In several recent papers on entanglement in relativistic quantum systems and relativistic Bell's inequalities, relativistic Bell-type two-particle states have been constructed in analogy to non-relativistic states. These constructions do not have the form suggested by relativistic invariance of the dynamics. Two relativistic formulations of Bell-type states are shown for massive particles, one using the standard Wigner spin basis and one using the helicity basis. The construction hinges on the use of Clebsch-Gordan coefficients of the Poincaré group to reduce the direct product of two unitary irreducible representations (UIRs) into a direct sum of UIRs.
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 Letter we show that in relativistic regime maximally entangled state of two spin-1/2 particles not only gives maximal violation of the Bell-CHSH inequality but also gives the largest violation attainable for any pairs of four spin observables that are noncommuting for both systems. Also we extend our results to three spin-1/2 particles. We obtain the largest eigenvalue of Bell operator and show that this value is equal to expectation value of Bell operator on GHZ state.
It is argued that the standard quantum mechanical description of the Bell correlations between entangled subsystems is in conflict with relativistic space-time symmetry. Proposals to abandon relativistic symmetry, in the sense of explicitly returning to an absolute time and preferred frame, are rejected on the grounds that the preferred frame is not empirically detectable, so the asymmetry is an unsatisfactory feature in physical theory. A "symmetric view" is proposed in which measurement events on space-like separated entangled subsystems are connected by a symmetric two-way mutual influence.…
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.
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…
We use the concept of quantum entanglement to analyze the Schwinger effect on an entangled state of a qubit and a bosonic mode coupled with the electric field. As a consequence of the Schwinger production of particle-antiparticle pairs, the electric field decreases both the correlation and the entanglement between the qubit and the particle mode. This work exposes a profound difference between bosons and fermions. In the bosonic case, entanglement between the qubit and the antiparticle mode cannot be caused by the Schwinger effect on the preexisting entanglement between the qubit and the parti…
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…
All information in quantum systems is, notwithstanding Bell's theorem, localised. Measuring or otherwise interacting with a quantum system S has no effect on distant systems from which S is dynamically isolated, even if they are entangled with S. Using the Heisenberg picture to analyse quantum information processing makes this locality explicit, and reveals that under some circumstances (in particular, in Einstein-Podolski-Rosen experiments and in quantum teleportation) quantum information is transmitted through 'classical' (i.e. decoherent) information channels.
We study the influence of Unruh effect on quantum non-zero sum games. In particular, we investigate the quantum Prisoners' Dilemma both for entangled and unentangled initial states and show that the acceleration of the noninertial frames disturbs the symmetry of the game. It is shown that for maximally entangled initial state, the classical strategy C (cooperation) becomes the dominant strategy. Our investigation shows that any quantum strategy does no better for any player against the classical strategies. The miracle move of Eisert et al (1999 Phys. Rev. Lett. 83 3077) is no more a superior …
Consistency with relativistic causality narrows down dramatically the class of measurable observables. We argue that by weakening the preparation role of ideal measurements, many of these observables become measurable. Particularly, we show by applying entanglement assisted remote operations, that all Hermitian observable of a $2\times2$-dimensional bipartite system are measurable.
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.
Entangled photon pairs are key to many novel applications in quantum technologies. Semiconductor quantum dots can be used as sources of on-demand, highly entangled photons. The fidelity to a fixed maximally entangled state is limited by the excitonic fine-structure splitting. This work demonstrates that, even if this splitting is absent, the degree of entanglement cannot reach unity when the excitation pulse in a two-photon resonance scheme has a finite duration. The degradation of the entanglement has its origin in a dynamically induced splitting of the exciton states caused by the laser puls…
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…
A silicon quantum photonic circuit was proposed and demonstrated as an integrated quantum light source for telecom band polarization entangled Bell state generation and dynamical manipulation. Biphoton states were firstly generated in four silicon waveguides by spontaneous four wave mixing. They were transformed to polarization entangled Bell states through on-chip quantum interference and quantum superposition, and then coupled to optical fibers. The property of polarization entanglement in generated photon pairs was demonstrated by two-photon interferences under two non-orthogonal polarizati…
Robust Preparation of Bell States by Time Boundary Effect
School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；School of Physics Science and Technology, Kunming University（昆明大学物理科学与技术学院）；National Laboratory of Solid State Microstructures, Department of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理系和先进微结构协同创新中心）
We study special relativistic effects on the entanglement between either spins or momenta of composite quantum systems of two spin-1/2 massive particles, either indistinguishable or distinguishable, in inertial reference frames in relative motion. For the case of indistinguishable particles, we consider a balanced scenario where the momenta of the pair are well-defined but not maximally entangled in the rest frame while the spins of the pair are described by a one-parameter ($η$) family of entangled bipartite states. For the case of distinguishable particles, we consider an unbalanced scenario…
We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field theories. We explicitly show how such a state can approximate and eventually converge to the free field theory vacuum and suggest a regularization-independent way of estimating the convergence via a universal term in the fidelity per-site. We also present a detailed bottom-up construction of the cPEPS as the continuum limit of the conventional lattice Projected En…
A possible causal solution to the problem of providing a spacetime description of the transmission of signals in quantum entangled states is described using a `bimetric' spacetime structure, in which the quantum entanglement measurements alter the structure of spacetime. Possible experimental tests to verify the suggested spacetime interpretation of quantum entangled states are proposed.
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.
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…
A possible solution to the problem of providing a spacetime description of the transmission of signals for quantum entangled states is obtained by using a bimetric spacetime structure, in which quantum entanglement measurements alter the structure of the classical relativity spacetime. A bimetric gravity theory locally has two lightcones, one which describes classical special relativity and a larger lightcone which allows light signals to communicate quantum information between entangled states, after a measurement device detects one of the entangled states. The theory would remove the tension…
We demonstrate how to construct a lorentz-invariant, hidden-variable interpretation of relativistic quantum mechanics based on particle trajectories. The covariant theory that we propose employs a multi-time formalism and a lorentz-invariant rule for the coordination of the space-time points on the individual particle trajectories. In this way we show that there is no contradiction between nonlocality and lorentz invariance in quantum mechanics. The approach is illustrated for relativistic bosons, using a simple model to discuss the individual non-locally correlated particle motion which ensue…
We study the transformation of maximally entangled states under the action of Lorentz transformations in a fully relativistic setting. By explicit calculation of the Wigner rotation, we describe the relativistic analog of the Bell states as viewed from two inertial frames moving with constant velocity with respect to each other. Though the finite dimensional matrices describing the Lorentz transformations are non-unitary, each single particle state of the entangled pair undergoes an effective, momentum dependent, local unitary rotation, thereby preserving the entanglement fidelity of the bipar…
Spontaneous collapse models are proposed modifications to quantum mechanics which aim to solve the measurement problem. In this article we will consider models which attempt to extend a specific spontaneous collapse model, the Ghirardi-Rimini-Weber model (GRW), to be consistent with special relativity. We will present a condition that a relativistic GRW model must meet for three cases: for single particle, for N distinguishable particles, and for indistinguishable particles. We will then show that this relativistic condition implies that one can have a relativistic GRW model for a single parti…
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…
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…
In 1935, Einstein, Podolsky and Rosen (EPR) considered two particles in an entangled state of motion to illustrate why they questioned the completeness of quantum theory. In the past decades, microscopic systems with entanglement in various degrees of freedom have successfully been generated, representing compelling evidence to support the completeness of quantum theory. Today, the generation of an EPR-entangled state of motion of two massive objects of up to the kilogram-scale seems feasible with state-of-the-art technology. Recently, the generation and verification of EPR-entangled mirror mo…
We show that a pair of massive relativistic spin-1/2 particles prepared in a maximally entangled spin state in general is not capable of maximally violating the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequalities without a post-selection of the particles momenta, representing a major difference in relation to non-relativistic systems. This occurs because the quantization axis of the measurements performed on each particle depends on the particle velocity, such that it is not possible to define a reduced density matrix for the particles spin. We also show that the amount of violati…
This is a pedagogical paper, where bispinors solutions to the four-dimensional massless Dirac equation are considered in relativistic quantum mechanics and in quantum computation, taking advantage of the common mathematical description of four dimensional spaces. First, Weyl and massless Majorana bispinors are shown to be unitary equivalent, closing a gap in the literature regarding their equivalence. A discrepancy in the number of linearly independent solutions reported in the literature is also addressed. Then, it is shown that Weyl bispinors are algebraically equivalent to two-qubit direct …
A Lagrangian formulation is constructed for particle interpretations of quantum mechanics, a well-known example of such an interpretation being the Bohm model. The advantages of such a description are that the equations for particle motion, field evolution and conservation laws can all be deduced from a single Lagrangian density expression. The formalism presented is Lorentz invariant. This paper follows on from a previous one which was limited to the single-particle case. The present paper treats the more general case of many particles in an entangled state. It is found that describing more t…
The nonlocal action of a measurement performed on a quantum entangled particle can determine the quantum state of a distant entangled particle instantly. Since the relativistic simultaneity of events is frame dependent therefore, a physically valid question arises, does the nonlocal action at a distance determine the quantum state of the distant particle in its past, when quantum state collapse is observed from a different inertial frame of reference? From the relativity of simultaneity, Lorentz invariance of the quantum entangled state of photons under consideration and the validity of Bell's…
We present a local interpretation of what is usually considered to be a nonlocal de Broglie-Bohm trajectory prescription for an entangled singlet state of massive particles. After reviewing various meanings of the term ``nonlocal'', we show that by using appropriately retarded wavefunctions (i.e., the locality loophole) this local model can violate Bell's inequality, without making any appeal to detector inefficiencies. We analyze a possible experimental configuration appropriate to massive two-particle singlet wavefunctions and find that as long as the particles are not ultra-relativistic, a …
The "problem of time" in present physics substantially consists in the fact that a straightforward quantization of the general relativistic evolution equation and constraints generates for the Universe wave function the Wheeler-De Witt equation, which describes a static Universe. Page and Wootters considered the fact that there exist states of a system composed by entangled subsystems that are stationary, but one can interpret the component subsystems as evolving: this leads them to suppose that the global state of the universe can be envisaged as one of this static entangled state, whereas th…
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 propose a mechanism to change the interaction strengths of a two component condensate. It is shown that the application of pi/2 pulses allows to alter the effective interspecies interaction strength as well as the effective interaction strength between particles of the same kind. This mechanism provides a simple method to transform spatially stable condensates into unstable once and vice versa. It also provides a means to store a squeezed spin state by turning off the interaction for the internal states and thus allows to gain control over many body entangled states.
We consider the environment-affected dynamics of $N$ self-interacting particles living in one-dimensional double wells. Two topics are dealt with. First, we consider the production of entangled states of two-level systems. We show that by adiabatically varying the well biases we may dynamically generate maximally entangled states, starting from initially unentangled product states. Entanglement degradation due to a common type of environmental influence is then computed by solving a master equation. However, we also demonstrate that entanglement production is unaffected if the system-environme…
The stability of two entangled spins dressed by electrons is studied by calculating the scattering phase shifts. The interaction between electrons is interpreted by fully relativistic QED and the screening effect is described phenomenologically in the Debye exponential form $e^{-αr}$. Our results show that if the (Einstein-Podolsky-Rosen-) EPR-type states are kept stable under the interaction of QED, the spatial wave function must be parity-dependent. The spin-singlet state $s=0$ and the polarized state $\frac 1{\sqrt{2}}(\mid +-> -\mid -+>)$ along the z-axis\QTR{bf}{\}give rise to two differe…
Quantum entanglement as the one of the most general quantum resources, can be quantified by von Neumann entropy. However, as we know, the von Neumann entropy is only statistical quantity or operator, it therefore has fluctuation. The quantum fluctuation of entanglement (QFE) between Unruh-Dewitt detector modeled by a two-level atom is investigated in a relativistic setting. The Unruh radiation and quantum fluctuation effects affect the precise measurement of quantum entanglement. Inspired by this we present how the relativistic motion effects QFE for two entangled Unruh-Dewitt detectors when o…
In this contribution I will review the analysis of the Einstein-Podolsky-Rosen argument, Bell's inequalities and of associated experiments for spins in terms of positive operator valued measures. Specifically, I will explore the relation between the Clauser-Horne-Shimony-Holt inequality and a fundamental \emph{classicality} property of observables -- their \emph{coexistence}. A derivation of Bell's inequalities for unsharp spins will be given which follows a reconstruction by Mittelstaedt and Stachow of the original EPR argument. In this context we discuss the need for a consistent relativisti…
Demonstrations of quantum entanglement which confirm the violation of Bell's inequality indicate that under certain conditions action at a distance is possible. This consequence seems to contradict the relativistic principle of causality, which asserts that an effect never precedes its cause, in any reference frame. By analyzing a numerical example of Bell's experiment with entangled pairs of photons, we show how observers in two inertial reference frames can disagree about the causality relation between two events. One observer claims that event 1 is the cause of event 2, while the other clai…
We report on a new kind of experimental investigations of the tension between quantum nonlocally and relativity. Entangled photons are sent via an optical fiber network to two villages near Geneva, separated by more than 10 km where they are analyzed by interferometers. The photon pair source is set as precisely as possible in the center so that the two photons arrive at the detectors within a time interval of less than 5 ps (corresponding to a path length difference of less than 1 mm). One detector is set in motion so that both detectors, each in its own inertial reference frame, are first to…
In this work we consider the following problem: in a Multi-Prover environment, how close can we get to prove the validity of an NP statement in Zero-Knowledge ? We exhibit a set of two novel Zero-Knowledge protocols for the 3-COLorability problem that use two (local) provers or three (entangled) provers and only require them to reply two trits each. This greatly improves the ability to prove Zero-Knowledge statements on very short distances with very minimal equipment.
A still widely debated question in the field of relativistic quantum information is whether entanglement and the degree of violation of Bell's inequalities for massive relativistic particles are frame independent or not. At the core of this question is the effect that spin gets entangled with the momentum degree of freedom at relativistic velocities. Here, we show that Bell's inequalities for a pair of particles can be maximally violated in a special-relativistic regime, even without any post-selection of the momentum of the particles. To this end, we use the methodology of quantum reference f…
Two types of quantum measurements, measuring the spins of an entangled pair and attempting to measure a spin at either of two positions, are analysed dynamically by apparatuses of the Curie-Weiss type. The outcomes comply with the standard postulates.
The principles and methods of the Conformal Quantum Geometrodynamics (CQG) based on the Weyl's differential geometry are presented. The theory applied to the case of the relativistic single quantum spin 1/2 leads a novel and unconventional derivation of Dirac's equation. The further extension of the theory to the case of two spins 1/2 in EPR entangled state and to the related violation of Bell's inequalities leads, by an exact albeit non relativistic analysis, to an insightful resolution of all paradoxes implied by quantum nonlocality.
The spin is the prime example of a qubit. Encoding and decoding information in the spin qubit is operationally well defined through the Stern-Gerlach set-up in the non-relativistic (i.e., low velocity) limit. However, an operational definition of the spin in the relativistic regime is missing. The origin of this difficulty lies in the fact that, on the one hand, the spin gets entangled with the momentum in Lorentz-boosted reference frames, and on the other hand, for a particle moving in a superposition of velocities, it is impossible to "jump" to its rest frame, where spin is unambiguously def…
