The generation of entangled states and their degree of entanglement is studied ab initio in a relativistic formulation for the case of two interacting spin-1/2 charged particles. In the realm of quantum electrodynamics we derive the interaction that produces entanglement between the spin components of covariant Dirac spinors describing the two particles. Following this consistent approach the relativistic invariance of the generated entanglement is discussed.
In this study, the spin-momentum correlation of one massive spin-1/2 and spin-1 particle states, which are made based on projection of a relativistic spin operator into timelike direction is investigated. It is shown that by using Non-Linear entanglement witnesses (NLEWs), the effect of Lorentz transformation would decrease both the amount and the region of entanglement.
This article considers dynamical entanglement in non-relativistic particle scattering. Three questions are explored: what kinds of entanglement occur in this system, how do global symmetries constrain entanglement, and how do the boundary conditions of scattering affect dynamical entanglement? First, a simple model of scattering spin systems is considered, then the full system is discussed.
This paper considers the use an entanglement breaking channel in the construction of a secure bit-commitment protocol. It is shown that this can be done via a depolarizing quantum channel.
The study of Entanglement of Formation of a mixed state of a bipartite system in high-dimensional Hilbert space is not easy in general. So, we focus on determining the amount of entanglement for a bipartite mixed state based on the concept of decomposable optimal entanglement witness (DOEW), that can be calculated as a minimum distance of an entangled state from the edge of positive partial transpose (PPT) states which has the most negative (positive) expectation value for non-PPT (bound) entangled states. We have constructed DOEWs based on the convex optimization method, then by using of it w…
This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important parameter to characterize this kind entanglement. ``Beam-like'' entanglement and ``shape-like'' entanglement are contrasted. One example of this kind of entanglement is between between the spin degrees of freedom and the momentum degrees of freedom for a non-relativistic particle. This intraparticle entanglement is Galilean invariant.
The entanglement between spins of a pair of particles may change because the spin and momentum become mixed when viewed by a moving observer [R.M. Gingrich and C. Adami, Phys. Rev. Lett. 89, 270402 (2002)]. In this paper, it is shown that, if the momenta are appropriately entangled, the entanglement between the spins of the Bell states can remain maximal when viewed by any moving observer. Further, we suggest a relativistic-invariant protocol for quantum communication, with which the non-relativistic quantum information theory could be invariantly applied to relativistic situations.
Recent work has argued that the concepts of entanglement and nonlocality must be taken seriously even in systems consisting of only a single particle. These treatments, however, are nonrelativistic and, if single particle entanglement is fundamental, it should also persist in a relativistic description. Here we consider a spin-1/2 particle in a superposition of two different velocities as viewed by an observer in a different relativistically-boosted inertial frame. We show that the entanglement survives right up to the speed of light and that the boosted observer would see single-particle viol…
I numerically simulate and compare the entanglement of two quanta using the conventional formulation of quantum mechanics and a time-symmetric formulation that has no collapse postulate. The experimental predictions of the two formulations are identical, but the entanglement predictions are significantly different. The time-symmetric formulation reveals an experimentally testable discrepancy in the original quantum analysis of the Hanbury Brown-Twiss experiment, suggests solutions to some parts of the nonlocality and measurement problems, fixes known time asymmetries in the conventional formul…
In this work we analyze the amount of entanglement associated with the spin and momentum degrees of freedom of a single massive spin-$\frac{1}{2}$ particle from a relativistic perspective. The effect of a Lorentz boost introduces a Wigner rotation that correlates the spin and momentum degrees of freedom. We show that the natural basis to discuss the geometrical effects of the boost are the helicity eigenstates in the rest frame. In the mid-relativistic regime (where the Wigner rotation angle is limited by $δ< \fracπ{2}$) we prove for states with equal helicity that the entanglement with respec…
In this work we study the entanglement properties under a Lorentz boost of a pair of spin- 1 massive particles, with spin and momentum as the sole degrees of freedom of the system. Different cases for entanglement between spins and momenta are considered as initial states and it is shown that entanglement between the different degrees of freedom is, in general, not invariant. We analyze the entanglement change in terms of the Wigner rotation induced by the transformation and show that, for the case of spin-1 particles, the relative entanglement change between different states depends strongly …
I present a schema for a superluminal telecommunication system based on polarization entangled photon pairs. Binary signals can be transmitted at superluminal speed in this system, if entangled photon pairs can really be produced. The existence of the polarization entangled photon pairs is in direct contradiction to the relativistic causality in this telecommunication system. This contradiction implies the impossibility of generating entangled photon pairs.
In this paper we explore the entanglement of two relativistic spin-$1/2$ particles with continuous momenta. The spin state is described by the Bell state and the momenta are given by Gaussian distributions of product form. Transformations of the spins are systematically investigated in different boost scenarios by calculating the orbits and concurrence of the spin degree of freedom. By visualizing the behavior of the spin state we get further insight into how and why the entanglement changes in different boost situations.
Efficiencies of quantum information protocols can be affected by the noninertial motion of involved parties, e.g., in a gravitational field. Most of the previous studies focused on the effects of such a motion on a bipartite entanglement as a resource. We show how a tripartite Gaussian resource state of continuous variables is affected by the acceleration of the observers. Specifically, we analyze how genuine tripartite entanglement degrades due to the motion for various initial states and trajectories of the involved parties.
In this paper, the Lorentz transformation of the entangled Bell states with momentum, not necessarily orthogonal to the boost direction, and spin, is studied. We extended quantum correlations and Bell's inequality to the relativistic regime by considering normalized relativistic observables. It is shown that quantum information, along the perpendicular direction to the boost, is eventually lost and Bell's inequality is not always violated for entangled states in special relativity. This could impose restrictions to certain quantum information processing such as quantum cryptography using massi…
Two kinds of Bell-states diagonal (BSD) entanglement witnesses (EW) are constructed by using the algebra of Dirac $γ$ matrices in the space-time of arbitrary dimension $d$, where the first kind can detect some BSD relativistic and non-relativistic $m$-partite multispinor bound entangled states in Hilbert space of dimension $2^{m\lfloor d/2\rfloor}$, including the bipartite Bell-type and iso-concurrence type states in the four-dimensional space-time ($d=4$). By using the connection between Hilbert-Schmidt measure and the optimal EWs associated with states, it is shown that as far as the spin qu…
Recent work has shown how single-particle entangled states are transformed when boosted in relativistic frames for certain restricted geometries. Here we extend that work to consider completely general inertial boosts. We then apply our single particle results to multiparticle entanglements by focussing on Cooper pairs of electrons. We show that a standard Cooper pair state consisting of a spin-singlet acquires spin-triplet components in a relativistically boosted inertial frame, regardless of the geometry. We also show that, if we start with a spin-triplet pair, two out of the three triplet s…
We revisit the properties of qubits under Lorentz transformations and, by considering Lorentz invariant quantum states in the Heisenberg formulation, clarify some misleading notation that has appeared in the literature on relativistic quantum information theory. We then use this formulation to consider the transformation properties of qubits and density matrices under space-time and gauge transformations. Finally we use our results to understand the behaviour of entanglement between different partitions of quantum systems. Our approach not only clarifies the notation, but provides a more intui…
Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.
We analyze multipartite entanglement in systems of spin-1/2 particles from a relativistic perspective. General conditions which have to be met for any classification of multipartite entanglement to be Lorentz invariant are derived, which contributes to a physical understanding of entanglement classification. We show that quantum information in a relativistic setting requires the partition of the Hilbert space into particles to be taken seriously. Furthermore, we study exemplary cases and show how the spin and momentum entanglement transforms relativistically in a multipartite setting.
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.
Anyonic systems are modeled by topologically protected Hilbert spaces which obey complex superselection rules restricting possible operations. These Hilbert spaces cannot be decomposed into tensor products of spatially localized subsystems, whereas the tensor product structure is a foundation of the standard entanglement theory. We formulate bipartite entanglement theory for pure anyonic states and analyze its properties as a non-local resource for quantum information processing. We introduce a new entanglement measure, asymptotic entanglement entropy (AEE), and show that it characterizes dist…
In this paper, the Lorentz transformation of entangled Bell states seen by a moving observer is studied. The calculated Bell observable for 4 joint measurements turns out to give a universal value, $<\hat{a}\otimes\vec{b}>+<\hat{a}\otimes\vec{b}'>+\lang le\hat{a}'\otimes\vec{b}> -<\hat{a}'\otimes\vec{b}'>=\frac{2}{\sqrt{2-β^2}}(1+\sqrt{1-\be ta^2})$, where $\hat{a}, \hat{b}$ are the relativistic spin observables derived from the Pauli-Lubanski pseudo vector and $β=\frac{v}{c}$. We found that the degree of violation of the Bell's inequality is decreasing with increasing velocity of the observer…
Entanglement distance is the maximal separation between two entangled electrons in a degenerate electron gas. Beyond that distance, all entanglement disappears. We relate entanglement distance to degeneracy pressure both for extreme relativistic and non-relativistic systems, and estimate the entanglement distance in a white dwarf. Treating entanglement as a thermodynamical quantity, we relate the entropy of formation and concurrence to relative electron distance, pressure, and temperature, to form a new equation of state for entanglement.
In this article we present an analysis to derive physical results in the entanglement amplification of fermonic systems in the relativistic regime, that is, beyond the single-mode approximation. This leads a recent work in [M. Montero and E. Martín-Martínez, JEHP 07 (2011) 006] to a physical result, and solidifies that phenomenon of entanglement amplification can actually happen in the relativistic regime.
The relativistic quantum theory of Stueckelberg, Horwitz and Piron (SHP) describes in a simple way the experiment on interference in time of an electron emitted by femtosecond laser pulses carried out by Lindner et al. In this paper, we show that, in a way similar to our study of the Lindner et al experiment (with some additional discussion of the covariant quantum mechanical description of spin and angular momentum), the experiment proposed by Palacios et al to demonstrate entanglement of a two electron state, where the electrons are separated in time of emission, has a consistent interpretat…
We study the structure of maps that Lorentz boosts induce on the spin degree of freedom of a system consisting of two massive spin-$1/2$ particles. We consider the case where the spin state is described by the Werner state and the momenta are discrete. Transformations on the spins are systematically investigated in various boost scenarios by calculating the orbit and concurrence of the bipartite spin state with different kinds of product and entangled momenta. We confirm the general conclusion that Lorentz boosts cause non-trivial behavior of bipartite spin entanglement. Visualization of the e…
We provide a simple argument showing that, in the limit of infinite acceleration, the entanglement in a fermionic field bipartite system must be independent of the choice of Unruh modes. This implies that most tensor product structures used previously to compute field entanglement in relativistic quantum information cannot give rise to physical results.
We discuss an alternative formulation of the problem of quantum optical fields in a curved space-time using localized operators. We contrast the new formulation with the standard approach and find observable differences for entangled states. We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields and find that the new formulation predicts de-correlation of the optical entanglement under experimentally realistic conditions.
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.
One of the most fundamental phenomena of quantum physics is entanglement. It describes an inseparable connection between quantum systems, and properties thereof. In a quantum mechanical description even systems far apart from each other can share a common state. This entanglement of the subsystems, although arising from mathematical principles, is no mere abstract concept, but can be tested in experiment, and be utilized in modern quantum information theory procedures, such as quantum teleportation. In particular, entangled states play a crucial role in testing our understanding of reality, by…
We make a critical comparison of relativistic and non-relativistic classical and quantum mechanics of particles in inertial frames and of the open problems in particle localization at the two levels. The solution of the problems of the relativistic center of mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled non-local (non-measurable) relativistic center of mass and with only relative variables for the particles (single particle subsystems do n…
Entanglement criteria for an $n$-partite quantum system with continuous variables are formulated in terms of Rényi entropies. Rényi entropies are widely used as a good information measure due to many nice properties. Derived entanglement criteria are based on several mathematical results such as the Hausdorff-Young inequality, Young's inequality for convolution and its converse. From the historical viewpoint, the formulations of these results with sharp constants were obtained comparatively recently. Using the position and momentum observables of subsystems, one can build two total-system meas…
In this thesis, entanglement under fully relativistic settings are discussed. The thesis starts with a brief review of the relativistic quantum mechanics. In order to describe the effects of Lorentz transformations on the entangled states, quantum mechanics and special relativity are merged by construction of the unitary irreducible representations of Poincar{é} group on the infinite dimensional Hilbert space of state vectors. In this framework, the issue of finding the unitary irreducible representations of Poincar{é} group is reduced to that of the little group. Wigner rotation for the massi…
The last two decades have witnessed an increasing effort of the scientific community toward pursuing a better framework for quantum resource covariance, with the focus predominantly posed on quantum entanglement. In this work, we move the discussion one step further by analyzing the behavior of both genuine multipartite entanglement and quantum coherence under Lorentz boosts. Specifically, we conduct a case study for the problem of an electron-positron pair created in a superposed multipartite pure state. Our approach is different from the standard treatments also in that we consider all the c…
We show that the relativistic motion of a quantum system can be used to generate quantum gates. The nonuniform acceleration of a cavity is used to generate well-known two-mode quantum gates in continuous variables. Observable amounts of entanglement between the cavity modes are produced through resonances which appear by repeating periodically any trajectory.
Entanglement has long been the subject of discussion by philosophers of quantum theory, and has recently come to play an essential role for physicists in their development of quantum information theory. In this paper we show how the formalism of algebraic quantum field theory (AQFT) provides a rigorous framework within which to analyze entanglement in the context of a fully relativistic formulation of quantum theory. What emerges from the analysis are new practical and theoretical limitations on an experimenter's ability to perform operations on a field in one spacetime region that can disenta…
We study the properties of entanglement entropy among scattering particles as observed from different inertial moving frames, based on an exemplary QED process $e^+e^-\rightarrowμ^+μ^-$. By the explicit calculation of the Wigner rotation, the entanglement entropy of scattering particles is found to be Lorentz invariant. We also study the behavior of the entanglement between spin degrees of freedom for scattering particles in moving frames. This quantity, being found to change with different inertial reference frames, does not exhibit as a Lorentz invariant.
Description of time evolution of the relativistic unstable electromagnetic system consisting of Fermi-Dirac particle interacting with electromagnetic field, in the framework of the Liouville space extension of quantum mechanics is done. The work was carried out on the basis of Prigogine's unified formulation of quantum and kinetic dynamics. The eigenvalues problem for the relativistic Hamiltonian of the electromagnetic system was solved. The obtained results can be used as the ground for the further studies of the observed physical processes such as bremsstrahlung, relaxation of excited states…
Superposition states are at the origin of many paradoxes in quantum mechanics. By unraveling the von Neumann equation for density matrices, we develop a superposition-free formulation of quantum mechanics. Stochastic quantum jumps are a key feature of this approach, in blatant contrast with the continuity of the deterministic Schrödinger equation. We explain how quantum entanglement arises. Our superposition-free formulation results offers a new perspective on quantum mechanics.
I present some general ideas about quantum entanglement in relativistic quantum field theory, especially entanglement in the physical vacuum. Here, entanglement is defined between different single particle states (or modes), parameterized either by energy-momentum together with internal degrees of freedom, or by spacetime coordinate together with the component index in the case of a vector or spinor field. In this approach, the notion of entanglement between different spacetime points can be established. Some entanglement properties are obtained as constraints from symmetries, e.g., under Lore…
Quantum computing is among the most far-reaching technologies of the 21st century, tackling challenges at the cutting edge of physics. This new paradigm in computer science harnesses quantum entanglement, one striking non-intuitive feature of quantum mechanics and a cornerstone of quantum information, to provide computation with a quantum speed-up over the best-known classical algorithms and to enable encrypted data communication against eavesdropping. The bulk of this article is focused on providing a deep and abiding understanding of non-relativistic matrix mechanics by demonstrating the fun…
On this PhD thesis we cover the results contained in arXiv:2001.07050, arXiv:2111.10096 and arXiv:2011.02822, while providing further details about their derivations. In the first two papers, we study the generation and detection of entangled non-Gaussian states of microwave radiation. These states are produced in a new parametric oscillator, built recently within the field of cQED, capable of down-converting a microwave tone into three different tones at once. These three photons share among their magnitudes quantum correlations, in particular genuine entanglement. In this text we refer to it…
The combination of quantum theory and special relativity leads to structures that differ in several respects from non-relativistic quantum mechanics of particles. These differences are quite familiar to practitioners of Algebraic Quantum Field Theory but less well known outside this community. The paper is intended as a concise survey of some selected aspects of relativistic quantum physics, in particular regarding localization and entanglement.
This article develops a variational formulation for the relativistic Klein-Gordon equation. The main results are obtained through an extension of the classical mechanics approach to a more general context, which in some sense, includes the quantum mechanics one. For the second part of the text, the definition of normal field and its relation with the wave function concept play a fundamental role in the main results establishment. Among the applications, we include a model with the presence of electromagnetic fields and also the modeling of a chemical reaction. Finally, in the last section, we …
Entanglement is defined between subsystems of a quantum system, and at fixed time two regions of space can be viewed as two subsystems of a relativistic quantum field. The entropy of entanglement between such subsystems is ill-defined unless an ultraviolet cutoff is introduced, but it still diverges in the continuum limit. This behaviour is generic for arbitrary finite-energy states, hence a conceptual tension with the finite entanglement entropy typical of nonrelativistic quantum systems. We introduce a novel approach to explain the transition from infinite to finite entanglement, based on co…
This paper was concerned with the spin-momentum correlation in single-particle quantum states, which is described by the mixed states under Lorentz transformations. For convenience, instead of using the superposition of momenta we use only two momentum eigen states (p1 and p2) that are perpendicular to the Lorentz boost direction. Consequently, in 2D momentum subspace we show that the entanglement of spin-momentum in the moving frame depends on the angle between them. Therefore, when spin and momentum are perpendicular the measure of entanglement is not observer-dependent quantity in inertial …
We calculate entanglement entropy in a non-relativistic field theory described by the Schrödinger operator. We demonstrate that the entropy is characterized by i) the area law and ii) UV divergences that are identical to those in the relativistic field theory. These observations are further supported by a holographic consideration. We use the non-relativistic symmetry and completely specify entanglement entropy in large class of non-relativistic theories described by the field operators polynomial in derivatives. We suggest that the area law of the entropy can be tested in experiments with con…
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits [Phys. Rev. A 61, 052306 (2000)] to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states [Phys. Rev. A 72, 022333 (2005)]. A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore, the formulation f…
We show that simulated relativistic motion can generate entanglement between artificial atoms and protect them from spontaneous emission. We consider a pair of superconducting qubits coupled to a resonator mode, where the modulation of the coupling strength can mimic the harmonic motion of the qubits at relativistic speeds, generating acceleration radiation. We find the optimal feasible conditions for generating a stationary entangled state between the qubits when they are initially prepared in their ground state. Furthermore, we analyze the effects of motion on the probability of spontaneous …
In this paper, an intuitive mathematical formulation is provided to generalize the residual entanglement for tripartite systems of qubits (Phys. Rev. A \textbf{61}, 052306 (2000)) to the tripartite systems in higher dimension. The spirit lies in the tensor treatment of tripartite pure states (Phys. Rev. A \textbf{72}, 022333 (2005)). A distinct characteristic of the present generalization is that the formulation for higher dimensional systems is invariant under permutation of the subsystems, hence is employed as a criterion to test the existence of genuine tripartite entanglement. Furthermore,…
Circuit locality from relativistic locality in scalar field mediated entanglement
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（维也纳量子光学与量子信息研究所）；Basic Research Community for Physics e.V.（基础物理社区协会）；Physics Department, Royal Holloway, University of London（伦敦大学皇家霍洛威学院物理系）；Quantum Group, Department of Computer Science, University of Oxford（牛津大学计算机科学系量子组）；Vienna Center for Quantum Science and Technology (VCQ), Faculty of Physics, University of Vienna（维也纳大学物理学院量子科学与技术中心）；Research Platform TURIS, University of Vienna（维也纳大学TURIS研究平台）；Aix-Marseille University, Université de Toulon, CPT-CNRS（艾克斯-马赛大学，土伦大学，CPT-CNRS）；Department of Philosophy and the Rotman Institute of Philosophy, Western University（韦仕敦大学哲学系及罗特曼哲学研究所）；Perimeter Institute（珀尔默特研究所）
