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. It is argued that the approach based on matching the density operator of the quantum state between the future and past most consistently avoids the paradoxes usually associated with time travel.
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.
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.
We present a machine-learning scheme based on the relativistic dynamics of a quantum system, namely a quantum detector inside a cavity resonator. An equivalent analog model can be realized for example in a circuit QED platform subject to properly modulated driving fields. We consider a reservoir-computing scheme where the input data are embedded in the modulation of the system (equivalent to the acceleration of the relativistic object) and the output data are obtained by linear combinations of measured observables. As an illustrative example, we have simulated such a relativistic quantum machi…
The charge spreading of ground and excited states of Klein-Gordon particles moving in a Coulomb potential is quantitatively analyzed by means of the ordinary moments and the Heisenberg measure as well as by use of the most relevant information-theoretic measures of global (Shannon entropic power) and local (Fisher's information) types. The dependence of these complementary quantities on the nuclear charge Z and the quantum numbers characterizing the physical states is carefully discussed. The comparison of the relativistic Klein-Gordon and non-relativistic Schrodinger values is made. The non-r…
As Lanzagorta and Crowder have shown in their Comment [Phys. Rev. A 96, 026101 (2017)], the linear application of the Wigner rotations to the quantum state of two massive relativistic particles does not entail the instantaneous transmission of information as we concluded in our paper [Phys. Rev. A 87, 042102 (2013)]. But in the new version of our paper in arXiv [arXiv:1303.4367v2] we show (and solve) another paradox that is generated by the linear application of the Wigner rotations to a system with a single relativistic particle. So the conclusion of our paper that we cannot in general linear…
In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. To show that our new formulation can be applied to practic…
We show that a passing gravitational wave may influence the spin entropy and spin negativity of a system of $N$ massive spin-1/2 particles, in a way that is characteristic of the radiation. We establish the specific conditions under which this effect may be nonzero. The change in spin entropy and negativity, however, is extremely small. Here, we propose and show that this effect may be amplified through entanglement swapping. Relativistic quantum information theory may have a contribution towards the detection of gravitational wave.
In this paper, a method is developed to investigate the relativistic quantum information of anyons. Anyons are particles with intermediate statistics ranging between Bose-Einstein and Fermi-Dirac statistics, with a parameter $α$ ($0<α<1$) characteristic of this intermediate statistics. A density matrix is also introduced as a combination of the density matrices of bosons and fermions with a continuous parameter, $α$, that represents the behavior of anyons. This density matrix reduces to bosonic and fermionic density matrices in the limits $α\rightarrow 0$ and $α\rightarrow 1$,respectively. We …
We present a new treatment for the spin of a massive relativistic particle in the context of quantum information based on a physical interpretation of the Wigner rotations, obtaining different results in relation to the previous works. We are lead to the conclusions that it is not possible to define a reduced density matrix for the particle spin and that the Pauli-Lubanski (or similar) spin operators are not suitable to describe measurements where spin couples to an electromagnetic field in the measuring apparatus. These conclusions contradict the assumptions made by most of the previous paper…
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…
The process of teleportation of a completely unknown single-photon relativistic state is considered. Analysis of the relativistic case reveals that the teleportation as it is understood in the non-relativistic quantum mechanics is impossible if no {\it a priori} information on the state to be teleported is available. It is only possible to speak of the amplitude of the propagation of the field (taking into account the measurement procedure) since the existence of a common vacuum state together with the microcausality principle (the field operators commutation relations) make the concept of the…
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…
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.
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.
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.
It is shown that a general model for particle detection in combination with a linear application of the Wigner rotations, which correspond to momentum-dependent changes of the particle spin under Lorentz transformations, to the state of a massive relativistic particle in a superposition of two counter-propagating momentum states leads to a paradox. The paradoxical behavior is that the probability of finding the particle at different positions would depend on the reference frame. A solution to the paradox is given when the physical construction of the corresponding state is taken into account, …
The first part of the paper reviews applications of 2-spinor methods to relativistic qubits (analogies between tetrads in Minkowski space and 2-qubit states, qubits defined by means of null directions and their role for elimination of the Peres-Scudo-Terno phenomenon, advantages and disadvantages of relativistic polarization operators defined by the Pauli-Lubanski vector, manifestly covariant approach to unitary representations of inhomogeneous SL(2,C)). The second part deals with electromagnetic fields quantized by means of harmonic oscillator Lie algebras (not necessarily taken in irreducibl…
Information theory is a statistical theory dealing with the relative state of detectors and physical systems. Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time. Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood. This review recapitulates some milestones along this road, and speculates about future ones.
This thesis collects my own and collaborative work I have been involved with finding localised systems in quantum field theory that are useful for quantum information. It draws from many well established physical theories such as quantum field theory in curved spacetimes, quantum optics and Gaussian state quantum information. The results are split between three chapters. For the first results, we set-up the basic framework for working with quantum fields confined to cavities. By considering the real Klein-Gordon field, we describe how to model the non-uniform motion of a rigid cavity through s…
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.
We investigate how special relativity influences the transmission of classical information through quantum channels by evaluating the Holevo bound when the sender and the receiver are in (relativistic) relative motion. By using the spin degrees of freedom of spin-1/2 fermions to encode the classical information we show that, for some configurations, the accessible information in the receiver can be increased when the spin detector moves fast enough. This is possible by allowing the momentum wave packet of one of the particles to be wide enough while the momentum wave packets of other particles…
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.
Relativistic quantum metrology studies the maximal achievable precision for estimating a physical quantity when both quantum and relativistic effects are taken into account. We study the relativistic quantum metrology of temperature in (3+1)-dimensional de Sitter and anti-de Sitter space. Using Unruh-DeWitt detectors coupled to a massless scalar field as probes and treating them as open quantum systems, we compute the Fisher information for estimating temperature. We investigate the effect of acceleration in dS, and the effect of boundary condition in AdS. We find that the phenomenology of the…
We address the teleportation of single- and two-qubit quantum states, parametrized by weight $θ$ and phase $ϕ$ parameters, in the presence of the Unruh effect experienced by a mode of a free Dirac field. We investigate the effects of the partial measurement (PM) and partial measurement reversal (PMR) on the quantum resources (QRs) and quantum Fisher information (QFI) of the teleported states. In particular, we discuss the optimal behavior of the QFI, quantum coherence (QC) as well as fidelity with respect to the PM and PMR strength and examine the effect of the Unruh noise on optimal estimatio…
We show that particle detectors, such as 2-level atoms, in non-inertial motion (or in gravitational fields) could be used to build quantum gates for the processing of quantum information. Concretely, we show that through suitably chosen non-inertial trajectories of the detectors the interaction Hamiltonian's time dependence can be modulated to yield arbitrary rotations in the Bloch sphere due to relativistic quantum effects.
We define a summoning task to require propagating an unknown quantum state to a point in space-time belonging to a set determined by classical inputs at points in space-time. We consider the classical analogue, in which a known classical state must be returned at precisely one allowed point. We show that, when the inputs are unconstrained, any summoning task that is possible in the classical case is also possible in the quantum case.
In nonrelativistic quantum mechanics, Hudsons theorem states that a Gaussian wavefunction is the only pure state corresponding to a positive Wigner function (WF). We explicitly construct non Gaussian Dirac spinors with positive relativistic WF. These pure states are coherent superpositions of particles and antiparticles, while the existence of positive WF exclusive composed of particles is conjectured. These observations challenge a common belief that states with positive WF are classical or have classical analogues, and may open new venues in relativistic quantum information.
A simple proof of the unconditional security of a relativistic quantum cryptosystem based on orthogonal states is proposed. Restrictions imposed by special relativity allow to substantially simplify the proof compared with the non-relativistic cryptosystems involving non-orthogonal states. Important for the proposed protocol is the spatio-temporal structure of the quantum states which is actually ignored in the non-relativistic protocols employing only the structure of the state space of the information carriers. As a consequence, the simplification arises because of the inefficiency of collec…
Summoning retrieves quantum information, prepared somewhere in spacetime, at another specified point in spacetime, but this task is limited by the quantum no-cloning principle and the speed-of-light bound. We develop a thorough mathematical framework for summoning quantum information in a relativistic system and formulate a quantum summoning protocol for any valid configuration of causal diamonds in spacetime. For single-qubit summoning, we present a protocol based on a Calderbank-Shor-Steane code that decreases the space complexity for encoding by a factor of two compared to the previous best…
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.
In [N. Friis, New J. Phys. 18, 033014 (2016)] the non-relativistic description of fermions is considered and in particular the role of the parity superselection rule in relation to the characterization of entanglement. An argument based on the spin-statistics connection is presented as a physical motivation for the parity superselection rule. Since the spin statistics connection was derived in the context of relativistic quantum mechanics it is argued that the inclusion of the parity superselection rule is motivated by Lorentz invariance. Based on this it is further argued that fermionic Quant…
We study a proposal for the resolution of the black hole information puzzle within the context of modified versions of quantum theory involving spontaneous reduction of the quantum state. The theories of this kind, which were developed in order to address the so called "measurement problem" in quantum theory have, in the past, been framed in a non-relativistic setting and in that form they were previously applied to the black hole information problem. Here, and for the first time, we show in a simple toy model, a treatment of the problem within a fully relativistic setting. We also discuss the…
We prove that the classical Dirac equation in the presence of an external (nondynamical) electromagnetic field is a relativistically causal theory. As a corollary, we show that it is impossible to use quantum tunneling to transmit particles or information faster than light. When an electron tunnels through a barrier, it is bound to remain within its future light cone. In conclusion, the relativistic quantum tunneling (if modeled using the Dirac equation) is an entirely subluminal process, and it is not instantaneous.
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…
Relativistic effects on the precision of quantum metrology for particle detectors, such as two-level atoms are studied. The quantum Fisher information is used to estimate the phase sensitivity of atoms in non-inertial motions or in gravitational fields. The Unruh-DeWitt model is applicable to the investigation of the dynamics of a uniformly accelerated atom weakly coupled to a massless scalar vacuum field. When a measuring device is in the same relativistic motion as the atom, the dynamical behavior of quantum Fisher information as a function of Rindler proper time are obtained. It is found ou…
We use the quantumcorrelation of both logarithmic negativity andmutual information between a qubit and a relativistic boson to analyze the dynamics of Universe expansion. These dynamical quantum correlations can encode the information about underlying spacetime structure, which suggests a promising application in observational cosmology. We find that the dynamics of both logarithmic negativity and mutual information between the qubit and the boson are very similar. They decrease monotonically with the growth of the expansion volume and the expansion rate. Smaller momentum and medium-sized mass…
We review Unruh-DeWitt detectors and other models of detector-field interaction in a relativistic quantum field theory setting as a tool for extracting detector-detector, field-field and detector-field correlation functions of interest in quantum information science, from entanglement dynamics to quantum teleportation. We in particular highlight the contrast between the results obtained from linear perturbation theory which can be justified provided switching effects are properly accounted for, and the nonperturbative effects from available analytic expressions which incorporate the backreacti…
In the e-print is discussed a few steps to introducing of "vocabulary" of relativistic physics in quantum theory of information and computation (QTI&C). The behavior of a few simple quantum systems those are used as models in QTI&C is tested by usual relativistic tools (transformation properties of wave vectors, etc.). Massless and charged massive particles with spin 1/2 are considered. Field theory is also discussed briefly.
We show how to reliably encode quantum information and send it between two arbitrary general-relativistic observers without a shared reference frame. Any information stored in a quantum field will inevitably be destroyed by an unknown Bogolyubov transformation relating the observers. However certain quantum correlations between different, independent fields will be preserved, no matter what transformation is applied. We show how to efficiently use these correlations in communication between arbitrary observers.
The techniques employed to solve the interaction of a detector and a quantum field typically require perturbation methods. We introduce mathematical techniques to solve the time evolution of an arbitrary number of detectors interacting with a quantum field. Our techniques apply to harmonic oscillator detectors and can be generalized to treat detectors modeled by quantum fields. Since the interaction Hamiltonian we introduce is quadratic in creation and annihilation operators, we are able to draw from continuous variable techniques commonly employed in quantum optics.
In this work we revisit the famous Fermi two-atom problem, which concerns how relativistic causality impacts atomic transition probabilities, using the tools from relativistic quantum information (RQI) and algebraic quantum field theory (AQFT). The problem has sparked different analyses from many directions and angles since the proposed solution by Buchholz and Yngvason (1994). Some of these analyses employ various approximations, heuristics, perturbative methods, which tends to render some of the otherwise useful insights somewhat obscured. It is also noted that they are all studied in flat s…
We investigate the ultimate estimation precision, characterized by the quantum Fisher information, of a two-level atom as a detector which is coupled to massless scalar field in the Minkowski vacuum. It has been shown that for an inertial detector moving with a constant velocity, its quantum Fisher information is completely unaffected by the velocity, however, it still decays over time due to the decoherence caused by the interaction between the atom and the field. In addition, for a uniformly accelerated detector ($w=0$) moving along spatially straight line, the accelerated motion will reduce…
This article elaborates on entanglement entropy and quantum information theory of geometric flows of (relativistic) Lagrange--Hamilton mechanical systems. A set of basic geometric and quantum mechanics and probability concepts together with methods of computation are developed in general covariant form for curved phase spaces modelled as cotangent Lorentz bundles. The constructions are based on ideas relating the Grigory Perelman's entropy for geometric flows and associated statistical thermodynamic systems to the quantum von Neumann entropy, classical and quantum relative and conditional entr…
The fundamental properties of quantum information and its applications to computing and cryptography have been greatly illuminated by considering information-theoretic tasks that are provably possible or impossible within non-relativistic quantum mechanics. I describe here a general framework for defining tasks within (special) relativistic quantum theory and illustrate it with examples from relativistic quantum cryptography and relativistic distributed quantum computation. The framework gives a unified description of all tasks previously considered and also defines a large class of new questi…
We describe two problems current relativistic quantum information suffers from. The first point is an explanation of an alleged ambiguity of entropic quantities detected in a number of publications and incorrectly resolved in [M. Montero and E. Martin-Martinez, Physical Review A 83, 062323 (2011)]. We found that the problem arises due to wrong algebraic manipulations with fermions and ignoring the superselection rule for bosons and fermions. This leads to a misinterpretation of certain entropic quantities when applied to fermion fields. The second discussed point is to alert to a conceptual mi…
