We introduce a relativistic version of quantum encryption protocol by considering two inertial observers who wish to securely transmit quantum information encoded in a free scalar quantum field state forming Minkowski particles. In a non-relativistic setting a certain amount of shared classical resources is necessary to perfectly encrypt the state. We show that in the case of a uniformly accelerated eavesdropper the communicating parties need to share (asymptotically in the limit of infinite acceleration) just half of the classical resources.
In a recent Letter (Phys. Rev. Lett. 95 (2005) 010503) Barrett, Hardy and Kent (BHK) considered a very interesting question which of the fundamental laws of physics ensure security of quantum cryptographic protocols. In particular, they presented quantum key distribution protocol and claimed its security in a very general framework, which allows - what they call - postquantum eavesdropping strategies i.e. which "allows for eavesdroppers who can break the laws of quantum mechanics, as long as nothing they can do implies the possibility of superluminal signaling". In this Comment, however, we sh…
A general framework of optimal eavesdropping on BB84 protocol was provided by Fuchs et al. [Phys. Rev. A, 1997]. An upper bound on mutual information was derived, which could be achieved by a specific type of interaction and the corresponding measurement. However, uniqueness of optimal interaction was posed as an unsolved problem there and it has remained open for almost two decades now. In this paper, we solve this open problem and establish the uniqueness of optimal interaction up to rotation. The specific choice of optimal interaction by Fuchs et al. is shown to be a special case of the for…
We generalise the study of fermionic and bosonic entanglement in non-inertial frames to fields of arbitrary spin and beyond the single mode approximation. After the general analysis we particularise for two interesting cases: entanglement between an inertial and an accelerated observer for massless fields of spin 1 (electromagnetic) and 3/2 (Rarita-Schwinger). We show that in the limit of infinite acceleration, no significant differences appear between the different spin fields for the states considered.
We analyse an ambiguity in previous works on entanglement of fermionic fields in non-inertial frames. This ambiguity, related to the anticommutation properties of field operators, leads to non-unique results when computing entanglement measures for the same state. We show that the ambiguity disappears when we introduce detectors, which are in any case necessary as a means to probe the field entanglement.
We study families of fermionic field states in non-inertial frames which show no entanglement survival in the infinite acceleration limit. We generalise some recent results where some particular examples of such states where found. We analyse the abundance and characteristics of the states showing this behaviour and discuss its relation with the statistics of the field. We also consider the phenomenon beyond the single mode approximation.
We analyse the entanglement tradeoff between particle and anti-particle modes of a Dirac field from the perspective of inertial and uniformly accelerated observers. Our results show that a redistribution of entanglement between particle and anti-particle modes plays a key role in the survival of fermionic field entanglement in the infinite acceleration limit.
We analyse the entanglement tradeoff between particle and anti-particle modes of a charged bosonic field between inertial and uniformly accelerated observers. In contrast with previous results for fermionic fields, we find that the entanglement redistribution between particle and antiparticle modes does not prevent the entanglement from vanishing in the infinite acceleration limit.
We study the response function of Unruh-deWitt detectors placed in a flat spacetime inside a thin matter shell. We show that the response function distinguishes between the local and global (Minkowski) inertial frames and picks up the presence of the shell even when the detector is switched on for a finite time interval within which a light signal cannot travel to the shell and back as required by a classical measurement. We also analyze how the response of the detector depends on its location within the shell.
We develop a general technique to analyse the quantum effects of acceleration on realistic spatially-localised electromagnetic field states entangled in the polarization degree of freedom. We show that for this setting, quantum entanglement may build up as the acceleration increases, providing a clear signature of the quantum effects of relativistic acceleration.
Classical, i.e. non-quantum, communications include configurations with multiple-input multiple-output (MIMO) channels. Some associated signal processing tasks consider these channels in a symmetric way, i.e. by assigning the same role to all channel inputs, and similarly to all channel outputs. These tasks especially include channel identification/estimation and channel equalization, tightly connected with source separation. Their most challenging version is the blind one, i.e. when the receivers have (almost) no prior knowledge about the emitted signals. Other signal processing tasks conside…
We show that quantum field correlations in non-inertial frames are not as persistent as previously thought. We perform a simple calculation showing that the geometric discord, a measure of quantum correlations, does decay to zero in the infinite acceleration limit. This result is seen to be a natural and expected consequence of considering correlations in an infinite dimensional system, and it sheds doubt on the existence of useable quantum correlations in this regime. We contrast our results with previous research showing that the acceleration-induced degradation of quantum discord was not st…
After a review of the existing theory of non-inertial frames and mathematical observers in Minkowski space-time we give the explicit expression of a family of such frames obtained from the inertial ones by means of point-dependent Lorentz transformations as suggested by the locality principle. These non-inertial frames have non-Euclidean 3-spaces and contain the differentially rotating ones in Euclidean 3-spaces as a subcase. Then we discuss how to replace mathematical accelerated observers with dynamical ones (their world-lines belong to interacting particles in an isolated system) and of how…
Recently relativistic quantum information has received considerable attention due to its theoretical importance and practical application. Especially, quantum entanglement in non-inertial reference frames has been studied for scalar and Dirac fields. As a further step along this line, we here shall investigate quantum entanglement of electromagnetic fields in non-inertial reference frames. In particular, the entanglement of photon helicity entangled state is extensively analyzed. Interestingly, the resultant logarithmic negativity and mutual information remain the same as those for inertial re…
Quantum channel discrimination is used to test quantum field theory in non-inertial frames. We search for optimal strategies which can best see the thermality of the Unruh effect. We find that the usual strategy of counting particles in the vacuum can be improved, thereby enhancing the discrimination. Coherent state probes, which are practical and feasible, give exponential improvement in the discrimination of the Unruh channel and come very close to optimal. In particular, we show that using a short pulse laser, the accelerations required to test the Unruh effect can be reduced by at least th…
We propose a scheme to study the effect of motion on measurements of a quantum field carried out by a finite-size detector. We introduce a model of projective detection of a localised field mode in an arbitrary reference frame. We apply it to extract vacuum entanglement by a pair of counter-accelerating detectors and to estimate the Unruh temperature of a single accelerated detector. The introduced method allows us to directly relate the observed effects with the instantaneous proper acceleration of the detector.
An open question in the field of relativistic quantum information is how parties in arbitrary motion may distribute and store quantum entanglement. We propose a scheme for storing quantum information in the field modes of cavities moving in flat space-time and analyze it in a quantum field theoretical framework. In contrast to previous work that found entanglement degradation between observers moving with uniform acceleration, we find the quantum information in such systems is protected. We further discuss a method for establishing the entanglement in the first place and show that in principle…
In this work, we describe the process of teleportation between Alice in an inertial frame, and Rob who is in uniform acceleration with respect to Alice. The fidelity of the teleportation is reduced due to Davies-Unruh radiation in Rob's frame. In so far as teleportation is a measure of entanglement, our results suggest that quantum entanglement is degraded in non-inertial frames. We discuss this reduction in fidelity for both bosonic and fermionic resources.
Two observers determine the entanglement between two free bosonic modes by each detecting one of the modes and observing the correlations between their measurements. We show that a state which is maximally entangled in an inertial frame becomes less entangled if the observers are relatively accelerated. This phenomenon, which is a consequence of the Unruh effect, shows that entanglement is an observer-dependent quantity in non-inertial frames. In the high acceleration limit, our results can be applied to a non-accelerated observer falling into a black hole while the accelerated one barely esca…
Thermal entanglement and teleportation properties in non-inertial frames are investigated when a two-qubit Heisenberg XXX model with Dzyaloshinski-Moriya (DM) interaction is used as the quantum channel. We find that thermal entanglement and the teleportation fidelity of a teleported state decrease with the acceleration parameter or temperature, in other words, the quantum entanglement teleportation will degenerate in non-inertial frames. Furthermore, our results also show that the average fidelity may be promoted by DM interaction for the ferromagnetic case, which is opposite to the antiferrom…
A relativistic theory of gravity like general relativity produces phenomena differing fundamentally from Newton's theory. An example, analogous to electromagnetic induction, is gravitomagnetism, or the dragging of inertial frames by mass-energy currents. These effects have recently been confirmed by classical observations. Here we show, for the first time, that they can be observed by a quantum detector. We study the response function of Unruh De-Witt detectors placed in a slowly rotating shell. We show that the response function picks up the presence of rotation even though the spacetime insi…
We study the effect of quantum memory in non-inertial frames under the influence of amplitude damping, depolarizing, phase flip and bit-phase flip channels. It is shown that the entanglement of initial state is heavily influenced by quantum correlations. It is seen that quantum memory compensates the loss of entanglement generated caused by the Unruh effect. It is interesting to note that the sudden death of entanglement disappears for any acceleration for higher values of memory. Therefore, it is possible to avoid ESD in non-inertial frames due to the presence of quantum memory. Furthermore, …
The effect of decoherence on a qubit-qutrit system under the influence of global and multilocal decoherence in non-inertial frames is investigated. It is shown that the entanglement sudden death (ESD) can be avoided in non-inertial frames in the presence of dephasing and bit-trit phase flip channels for entire range of decoherence. However, ESD behaviour is seen for higher level of decoherence in case of phase flip and bit-trit flip channels. Irrespective of the entanglement degradation caused by the Unruh effect, no ESD occurs for the dephasing environment. Furthermore, flipping channels have…
We study the distribution of entanglement between modes of a free scalar field from the perspective of observers in uniform acceleration. We consider a two-mode squeezed state of the field from an inertial perspective, and analytically study the degradation of entanglement due to the Unruh effect, in the cases of either one or both observers undergoing uniform acceleration. We find that for two observers undergoing finite acceleration, the entanglement vanishes between the lowest frequency modes. The loss of entanglement is precisely explained as a redistribution of the inertial entanglement i…
We estimate the teleported and the gained parameters by means of Fisher information in a non-inertial frame. The sender and the receiver share an accelerated maximum or partial entangled state. The estimation degree of these parameters depends on Unruh acceleration, the used single mode approximation(within/ beyond), the structure of the initial teleported state, and the entanglement of the initial communication channel. The maximization and minimization estimation degree of the teleported parameters depend on the initial encoded information. The estimation degree of the parameters can be maxi…
We study the effect of decoherence on a qubit-qutrit system under the influence of global, local and multilocal decoherence in non-inertial frames. We show that the entanglement sudden death can be avoided in non-inertial frames in the presence of amplitude damping, depolarizing and phase damping channels. However, degradation of entanglement is seen due to Unruh effect. It is shown that for lower level of decoherence, the depolarizing channel degrades the entanglement more heavily as compared to the amplitude damping and phase damping channels. However, for higher values of decoherence parame…
Inertial effects in non-inertial reference frames are compared with quantum properties of tests objects. The real space-time and perfect inertial reference frame can be compared accurate to the uncertainty relation. Complexities if describing micro-object in non-inertial reference-frames are avoidable using Ostrogradski's Canonical Formalism.
In quantum communication protocols the existence of a shared reference frame between two spatially separated parties is normally presumed. However, in many practical situations we are faced with the problem of misaligned reference frames. In this paper, we study communication between two inertial observers who have partial knowledge about the Lorentz transformation that relates their frames of reference. Since every Lorentz transformation can be decomposed into a pure boost followed by a rotation, we begin by analysing the effects on communication when the parties have partial knowledge about …
The influence of acceleration and rotation on spintronic applications is theoretically investigated. In our formulation, considering a Dirac particle in a non-inertial frame, different spin related aspects are studied. The spin current appearing due to the inertial spin-orbit coupling (SOC) is enhanced by the interband mixing of the conduction and valence band states. Importantly, one can achieve a large spin current through the $\vec{k}. \vec{p}$ method in this non-inertial frame. Furthermore, apart from the inertial SOC term due to acceleration, for a particular choice of the rotation freque…
In an ideal test of the equivalence principle, the test masses fall in a common inertial frame. A real experiment is affected by gravity gradients, which introduce systematic errors by coupling to initial kinematic differences between the test masses. We demonstrate a method that reduces the sensitivity of a dual-species atom interferometer to initial kinematics by using a frequency shift of the mirror pulse to create an effective inertial frame for both atomic species. This suppresses the gravity-gradient-induced dependence of the differential phase on initial kinematic differences by a facto…
Decoherence effect on multipartite entanglement in non-inertial frames is investigated. GHZ state is considered to be shared between the partners with one partner in inertial frame whereas the other two in accelerated frames. One-tangle and π-tangles are used to quantify the entanglement of the multipartite system influenced by phase damping and phase flip channels. It is seen that for phase damping channel, entanglement sudden death (ESD) occurs for p>0.5 in the infinite acceleration limit. On the other hand, in case of phase flip channel, ESD behaviour happens around 50% decoherence. It is a…
Validity conditions for the adiabatic approximation are useful tools to understand and predict the quantum dynamics. Remarkably, the resonance phenomenon in oscillating quantum systems has challenged the adiabatic theorem. In this scenario, inconsistencies in the application of quantitative adiabatic conditions have led to a sequence of new approaches for adiabaticity. Here, by adopting a different strategy, we introduce a validation mechanism for the adiabatic approximation by driving the quantum system to a non-inertial reference frame. More specifically, we begin by considering several rele…
The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum-mechanics formulated in the absolute synchronization framework. The results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical system in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin opeartor with proper transformation properties under the action of the Lorentz group. Some …
The three-tangle-dependence of $S_{max} = \max <S>$, where $S$ is Svetlichny operator, are explicitly derived when one party moves with an uniform acceleration with respect to other parties in the generalized Greenberger-Horne-Zeilinger and maximally slice states. The $π$-tangle-dependence of $S_{max}$ are also derived implicitly. From the dependence we conjecture that the multipartite entanglement is not the only physical resource for quantum mechanical multipartite non-locality.
In this paper, some properties of multi-qubit states traveling in non-inertial frames are investigated, where we assume that all particles are accelerated. These properties are including fidelities, capacities and entanglement of the accelerated channels for three different states, namely, Greeberger-Horne-Zeilinger (GHZ) state, GHZ-like state and W-state. It is shown here that all these properties are decreased as the accelerations of the moving particles are increased. The obtained results show that the GHZ-state is the most robust one comparing to the others, where the degradation rate is l…
An atom attached to a micrometer-scale wire that is vibrating at a frequency of 100 MHz and with displacement amplitude 1 nm experiences an acceleration magnitude 10^9 ms^-2, approaching the surface gravity of a neutron star. As one application of such extreme non-inertial forces in a mesoscopic setting, we consider a model two-path atom interferometer with one path consisting of the 100 MHz vibrating wire atom guide. The vibrating wire guide serves as a non-inertial reference frame and induces an in principle measurable phase shift in the wave function of an atom traversing the wire frame. We…
We study quantum optics with the atoms coupled to the quantized electromagnetic (EM) field in a non-inertial reference frame by making use of quantum field theory in curved spacetime. We rigorously establish the microscopic model for a two-level atom interacting with the quantized EM field in a rotating ring cavity by deriving a Jaynes-Cummings (JC) type Hamiltonian. Due to the two fold degeneracy of the ring cavity modes, the Rabi splitting exhibits three rather than two resonant frequency peaks. We find that the heights of the two side peaks show a sensitive linear dependence on the rotating…
A helicity entangled tripartite state is considered in which the degree of entanglement is preserved in non-inertial frames. It is shown that Quantum Entanglement remains observer independent. As another measure of quantum correlation, Quantum Discord has been investigated. It is explicitly shown that acceleration has no effect on the degree of quantum correlation for the bipartite and tripartite helicity entangled states. Geometric Quantum Discord as a Hilbert-Schmidt distance is computed for helicity entangled states. It is shown that living in non-inertial frames does not make any influence…
Under amplitude damping channel, the dependence of the entanglement on the initial states $|Θ>_{1}$ and $|Θ>_{2}$, which reduce to four orthogonal Bell states if we take the parameter of states $α=\pm 1/\sqrt{2}$ are investigated. We find that the entanglements for different initial states will decay along different curves even with the same acceleration and parameter of the states. We note that, in an inertial frame, the sudden death of the entanglement for $|Θ>_{1}$ will occur if $α>1/\sqrt{2}$, while it will not take place for $|Θ>_{2}$ for any $α$. We also show that the possible range of t…
The capacity of accelerated channel is investigated for different classes of initial states. It is shown that, the capacities of the travelling channels depend on the frame in which the accelerated channels are observed in and the initial shared state between the partners. In some frames, the capacities decay as the accelerations of both qubit increase. The decay rate is larger if the partners are initially share a maximum entangled state. The possibility of using the accelerated quantum channels to perform quantum coding protocol is discussed. The amount of decoded information is quantified f…
Entanglement degradation caused by the Unruh effect is discussed for the tripartite GHZ or W states constructed by modes of a non-interacting quantum field viewed by one inertial observer and two uniformly accelerated observers. For fermionic states, the Unruh effect even for infinite accelerations cannot completely remove the entanglement. However, for the bosonic states, the situation is different and the entanglement vanishes asymptotically. Also, the entanglement is studied for the bipartite subsystems. While for the GHZ states all the bipartite subsystems are identically disentangled, for…
Let Alice, Bob, and Charlie initially share an arbitrary fermionic three-qubit pure state, whose three-tangle is $τ_3^{(0)}$. It is shown within the single-mode approximation that if one party among the three of them moves with a uniform acceleration with respect to the other parties, the three-tangle reduces to $τ_3^{(0)} \cos^2 r$, where $r$ denotes a statistical factor in Fermi-Dirac statistics.
This is the fourth in a series of papers on developing a formulation of quantum mechanics in non-inertial reference frames. This formulation is grounded in a class of unitary cocycle representations of what we have called the Galilean line group, the generalization of the Galilei group to include transformations amongst non-inertial reference frames. These representations show that in quantum mechanics, just as the case in classical mechanics, the transformations to accelerating reference frames give rise to fictitious forces. In previous work, we have shown that there exist representations of…
We present a formalism of Galilean quantum mechanics in non-inertial reference frames and discuss its implications for the equivalence principle. This extension of quantum mechanics rests on the Galilean line group, the semidirect product of the real line and the group of analytic functions from the real line to the Euclidean group in three dimensions. This group provides transformations between all inertial and non-inertial reference frames and contains the Galilei group as a subgroup. We construct a certain class of unitary representations of the Galilean line group and show that these repre…
