Daniel R. Terno
I discuss the role that relativistic considerations play in quantum information processing. First I describe how the causality requirements limit possible multi-partite measurements. Then the Lorentz transformations of quantum states are introduced, and their implications on physical qubits are described. This is used to describe relativistic effects in communication and entanglement.
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On the basis of a 5-dimensional form of space-time transformations non-relativistic quantum mechanics is reformulated in a manifestly covariant manner. The resulting covariance resembles that of the conventional relativistic quantum mechanics.
A detailed study is presented of the relativistic Wigner function for a quantum spinless particle evolving in time according to the Salpeter equation.
The role of quantum degrees of freedom of relativistic fields in quantum information protocols
该研究分析相对论量子信息协议中有无量子自由度的相对论场的差异，分类量子自由度必要的区间，明确量子场可被量子调控经典场良好近似的区间，助力区分经典与量子场论的本质差异特征。
Through the constant potential and the linear potential, we establish the existence of nodes for the relativistic quantum trajectories as the same way as for the quantum trajectories. We establish the purely relativistic limit $(\hbar \to 0)$ for these trajectories, and link the nodes to de Broglie's wavelength.
I present a short overview of my recent achievements on the Bohmian interpretation of relativistic quantum mechanics, quantum field theory and string theory. This includes the relativistic-covariant Bohmian equations for particle trajectories, the problem of particle creation and destruction, the Bohmian interpretation of fermionic fields and the intrinsically Bohmian quantization of fields and strings based on the De Donder-Weyl covariant canonical formalism.
The general and explicit relation between the phase time and the dwell time for quantum tunneling of a relativistically propagating particle is investigated and quantified. In analogy with previously obtained non-relativistic results, it is shown that the group delay can be described in terms of the dwell time and a self-interference delay. Lessons concerning the phenomenology of the relativistic tunneling are drawn.
The de Broglie-Bohm interpretation of quantum mechanics and quantum field theory is generalized in such a way that it describes trajectories of relativistic fermionic particles and antiparticles and provides a causal description of the processes of their creation and destruction. A general method of causal interpretation of quantum systems is developed and applied to a causal interpretation of fermionic quantum field theory represented by c-number valued wave functionals.
For a one-dimensional stationary system, we derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. We then integrate this equation in the constant potential case and calculate the time spent by a particle tunneling through a potential barrier.
We investigate the feasibility of performing quantum non-demolition (QND) measurements in relativistic quantum systems, using the one-dimensional Dirac oscillator as a specific example. We derive general expressions for its QND observables and find that they are intricate combinations of the position, momentum, and spin operators, which makes them challenging to realize experimentally in general. However, the situation is considerably simplified in both the weakly and strongly relativistic limits, where their experimental realization will be possible.
A general formulation of classical relativistic particle mechanics is presented, with an emphasis on the fact that superluminal velocities and nonlocal interactions are compatible with relativity. Then a manifestly relativistic-covariant formulation of relativistic quantum mechanics (QM) of fixed number of particles (with or without spin) is presented, based on many-time wave functions and the spacetime probabilistic interpretation. These results are used to formulate the Bohmian interpretation of relativistic QM in a manifestly relativistic-covariant form. The results are also generalized to …
In this work, we give the wave equations of relativistic and non-relativistic quantum mechanics which are different from the Schrödinger and Klein-Gordon equation, and we also give the new relativistic wave equation of a charged particle in an electromagnetic field
We compute deviations from ideal gas behavior of the pressure, density, and Bose-Einstein condensation temperature of a relativistic gas of charged scalar bosons caused by the current-current interaction induced by electromagnetic quantum fluctuations treated via scalar quantum electrodynamics. We obtain expressions for those quantities in the ultra-relativistic and nonrelativistic limits, and present numerical results for the relativistic case.
The article presents an introductory review of quantum algorithms for non-relativisitc as well as relativistic four component molecular energy calculations developed in past few years.
I draw attention to previous work that shows that the observables corresponding to relativistic quantum field modes commonly employed in papers on "relativistic quantum information" cannot be measured by ideal measurements.
In this work we provide a genuine relativistic quantum teleportation protocol whose classical communication component makes use of relativistic causal propagation of a quantum field. Consequently, the quantum teleportation is fully relativistic by construction. Our scheme is based on Unruh-DeWitt qubit detector model, where the quantum state being teleported is associated to an actual qubit rather than a field mode considered by Alsing and Milburn [PRL 91, 180404 (2003)]. We show that the existing works in (relativistic) quantum information, including good definitions of one-shot and asymptoti…
In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.
As an extension of our recent work (Results in Physics 12, 147-152 (2019)), we show, both theoretically and numerically, that the breakdown of agreement between the non-relativistic and relativistic quantum dynamical predictions in the non-relativistic regime also occurs for an electron subjected to a time-dependent force.
We present some informal remarks on aspects of relativistic quantum computing.
Using the relativistic quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding one self on both relativistic and quantum Lagrangians, we construct a Lagrangian of relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we investigate the free particle case and establish the photon's trajectories.
Using the relativistic quantum stationary Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding oneself on both relativistic and quantum Lagrangians, we construct a Lagrangian of a relativistic quantum system in one dimension and derive a third order equation of motion representing a first integral of the relativistic quantum Newton's law. Then, we plot the relativistic quantum trajectories of a particle moving under the constant and the linear potentials. We establish the existence of nodes and link them to the de Broglie's wavelength.
To study quantum dynamics in the non-relativistic regime, the standard practice is to use non-relativistic quantum mechanics, instead of the relativistic theory, because it is thought the approximate non-relativistic result is always close to the relativistic one. Here we present a theoretical argument that this expectation is not true in general. In addition, supporting numerical evidence for the free rotor and hydrogen atom also shows the agreement between the two theories can break down quickly. For the radial Rydberg wave packet in hydrogen atom, the breakdown can occur before spontaneous …
A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.
We study the quantum theory of a simple general relativistic quantum model of two coupled harmonic oscillators and compute the two-point function following a proposal first introduced in the context of loop quantum gravity.
Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum Langevin equation is derived and explicit expressions for quantum-noise and dynamical variables of the system are obtained. The equations of motion for the canonical variables are solved explicitly and an expression for the radiation-reaction of a charged particle in the presence of a dissipative-medium is obtained. Some examples are given to elucidate the …
A summary of some lines of ideas leading to model-independent frameworks of relativistic quantum field theory is given. It is followed by a discussion of the Reeh-Schlieder theorem and geometric modular action of Tomita-Takesaki modular objects associated with the quantum field vacuum state and certain algebras of observables. The distillability concept, which is significant in specifying useful entanglement in quantum information theory, is discussed within the setting of general relativistic quantum field theory.
A special relativistic perturbation to non-relativistic quantum mechanics is shown to lead to the special relativistic prediction for the rate of precession for quantum states in the Coulomb potential. This behavior is shown using SO(4) coherent states as examples. These states are localized on Kepler ellipses and precess in the presence of a relativistic perturbation.
We find the quantum power emitted and distribution in $3+1$-dimensions of relativistic acceleration radiation using a single perfectly reflecting mirror via Lorentz invariance demonstrating close analogies to point charge radiation in classical electrodynamics.
A relativistic quantum information exchange protocol is proposed allowing two distant users to realize ``coin tossing'' procedure. The protocol is based on the point that in relativistic quantum theory reliable distinguishing between the two orthogonal states generally requires a finite time depending on the structure of these states.
After a review of the problems induced by the Lorentz signature of Minkowski space-time, like the need of a clock synchronization convention for the definition of 3-space and the complexity of the notion of relativistic center of mass, there is the introduction of a new formulation of relativistic quantum mechanics compatible with the theory of relativistic bound states. In it the zeroth postulate of non-relativistic quantum mechanics is not valid and the physics is described in the rest frame by a Hilbert space containing only relative variables. The non-locality of the Poincare' generators i…
The star product formalism has proved to be an alternative formulation for nonrelativistic quantum mechanics. We want introduce here a covariant star product in order to extend the star product formalism to relativistic quantum mechanics in the proper time formulation.
Superquantum ("PR-box") correlations, though designed to respect relativistic causality, violate relativistic causality in the classical limit. Generalizing to all stronger-than-quantum bipartite correlations, I derive Tsirelson's bound from the axioms of nonlocality, relativistic causality and the existence of a classical limit. This derivation of Tsirelson's bound does not assume quantum mechanics yet suggests how Hilbert space is implicit in quantum correlations.
The recently reported relativistic formulation of the well-known non-relativistic quantum state diffusion is seriously mistaken. It predicts, for instance, inconsistent measurement outcomes for the same system when seen by two different inertial observers.
We show that quantum information can be encoded into entangled states of multiple indistinguishable particles in such a way that any inertial observer can prepare, manipulate, or measure the encoded state independent of their Lorentz reference frame. Such relativistically invariant quantum information is free of the difficulties associated with encoding into spin or other degrees of freedom in a relativistic context.
It is shown that relativistic wave equations for free, massless fields display quantum-classical complementarity.
The frequency of a classical periodic system and the energy levels of the corresponding quantum system can both be obtained using action variables. We demonstrate the construction of two forms of the action variable for a one dimensional harmonic oscillator in classical, relativistic and quantum regimes. The relativistic effects are considered as perturbative, within the context of a non-relativistic quantum formalism. The transition of the relativistic quantum system to both classical relativistic and classical non-relativistic regimes is illustrated in a unified framework. Formulas for the f…
We use the laws of relativistic physics to show that classically motivated counterfactual statements are inadequate when discussing the principles of quantum physics and that EPR style arguments against state reduction are incorrect.
In this paper, we develop a formalism describing in a relativistic way a system which consists of a classical and a quantum part being coupled. The formalism models one particle with spin 1/2 and it is a possible relativistic extension of the Event-Enhanced Quantum Theory. We postulate a covariant algorithm which plays the role of the standard reduction postulate in non-relativistic quantum mechanics. Furthermore, we present an algorithm to simulate detections of the particle.
We study the quantum correlation dynamics of two relativistic particles which is transmitted through one of the Pauli channels $ σ_{x}, σ_{y},$ and $σ_{z}$. We compare sudden death and robustness of entanglement and geometric discord and quantum discord of two relativistic particles under noisy Pauli channels. we find out geometric discord and quantum discord may be more robust than entanglement against decoherence.
In nonrelativistic quantum mechanics and in relativistic quantum field theory, time t is a parameter and thus the time-reversal operator T does not actually reverse the sign of t. However, in relativistic quantum mechanics the time coordinate t and the space coordinates x are treated on an equal footing and all are operators. In this paper it is shown how to extend PT symmetry from nonrelativistic to relativistic quantum mechanics by implementing time reversal as an operation that changes the sign of the time coordinate operator t. Some illustrative relativistic quantum-mechanical models are c…
The quantum predictions for a single nonrelativistic spin-1/2 particle can be reproduced by noncontextual hidden variables. Here we show that quantum contextuality for a relativistic electron moving in a Coulomb potential naturally emerges if relativistic effects are taken into account. The contextuality can be identified through the violation of noncontextuality inequalities. We also discuss quantum contextuality for the free Dirac electron as well as the relativistic Dirac oscillator.
A novel quantum time dilation effect is shown to arise when a clock moves in a quantum superposition of two relativistic velocities. This effect is argued to be measurable using existing atomic interferometry techniques, potentially offering a new test of relativistic quantum theory.
The difficulties encountered up till now in the theory of identifying the spin and orbital angular momentum of the photon stem from the approach of dividing the angular momentum of the photon into spin and orbital parts. Here we derive the spin of the photon from a set of two relativistic quantum equations that was first cast from the free-space Maxwell equations by Darwin in 1932. Much attention is focused on the nonlocal properties of the photon spin that are determined by the relativistic quantum constraint, one of the so-called Darwin equations. Meanwhile, we point out that for the Darwin …
The quantum conditions of the relativistic integrable systems whose classical motion is multiply periodic are given by considering the single-valuedness of the linear superposition of the approximate solutions $R_{i}\exp {\{iS_{i}/\hbar \}}$ with $R_{i}$ and $S_{i}$ being the solutions of the different branches of the current conservation equation and the relativistic Hamilton-Jacobian equation, respectively.
We extend the ideas of L.P. Horwitz and C. Piron and we propose a relativistic version of Event Enhanced Quantum Theory, with an event generating algorithm for spin one-half particle detectors. The algorithm is based on proper time formulation of the relativistic quantum theory. Although we use indefinite metric, all the probabilities controlling the random process of the detector clicks are non--negative.
The spin-statistics connection has been proved for nonrelativistic quantum mechanics (Jabs, A., 2010: Found. Phys., {\bf 40}, 776-792). The proof is extended here to the relativistic regime using the parametrized Dirac equation. A causality condition is not required.
Antiparticles in non-relativistic quantum mechanics
本文基于几何量子化方法，在不依赖量子场论的前提下，展示了如何在非相对论量子力学中引入反粒子概念，并以一维谐振子为例进行了详细讨论。
Relativistic quantum field theory imposes additional fundamental restrictions on the distinguishability of quantum states. Because of the unavoidable delocalization of the quantum field states in the Minkowski space-time, the reliable (with unit probability) distinguishability of orthogonal states formally requires infinite time. For the cryptographic protocols which are finite in time the latter means that the effective ``noise'' is present even in the ideal communication channel because of the non-localizability of the quantum field states.
Last years witnessed a remarkable interest in application of quantum computing for solving problems in quantum chemistry more efficiently than classical computers allow. Very recently, even first proof-of-principle experimental realizations have been reported. However, so far only the non-relativistic regime (i.e. Schroedinger equation) has been explored, while it is well known that relativistic effects can be very important in chemistry. In this letter we present the first quantum algorithm for relativistic computations of molecular energies. We show how to efficiently solve the eigenproblem …
Recently, there has been increased interest in understanding entanglement and quantum communication in black hole spacetimes and in using quantum information techniques to address questions in gravity. Studies on relativistic entanglement show the emergence of conceptually important qualitative differences to a non-relativistic treatment. For instance, entanglement was found to be an observer-dependent property that changes from the perspective of accelerated observers moving in flat spacetime. Relativisitic quantum information theory uses well-known tools coming from quantum information and q…
Relativistic Quantum Simulation of Hydrogen Sulfide for Hydrogen Energy via Hybrid Quantum-Classical Algorithms
该研究提出结合狄拉克-库仑相对论量子化学与变分量子本征求解器（VQE）的混合量子-经典框架，模拟氢能相关H₂S分解，正确重现分子能量偏移与趋势，为可扩展重原子系统量子模拟提供见解。
A Wigner-Klein-Kramers equation is proposed, which merges relativistic, quantum and thermo dynamics. The relativistic effect on quantum Brownian motion is studied via the Breit-Fermi Hamiltonian applied into a dissipative Madelung hydrodynamics. A new thermo-quantum Smoluchowski equation is derived, which accounts for the relativistic correction of the Bohm quantum potential.
Conventional relativistic quantum mechanics, based on the Klein-Gordon equation, does not possess a natural probabilistic interpretation in configuration space. The Bohmian interpretation, in which probabilities play a secondary role, provides a viable interpretation of relativistic quantum mechanics. We formulate the Bohmian interpretation of many-particle wave functions in a Lorentz-covariant way. In contrast with the nonrelativistic case, the relativistic Bohmian interpretation may lead to measurable predictions on particle positions even when the conventional interpretation does not lead t…
Propagation in quantum walks is revisited by showing that very general 1D discrete-time quantum walks with time- and space-dependent coefficients can be described, at the continuous limit, by Dirac fermions coupled to electromagnetic fields. Short-time propagation is also established for relativistic diffusions by presenting new numerical simulations of the Relativistic Ornstein-Uhlenbeck Process. A geometrical generalization of Fick's law is also obtained for this process. The results suggest that relativistic diffusions may be realistic models of decohering or random quantum walks. Links wit…
A new relativistic quantum protocol is proposed allowing to implement the bit commitment scheme. The protocol is based on the idea that in the relativistic case the field propagation to the region of space accessible to measurement requires, contrary to the non-relativistic case, a finite non-zero time which depends on the structure of the particular state of the field. In principle, the secret bit can be stored for arbitrarily long time with the probability arbitrarily close to unit.
Relativistic quantum entanglement in a bipartite charged scalar system
研究利用连续变量可分性判据分析中心对称库仑势作用下两带电标量介子系统，严格证明相对论情形存在纠缠而非相对论情形可分。
Relativistic quantum information combines the informational approach to understanding and using quantum mechanics systems - quantum information - with the relativistic view of the universe. In this introductory review we examine key results to emerge from this new field of research in physics and discuss future directions. A particularly active area recently has been the question of what happens when quantum systems interact with general relativistic closed timelike curves - effectively time machines. We discuss two different approaches that have been suggested for modelling such situations. I…
Quantum walks are not only algorithmic tools for quantum computation but also not trivial models which describe various physical processes. The paper compares one-dimensional version of the free particle Dirac equation with discrete time quantum walk (DTQW). We show that the discretized Dirac equation when compared with DTQW results in interesting relations. It is also shown that two relativistic effects associated with the Dirac equation, namely Zitterbewegung (quivering motion) and Klein's paradox, are present in DTQW, which can be implemented within non-relativistic quantum mechanics.
For the electric polarizability of a bound system in relativistic quantum theory, there are two definitions that have appeared in the literature. They differ depending on whether or not the vacuum background is included in the system. A recent confusion in this connection is clarified.
In this work, we follow the idea of the De Broglie's matter waves and the analogous method that Schrödinger founded wave equation, but we apply the more essential Hamilton principle instead of the minimum action principle of Jacobi which was used in setting up Schrödinger wave equation. Thus, we obtain a novel non-relativistic wave equation which is different from the Schrödinger equation, and relativistic wave equation including free and non-free particle. In addition, we get the spin 1/2 particle wave equation in potential field.
By pursuing the deep relation between the one-dimensional Dirac equation and quantum walks, the physical role of quantum interference in the latter is explained. It is shown that the time evolution of the probability density of a quantum walker, initially localized on a lattice, is directly analogous to relativistic wave-packet spreading. Analytic wave-packet solutions reveal a striking connection between the discrete and continuous time quantum walks.
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