in Quantum Field Theory for inertial and accelerated observers
从惯性及加速观测者视角研究QFT定域化，对比三种方案发现仅AQFT满足因果性与微分同胚不变性，并在Rindler框架非相对论极限下揭示了态制备与测量独立性失效的条件。
We study communication between an inertial observer and one of two causally-disconnected counter accelerating observers. We will restrict the quantum channel considering inertial-to-accelerated bipartite classical and quantum communication over different sets of Unruh modes (single-rail or dual-rail encoding). We find that the coherent information (and therefore, the amount of entanglement that can be generated via state merging protocol) in this strongly restricted channel presents some interesting monogamy properties between the inertial and only one of the accelerated observers if we take a…
We consider a continuous-variable quantum teleportation protocol between a uniformly accelerated sender in the right Rindler wedge, a conformal receiver restricted to the future light cone, and an inertial observer in the Minkowski vacuum. Using a non-perturbative quantum circuit model, the accelerated observer interacts unitarily with the Rindler modes of the field, thereby accessing entanglement of the vacuum as a resource. We find that a Rindler-displaced Minkowski vacuum state prepared and teleported by the accelerated observer appears mixed according to the inertial observer, despite a re…
Fulling-Davies-Unruh effect for accelerated two-level single and entangled atomic systems
该研究探究真空及腔中匀加速二能级单原子与纠缠原子系统的跃迁率，分析原子与无质量标量场的相互作用，验证惯性观测者视角下匀加速效应与共动观测者视角下热浴效应的等价性，还发现最大纠缠超辐射初态无跃迁，可用于量子信息。
We study the radiation produced by an accelerated time-delay acting on the left moving modes. Through analysis via the Schrodinger picture, we find that the final state is a two-mode squeezed state of the left moving Unruh modes, implying particle production. We analyse the system from an operational point of view via the use of self-homodyne detection with broad-band inertial detectors. We obtain semi-analytical solutions that show that the radiation appears decohered when such an inertial observer analyses the information of the radiation from the accelerated time-delay source. We make conne…
Using the single-mode approximation, we first calculate entanglement measures such as negativity ($1-3$ and $1-1$ tangles) and von Neumann entropy for a tetrapartite W-Class system in noninertial frame and then analyze the whole entanglement measures, the residual $π_{4}$ and geometric $Π_{4}$ average of tangles. Notice that the difference between $π_{4}$ and $Π_{4}$ is very small or disappears with the increasing accelerated observers. The entanglement properties are compared among the different cases from one accelerated observer to four accelerated observers. The results show that there sti…
Building on the well-known Unruh-Davies effect, we examine the effects of projective measurements and quantum communications between accelerated and stationary observers. We find that the projective measurement by a uniformly accelerated observer can excite real particles from the vacuum in the inertial frame, even if no additional particles are created by the measurement process in the accelerating frame. Furthermore, we show that the particles created by this accelerating measurement can be highly entangled in the inertial frame, and it is also possible to use this process to generate even m…
We study the accelerated motion of mirrors and the photonic Unruh effect. The solutions of Maxwell's equations with appropriate boundary conditions in Rindler coordinates are found. The canonical quantization of the field is carried out properly. Important consequences arise from the presence of mirrors or polarizers. It is shown that a single reflective surface produces frequency quantization due to Dirichlet conditions applied to the $-1/(αx)^2$ anomalous potential for non-inertial observers. The number of photons per accelerated mode is estimated via Hankel functions.
Orbital angular momentum spectrum and entanglement in a rotating accelerated reference frame
该研究分析了旋转加速参考系中的轨道角动量谱与纠缠特性，发现加速度主要影响纠缠维度、旋转主要影响 OAM 模式最高阶，并将结论推广到所有稳态轨迹。
We use the formalism of noisy Gaussian channels to derive explicit transformation laws describing how an arbitrary multimode Gaussian state of a scalar quantum field is perceived by a number of accelerating observers, each having access to at least one of the modes. Our work, which generalizes earlier results of Ahmadi, et al., Phys. Rev. D 93, 124031 (2016), is the next step torwards a better understanding of the effect of gravity on the states of quantum fields.
The Unruh effect is the phenomenon that accelerated observers detect particles even when inertial observers experience the vacuum state. In particular, uniformly accelerated observers are predicted to measure thermal radiation that is proportional to the acceleration. Here we consider the Unruh effect for a detector that follows a quantum superposition of different accelerated trajectories in Minkowski spacetime. More precisely, we analyse the excitations of a pointlike multilevel particle detector coupled to a massless real scalar field and moving in the superposition of accelerated trajector…
The existence of Davies-Unruh temperature in a uniformly accelerated frame shows that quantum fluctuations of the inertial vacuum state appears as thermal fluctuations in the accelerated frame. Hence thermodynamic experiments cannot distinguish between phenomena occurring in a thermal bath of temperature T in the inertial frame from those in a frame accelerating through inertial vacuum with the acceleration $a=2πT$. We show that this indisguishability between quantum fluctuations and thermal fluctuations goes far beyond the fluctuations in the vacuum state. We show by an exact calculation, tha…
We report the existence of an Unruh like effect, for physical observers (cosmological and comoving observers) in the radiation dominated early universe, which is possible due to the discovery of a new vacuum state (referred here as the $T-$vacuum). Both the comoving and the cosmological observers, who are crucial in our understanding of cosmology, observe this $T-$vacuum as a particle excited state and are able to detect radiation due to particle creation. We draw a robust analogy with the Unruh effect, whereby -- (i) the physical observers here are closely analogous to the accelerated (Rindle…
Entanglement degradation caused by the Unruh effect is discussed for the tripartite GHZ or W states constructed by modes of a non-interacting quantum field viewed by one inertial observer and two uniformly accelerated observers. For fermionic states, the Unruh effect even for infinite accelerations cannot completely remove the entanglement. However, for the bosonic states, the situation is different and the entanglement vanishes asymptotically. Also, the entanglement is studied for the bipartite subsystems. While for the GHZ states all the bipartite subsystems are identically disentangled, for…
We show that nonorthogonal states achieve a higher level of entanglement when one party undergoes uniform acceleration. We also show that in this regime non-orthogonal states achieve a higher fidelity for teleportation. A quantum field as observed by an observer confined to a Rindler wedge acts as an open system. When one traces over the field modes in the causally disconnected region of space time, one finds that, for a qubit derived from the modes of a scalar field, the effective state space of a qubit is deformed. In order to show this we numerically calculate the Bures angle between states…
It is shown that a general radial conformal Killing vector in Minkowski space-time can be associated to a generator of time evolution in conformal quantum mechanics. Among these conformal Killing vectors one finds a class which maps causal diamonds in Minkowski space-time into themselves. The flow of such Killing vectors describes worldlines of accelerated observers with a finite lifetime within the causal diamond. Time evolution of static diamond observers is equivalent to time evolution in conformal quantum mechanics governed by a hyperbolic Hamiltonian and covering only a segment of the tim…
We investigate the amount of entanglement and quantum discord extractable from a two mode squeezed state as considered from the viewpoint of two observers, Alice (inertial) and Rob (accelerated). We find that using localized modes produces qualitatively different correlation properties for large accelerations than do Unruh modes. Specifically, the entanglement undergoes a sudden death as a function of acceleration and the discord asymptotes to zero in the limit of infinite acceleration. We conclude that the previous Unruh mode analyses do not determine the acceleration dependent entanglement a…
Quantum discord of Gaussian states in non-inertial frames
研究非惯性框架下高斯态的量子失谐在Unruh效应下的重新分布，揭示其随加速度的衰减规律及压缩参数、场频率对不同模式对失谐的影响。
Effect of decoherence and correlated noise on the entanglement of X-type state of the Dirac fields in the non-inertial frame is investigated. A two qubit X-state is considered to be shared between the partners where Alice is in inertial frame and Rob in an accelerated frame. The concurrence is used to quantify the entanglement of the X-state system influenced by time correlated amplitude damping, depolarizing and bit flip channels. It is seen that amplitude damping and bit flip channels heavily influence the entanglement of the system as compared to the depolarizing channel. It is found possib…
A way to encode acceleration directly into fields has recently being proposed, thus establishing a new kind of fields, the accelerated fields. The definition of accelerated fields points to the quantization of space and time, analogously to the way quantities like energy and momentum are quantized in usual quantum field theories. Unruh effect has been studied in connection with quantum field theory in curved spacetime and it is described by recruiting a uniformly accelerated observer. In this work, as a first attempt to demonstrate the utility of accelerated fields, we present an alternative w…
We study the effect of the acceleration of the observer on a parameter estimation protocol using NOON states. An inertial observer, Alice, prepares a NOON state in Unruh modes of the quantum field, and sends it to an accelerated observer, Rob. We calculate the quantum Fisher information of the state received by Rob. We find the counter-intuitive result that the single rail encoding outperforms the dual rail. The NOON states have an optimal $N$ for the maximum information extractable by Rob, given his acceleration. This optimal $N$ decreases with increasing acceleration.
Single quantum system, such as Unruh-DeWitt detector, can be used to determine absolute acceleration by local measurements on a quantum field. To show this, we consider two kinematically indistinguishable scenarios: an inertial observer, Bob, measuring the field of an uniformly accelerated cavity, and his non-inertial twin Rob accelerating and making measurements in a stationary cavity. We find that these scenarios can be distinguished in the non-relativistic regime only by measurements on highly excited massive fields, allowing one to detect non-inertialness of the reference frame.
What happens once an accelerating observer has detected a Rindler particle?
本文重新审视Unruh和Wald的Rindler粒子探测框架，分析测量后场态的非定域变化可能引发的超光速通信问题，并探讨物理学阻止这类测量诱导超光速信号协议的可能途径。
The π-tangle is used to study the behavior of entanglement of a nonmaximal tripartite state of both Dirac and scalar fields in accelerated frame. For Dirac fields, the degree of degradation with acceleration of both one-tangle of accelerated observer and π-tangle, for the same initial entanglement, is different by just interchanging the values of probability amplitudes. A fraction of both one-tangles and the π-tangle always survives for any choice of acceleration and the degree of initial entanglement. For scalar field, the one-tangle of accelerated observer depends on the choice of values of …
Decoherence is an unavoidable phenomenon that results from the interaction of the system with its surroundings. The study of decoherence due to the relativistic effects has the fundamental importance. The Unruh effect is observed by the relativistically accelerator observer. The unruh effect acts as a quantum channel and we call it the Unruh Channel. The Unruh channel can be characterize by providing its Kraus representation. We consider the bipartite scheme in which the quantum information is shared between an inertial observer (Alice) and an accelerated observer (Rob) in the case of Dirac fi…
Observers following special classes of finite-lifetime trajectories have been shown to experience an effective temperature, a generalisation of the Unruh temperature for uniformly accelerated observers. We consider a mirror following such a trajectory - and is hence localised to a strictly bounded causal diamond - that perfectly reflects incoming field modes. We find that inertial observers in the Minkowski vacuum detect particles along the half null-rays at the beginning and end of the mirror's lifetime. These particle distributions exhibit multi-partite entanglement, which reveals novel stru…
It has been proved in the context of quantum fields in Minkowski spacetime that the vacuum state is a thermal state according to uniformly accelerated observers -- a seminal result known as the Unruh effect. Recent claims, however, have challenged the validity of this result for extended systems, thus casting doubts on its physical reality. Here, we study the dynamics of an extended system, uniformly accelerated in the vacuum. We show that its reduced density matrix evolves to a Gibbs thermal state with local temperature given by the Unruh temperature. This proves that the vacuum state does in…
Driving the Unruh Response
研究通过双局部驱动源生成的纠缠非热激发，探索Unruh响应的来源，并利用模自同构和抛物线柱函数构建波包近似，揭示热性与局域源结构的关系。
Decoherence is the process via which quantum superpositions states are reduced to classical mixtures. Decoherence has been predicted for relativistically accelerated quantum systems, however examples to date have involved restricting the detected field modes to particular regions of space-time. If the global state over all space-time is measured then unitarity returns and the decoherence is removed. Here we study a decoherence effect associated with accelerated systems that cannot be explained in this way. In particular we study a uniformly accelerated source of a quantum field state - a singl…
The thermal radiance felt by a uniformly accelerated detector/oscillator/atom--the Unruh effect-- is often mistaken to be some emitted radiation detectable by an observer/probe/sensor. Here we show by an explicit calculation of the energy momentum tensor of a quantum scalar field that, at least in 1+1 dimension, while a polarization cloud is found to exist around the particle trajectory, there is no emitted radiation from a uniformly accelerated oscillator in equilibrium conditions. Under nonequilibrium conditions which can prevail for non-uniformly accelerated trajectories or before the atom …
The relativistic free particle system in 1+1 dimensions is formulated as a ``bi-Hamiltonian system''. One Hamiltonian generates ordinary time translations, and another generates (essentially) boosts. Any observer, accelerated or not, sees evolution as the continuous unfolding of a canonical transformation which may be described using the two Hamiltonians. When the system is quantized both Hamiltonians become Hermitian operators in the standard positive definite inner product. Hence, each observer sees the evolution of the wave function as the continuous unfolding of a unitary transformation in…
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