The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.
The phenomenon of nonlocality without entanglement(NLWE) arises in discriminating multi-party quantum separable states. Recently, it has been found that the post-measurement information about the prepared subensemble can lock or unlock NLWE in minimum-error discrimination of non-orthogonal separable states. Thus, it is natural to ask whether the availability of the post-measurement information can influence on the occurrence of NLWE even in other state-discrimination strategies. Here, we show that the post-measurement information can be used to lock as well as unlock the occurrence of NLWE in …
We consider a pair of three - level atoms interacting with a common vacuum and analyze the process of entanglement production due to spontaneous emission. We show that in the case of closely separated atoms, collective damping can generate robust entanglement of the asymptotic states.
Unlocking Exponential and Unbounded Robust Gains in Shannon Capacity of Classical Multiple Access Channels with Causal CSIT via Quantum Entanglement Assistance
We propose a scheme for generating the superposition and the entanglement of squeezed vacuum states of electromagnetical fields. The scheme involves single-photon source, single photon detector, and cross Kerr nonlinearity. The Kerr nonlinearity required for generating the superposition of squeezed vacuum states is 1/2 of that required for generating the superposition of coherent states. The proposal can also be extended to generate the entanglement states between two coherent states and that between one coherent state and one squeezed vacuum state.
We derive sufficient conditions for infinite-dimensional systems whose entanglement is not completely lost in a finite time during its decoherence by a passive interaction with local vacuum environments. The sufficient conditions allow us to clarify a class of bipartite entangled states which preserve their entanglement or, in other words, are tolerant against decoherence in a vacuum. We also discuss such a class for entangled qubits.
The so-called entanglement with vacuum is not a property of the Fock space, but of some rather pathological representations of CCR/CAR algebras. In some other Fock space representations the notion simply does not exist. We have checked all the main Gedanken experiments where the notion of entanglement with vacuum was used, and found that all the calculations could be performed at a representation-independent level. In particular any such experiment can be formulated in a Fock-space representation where the notion of entanglement with vacuum is meaningless. So, for the moment there is no single…
I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in usual experimental situations.
Recently, it has been shown that the massless quantum vacuum state contains entanglement between timelike separated regions of spacetime, in addition to the entanglement between the spacelike separated regions usually considered. Here, we show that timelike entanglement can be extracted from the Minkowski vacuum and converted into ordinary entanglement between two inertial, two-state detectors at the same spatial location -- one coupled to the field in the past and the other coupled to the field in the future. The procedure used here demonstrates a clear time correlation as a requirement for e…
We note that massless fields within the future and past light cone may be quantized as independent systems. We show that the vacuum is an entangled state of these systems, exactly mirroring the known entanglement between the spacelike separated Rindler wedges. We describe a detector which exhibits a thermal response to the vacuum when switched on at t=0. The feasibility of experimentally detecting this effect is discussed.
We propose a method to refine entanglement via swapping from a pair of squeezed vacuum states by performing the Bell measurement of number sum and phase difference. The resultant states are maximally entangled by adjusting the two squeezing parameters to the same value. We then describe the teleportation of number states by using the entangled states prepared in this way.
Quantum entanglement is a fascinating phenomenon, especially if it is observed at the macroscopic scale. Importantly, macroscopic quantum correlations can be revealed only by accurate measurement outcomes and strategies. Here, we formulate feasible entanglement witnesses for bright squeezed vacuum in the form of the macroscopically populated polarization triplet Bell states. Their testing involves efficient photodetection and the measurement of the Stokes operators variances. We also calculate the measures of entanglement for these states such as the Schmidt number and the logarithmic negativi…
Entanglement plays a crucial role in quantum information protocols, thus the dynamical behavior of entangled states is of a great importance. In this paper we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized in the cavity-QED technology utilizing atoms as fying qubits. To quantify entanglement we use the concurrence. We derive the conditions, which assure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of sudden death entanglement (ESD) in a bipartite system subjected to squeezed v…
We propose and study a method for detecting ground-state entanglement in a chain of trapped ions, which realizes a suggested scheme for detecting vacuum entanglement in quantum field theory. We show that the entanglement between single ions or groups of ions can be swapped to the internal levels of two ions by sending laser pulses that couple the internal and motional degrees of freedom. This allows to entangle two ions without actually doing gates. A proof of principle of the effect can be realized with two trapped ions and is feasible with current technology.
We study the structure of vacuum entanglement for two complimentary segments of a linear harmonic chain, applying the modewise decomposition of entangled gaussian states discussed in \cite {modewise}. We find that the resulting entangled mode shape hierarchy shows a distinctive layered structure with well defined relations between the depth of the modes, their characteristic wavelength, and their entanglement contribution. We re-derive in the strong coupling (diverging correlation length) regime, the logarithmic dependence of entanglement on the segment size predicted by conformal field theory…
We study the dynamics of a pair of molecular ensembles trapped inside a superconducting resonator through which they are strongly coupled via a microwave field mode. We find that entanglement can be generated via "vacuum fluctuations" even when the molecules and cavity field are initially prepared in their ground state. This entanglement is created in a relatively short time and without the need for further manipulation of the system. It does, therefore, provide a convenient scheme to entangle two mesoscopic systems, and may well be useful quantum information processing.
Using two crystals for spontaneous parametric down-conversion in a parallel setup, we observe two-photon interference with high visibility. The high visibility is consistent with complementarity and the absence of which-path information. The observations are explained as effects of entanglement or equivalently in terms of interfering probability amplitudes, and also by the calculation of a second-order field correlation function in the Heisenberg picture. The latter approach brings out explicitly the role of the vacuum fields in the down-conversion at the crystals and in the photon coincidence…
Recently, there have been a number of works investigating the entanglement properties of distinct noncomplementary parts of discrete and continuous Bosonic systems in ground and thermal states. The Fermionic case, however, has yet to be expressly addressed. In this paper we investigate the entanglement between a pair of far-apart regions of the 3+1 dimensional massless Dirac vacuum via a previously introduced distillation protocol [B. Reznik et al., Phys. Rev. A 71, 042104 (2005)]. We show that entanglement persists over arbitrary distances, and that as a function of L/R, where L is the distan…
We investigate the entanglement patterns of photon-added and -subtracted four-mode squeezed vacuum states. Entanglements in different scenarios are analyzed by varying the number of photons added or subtracted in certain modes, which are referred to as the "player" modes, the others being "spectators." We find that the photon-subtracted state can give us higher entanglement than the photon-added state which is in contrast of the two-mode situation. We also study the logarithmic negativity of the two-mode reduced density matrix obtained from the four-mode state which again shows that the state …
We investigate the correlations between any number of arbitrarily far-apart regions of the vacuum of the free Klein-Gordon field by means of its finite duration coupling to an equal number of localized detectors. We show that the correlations between any N such regions enable us to distill an N-partite W state, and therefore exhibit true $N$-fold entanglement. Furthermore, we show that for N=3, the correlations cannot be reproduced by a hybrid local-nonlocal hidden-variable model. For N >= 4 the issue remains open.
We quantify multiparticle quantum entanglement in a system of N two-level atoms interacting with a squeezed vacuum state of the electromagnetic field. We calculate the amount of quantum entanglement present among one hundred such two-level atoms and also show the variation of that entanglement with the radiation field parameter. We show the continuous variation of the amount of quantum entanglement as we continuously increase the number of atoms from N=2 to N=100. We also discuss that the multiparticle correlations among the N two-level atoms are made up of all possible bipartite correlations …
We demonstrate and characterize the extraction of genuine tripartite entanglement from the vacuum of a periodic cavity field. That is, three probe quantum systems (detectors) can become both bipartitely and tripartitely entangled without coming into causal contact, by means of interaction with a common quantum field. We do this by using an oscillator-detector model that forgoes the need for perturbation theory and which instead is solved exactly. We find that the extraction of tripartite entanglement is considerably easier than that of bipartite. As a secondary result, we also compare a period…
The dynamics of entanglement between three - level atoms coupled to the common vacuum is investigated. We show that the collective effects such as collective damping, dipole - dipole interaction and the cross coupling between orthogonal dipoles, play a crucial role in the process of creation of entanglement. In particular, the additional cross coupling enhances the production of entanglement. For the specific initial states we find that the effect of delayed sudden birth of entanglement, recently invented by Ficek and Tanas [Phys. Rev. A 77, o54301(2008)] in the case of two - level atoms, can …
We analyze an example of a photon in superposition of different modes, and ask what is the degree of their entanglement with vacuum. The problem turns out to be ill-posed since we do not know which representation of the algebra of canonical commutation relations (CCR) to choose for field quantization. Once we make a choice, we can solve the question of entanglement unambiguously. So the difficulty is not with mathematics, but with physics of the problem. In order to make the discussion explicit we analyze from this perspective a popular argument based on a photon leaving a beam splitter and in…
I theoretically investigate how the entanglement properties of a two-mode squeezed vacuum state (TMSVS) can be enhanced by operating quantum-optical catalysis on each mode of the TMSVS. The quantum-optical catalysis is simply mixing one photon at the beam splitter and post-select the beam-splitter (BS) output based on detection of one photon, first proposed by Lvovsky and Mlynek [Phys. Rev. Lett. 88, 250401 (2002)]. I find that there exists some enhancement in the entanglement properties (namely, entanglement entropy, second-order Einstein-Podolsky-Rosen correlation, and the fidelity of quantu…
It is well known that magnons, elementary excitations in a magnetic material, behave as bosons when their density is low. We study how the bosonic character of magnons is governed by the amount of a multipartite entanglement in the vacuum state on which magnons are excited. We show that if the multipartite entanglement is strong, magnons cease to be bosons. We also consider some examples, such as ground states of the Heisenberg ferromagnet and the transverse Ising model, the condensation of magnons, the one-way quantum computer, and Kitaev's toric code. Our result provides insights into the qu…
It has been shown that the vacuum state of a free quantum field is entangled and such vacuum entanglement can be harvested by a pair of initially uncorrelated detectors interacting locally with the vacuum field for a finite time. In this paper, we examine the entanglement harvesting phenomenon of two non-identical inertial detectors with different energy gaps locally interacting with massless scalar fields via a Gaussian switching function. We focus on how entanglement harvesting depends on the energy gap difference from two perspectives: the amount of entanglement harvested and the harvesting…
In this thesis we focus on the influence of uniform acceleration on quantum states and their properties, as well as on quantum entanglement contained in the vacuum. First, we analyze a quantum clock measuring time in terms of the decay of an unstable particle. We compare the rate of ticking of a stationary clock to the one of a uniformly accelerating clock. We discover that there exists a deviation from what the discrepancy between those rates is predicted to be by special relativity. In a further part of this thesis we focus on the family of two-mode Gaussian states of two localized modes of …
We study entanglement concentration of continuous variable Gaussian states by local photon subtractions enhanced by coherent displacements. Instead of the previously considered symmetric two-mode squeezed vacuum states, we investigate the protocol for input states in the form of split single-mode squeezed vacuum, i.e., states obtained by mixing a single-mode squeezed vacuum with a vacuum state on a beam splitter, which is an experimentally highly relevant configuration. We analyze two scenarios in which the displacement-enhanced photon subtraction is performed either only on one, or on both of…
Applying the recently developed formalism of quantum-state transformation at absorbing dielectric four-port devices [L.~Knöll, S.~Scheel, E.~Schmidt, D.-G.~Welsch, and A.V.~Chizhov, Phys. Rev. A {\bf 59}, 4716 (1999)], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres--Horodecki separability criterion for continuous variable systems [R.~Simon, Phys. Rev. Lett. {\bf 84}, 2726 (2000)], we compute the maximal length of transmission of a two-mode squeezed vacuum through an absorbin…
Monogamy and polygamy relations characterize the distributions of entanglement in multipartite systems. We investigate the monogamy and polygamy relations with respect to any partitions for a superposition of the generalized $W$-class state and vacuum in terms of the Tsallis-$q$ entanglement and the Rényi-$α$ entanglement. By using the Hamming weight of the binary vectors related to the partitions of the subsystems, new classes of monogamy and polygamy inequalities are derived, which are shown to be tighter than the existing ones. Detailed examples are presented to illustrate the finer charact…
Separate regions in space are generally entangled, even in the vacuum state. It is known that this entanglement can be swapped to separated Unruh-DeWitt detectors, i.e., that the vacuum can serve as a source of entanglement. Here, we demonstrate that, in the presence of curvature, the amount of entanglement that Unruh-DeWitt detectors can extract from the vacuum can be increased.
We report the experimental realization of a recently discovered quantum information protocol by Asher Peres implying an apparent non-local quantum mechanical retrodiction effect. The demonstration is carried out by applying a novel quantum optical method by which each singlet entangled state is physically implemented by a two-dimensional subspace of Fock states of a mode of the electromagnetic field, specifically the space spanned by the vacuum and the one photon state, along lines suggested recently by E. Knill et al., Nature 409, 46 (2001) and by M. Duan et al., Nature 414, 413 (2001). The s…
It is shown that by means of local interactions between a quantized relativistic field and a pair of non-entangled atoms, entanglement can be extracted from the vacuum and delivered to the atoms. The resulting mixed state of the atoms can be further distilled to EPR pairs. Therefore, in principle, teleportation and other entanglement assisted quantum communication tasks can rely on the vacuum alone as a resource for entanglement.
We propose a single-particle experiment that is equivalent to the conventional two-particle experiment used to demonstrate a violation of Bell's inequalities. Hence, we argue that quantum mechanical nonlocality can be demonstrated by single-particle states. The validity of such a claim has been discussed in the literature, but without reaching a clear consensus. We show that the disagreement can be traced to what part of the total state of the experiment one assigns to the (macroscopic) measurement apparatus. However, with a conventional and legitimate interpretation of the measurement process…
We introduce a framework for probing the spacetime structure of vacuum entanglement that exhibits infinite range correlations between the future and the past, as well as spatially separated regions. Our results are non-perturbative and analytical.
We propose a photonics-based, continuous-variable (CV) form of remote entanglement utilizing strictly second-order nonlinear optical interactions that does not require the implementation of a state-projective measurement (i.e. remote entanglement without conditioning). This scheme makes use of two separate down-converters, wherein the corresponding nonlinear crystals are driven by strong classical fields as prescribed by the parametric approximation, as well as a fully quantum mechanical model of nondegenerate second harmonic generation (SHG) whose evolution is described by the trilinear Hamil…
In this paper, we study the interaction between the two-level atom and a bimodal cavity field, namely, two-mode Jaynes-Cummings model when the atom and the modes are initially in the atomic superposition state and two-mode squeezed vacuum state, respectively. For this system we investigate the atomic inversion, linear entropy and atomic Wehrl entropy. We show that there is a connection between all these quantities. Also we prove that the atomic Wehrl entropy exhibits behaviors similar to those of the linear entropy and the von Neumann entropy. Moreover, we show that the bipartite exhibits peri…
A quantum cryptography scheme based on entanglement between a single particle state and a vacuum state is proposed. The scheme utilizes linear optics devices to detect the superposition of the vacuum and single particle states. Existence of an eavesdropper can be detected by using a variant of Bell's inequality.
We have experimentally realized the scheme initially proposed as quantum dense coding with continuous variables [Ban, J. Opt. B \textbf{1}, L9 (1999), and Braunstein and Kimble, \pra\textbf{61}, 042302 (2000)]. In our experiment, a pair of EPR (Einstein-Podolski-Rosen) beams is generated from two independent squeezed vacua. After adding two-quadrature signal to one of the EPR beams, two squeezed beams that contain the signal were recovered. Although our squeezing level is not sufficient to demonstrate the channel capacity gain over the Holevo limit of a single-mode channel without entanglement…
It is shown that accelerated projective measurements on the vacuum of a free Dirac spinor field results in an entangled state for an inertial observer. The physical mechanism at work is the Davies-Unruh effect. The produced state is always entangled and its entanglement increases as a function of the acceleration, reaching maximal entanglement in the asymptotic limit of infinite acceleration where Bell states are produced.
We propose a very simple scheme to test the quantum enatanglement swapping in a priori. In the scheme, we only assume the photon detector can distinguish the vacuum and non-vacuum Fock state rather than the exact Fock number states.
We analyze entanglement generation between a pair of neutral two level atoms that are initially excited in a common electromagnetic vacuum. The nonlocal correlations that appear due to the interaction with the field can become entanglement when the field state is known. We distinguish two different situations: in the first, the field remains in the vacuum state, and second two photons are present in the final state. In both cases we study the dependence of the entanglement with time and interatomic distance, at ranges related with locality issues.
We show that vacuum induced coherence in three level atomic systems can lead to preservation of bi-partite entanglement, when two such atoms are prepared as two initially entangled qubits each independently interacting with their respective vacuum reservoirs. We explicitly calculate the time evolution of concurrence for two different Bell states and show that a large amount of entanglement can survive in the long time limit. The amount of entanglement left among the two qubits depends strongly on the ratio of the non- orthogonal transitions in each qubit and can be more than 50%
We study the effects of acceleration on fermionic Gaussian states of localized modes of a Dirac field. We consider two wave-packets in a Gaussian state and transform these to an accelerated frame of reference. In particular, we formulate the action of this transformation as a fermionic quantum channel. Having developed the general framework for fermions, we then investigate the entanglement of the vacuum, as well as the entanglement in Bell states. We find that with increasing acceleration vacuum entanglement increases, while the entanglement of Bell states decreases. Notably, our results have…
We have considered the interaction of a pair of spatially separated two-level atoms with the electromagnetic field in its vacuum state and we have analyzed the amount of entanglement induced between the two atoms by the non local field fluctuations. This has allowed us to characterize the quantum nature of the non local correlations of the electromagnetic field vacuum state as well as to link the induced quantum entanglement with Casimir-Polder potentials.
Mixing transformations in quantum field theory are non-trivial, since they are intimately related to the unitary inequivalence between Fock spaces for fields with definite mass and fields with definite flavor. Considering the superposition of two neutral scalar (spin-0) bosonic fields, we investigate some features of the emerging condensate structure of the flavor vacuum. In particular, we quantify the flavor vacuum entanglement in terms of the von Neumann entanglement entropy of the reduced state. Furthermore, in a suitable limit, we show that the flavor vacuum has a structure akin to the the…
We study a limited set of optical circuits for creating near maximal polarisation entanglement {\em without} the usual large vacuum contribution. The optical circuits we consider involve passive interferometers, feed-forward detection, down-converters and squeezers. For input vacuum fields we find that the creation of maximal entanglement using such circuits is impossible when conditioned on two detected auxiliary photons. So far, there have been no experiments with more auxiliary photons. Thus, based on the minimum complexity of the circuits required, if near maximal polarisation entanglement…
A system of two two-level atoms interacting with a squeezed vacuum field can exhibit stationary entanglement associated with nonclassical two-photon correlations characteristic of the squeezed vacuum field. The amount of entanglement present in the system is quantified by the well known measure of entanglement called concurrence. We find analytical formulas describing the concurrence for two identical and nonidentical atoms and show that it is possible to obtain a large degree of steady-state entanglement in the system. Necessary conditions for the entanglement are nonclassical two-photon corr…
We report the suitability of an Einstein-Podolsky-Rosen (EPR) entanglement source for gaussian continuous-variable quantum key distribution at 1550 nm. Our source is based on a single continuous-wave squeezed vacuum mode combined with a vacuum mode at a balanced beam splitter. Extending a recent security proof, we characterize the source by quantifying the extractable length of a composable secure key from a finite number of samples under the assumption of collective attacks. We show that distances in the order of 10 km are achievable with this source for a reasonable sample size despite the f…
Entanglement drives nearly all proposed quantum information technologies. By up-converting part of a 1550 nm two-mode squeezed vacuum state to 532 nm, we demonstrate the generation of strong continuous-variable entanglement between widely separated frequencies. Nonclassical correlations were observed in joint quadrature measurements of the 1550 and 532 nm fields, showing a maximum noise suppression 5.5 dB below vacuum. Our versatile technique combines strong nonclassical correlations, large bandwidth, and in principle, the ability to entangle the telecommunication wavelength of 1550 nm with an…
The Minkowski vacuum state is expressed as an entangled state between the left and right Rindler wedges when it is constructed on the Rindler vacuum. In this paper, we further examine the entanglement structure and extend the expression to the future (expanding) and past (shrinking) Kasner spacetimes. This clarifies the origin of the quantum radiation produced by an Unruh--DeWitt detector in uniformly accelerated motion in the four-dimensional Minkowski spacetime. We also investigate the two-dimensional massless case where the quantum radiation vanishes but the same entanglement structure exis…
Entangled states play a crucial role in quantum information protocols, thus the dynamical behavior of entanglement is of a great importance. In this paper we consider a two-mode squeezed vacuum state coupled to one thermal reservoir as a model of an entangled state embedded in an environment. As a criterion for entanglement we use a continuous-variable equivalent of the Peres-Horodecki criterion, namely the Simon criterion. To quantify entanglement we use the logarithmic negativity. We derive a condition, which assures that the state remains entangled in spite of the interaction with the reser…
