We analyze the resilience under photon loss of the bi-partite entanglement present in multi-photon states produced by parametric down-conversion. The quantification of the entanglement is made possible by a symmetry of the states that persists even under polarization-independent losses. We examine the approach of the states to the set of states with a positive partial transpose as losses increase, and calculate the relative entropy of entanglement. We find that some bi-partite distillable entanglement persists for arbitrarily high losses.
The benefits of entanglement can outlast entanglement itself. In quantum illumination, entanglement is employed to better detect reflecting objects in environments so noisy that all entanglement is destroyed. Here, we show that quantum discord - a more resilient form of quantum correlations - explains the resilience of quantum illumination. We introduce a quantitative relation between the performance gain in quantum illumination and the amount of discord used to encode information about the presence or absence of a reflecting object. This highlights discord's role preserving the benefits of en…
Loss resilience of driven-dissipative remote entanglement in chiral waveguide quantum electrodynamics
University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）；Pritzker School of Molecular Engineering, University of Chicago（芝加哥大学普里茨克分子工程学院）；Department of Physics, University of Chicago（芝加哥大学物理系）
The orbital angular momentum of light (OAM) provides a promising approach for the implementation of multidimensional states (qudits) for quantum information purposes. In order to characterize the degradation undergone by the information content of qubits encoded in a bidimensional subspace of the orbital angular momentum degree of freedom of photons, we study how the state fidelity is affected by a transverse obstruction placed along the propagation direction of the light beam. Emphasis is placed on the effects of planar and radial hard-edged aperture functions on the state fidelity of Laguerr…
The speed-up provided by quantum algorithms with respect to their classical counterparts is at the origin of scientific interest in quantum computation. However, the fundamental reasons for such a speed-up are not yet completely understood and deserve further attention. In this context, the classical simulation of quantum algorithms is a useful tool that can help us in gaining insight. Starting from the study of general conditions for classical simulation, we highlight several important differences between two non-equivalent classes of quantum algorithms. We investigate their performance under…
Single-photon entanglement is one of the primary resources for quantum networks, including quantum repeater architectures. Such entanglement can be revealed with only local homodyne measurements through the entanglement witness presented in [Morin et al. Phys. Rev. Lett. 110, 130401 (2013)]. Here, we provide an extended analysis of this witness by introducing analytical bounds and by reporting measurements confirming its great robustness with regard to losses. This study highlights the potential of optical hybrid methods, where discrete entanglement is characterized through continuous-variable…
The dynamics of a cascaded system that consists of two atom-cavity subsystems is studied by using the quantum trajectory method. Unwanted losses are included, such as photon absorption and scattering by the cavity mirrors and spontaneous emission of the atoms. Considering an initially excited two-level atom in the source subsystem, analytical solutions are obtained. The entanglement evolution is studied for the two atoms and for the two intracavity fields.
Entanglement distribution task encounters a problem of how the initial entangled state should be prepared in order to remain entangled the longest possible time when subjected to local noises. In the realm of continuous-variable states and local Gaussian channels it is tempting to assume that the optimal initial state with the most robust entanglement is Gaussian too; however, this is not the case. Here we prove that specific non-Gaussian two-mode states remain entangled under the effect of deterministic local attenuation or amplification (Gaussian channels with the attenuation factor/power ga…
Multipartite quantum entanglement in $\mathcal{PT}$-symmetric molecular optomechanics: Nonreciprocal enhancement and thermal resilience to \SI{500}{\kelvin}
We present analytical compact solution for the density matrix and correlation functions of two collective-macroscopic spins evolving via Ising-like Hamiltonian in the presence of particle losses. The losses introduce non-local phase noise which destroys highly entangled states arising in the evolution. On the other hand, the states appearing at relatively short timescales, possessing EPR-like entanglement will survive. Applying our solutions to the recently proposed scheme to entangle two Bose-Einstein condensates, we estimate the optimal number of atoms for EPR correlations.
Most quantum systems that are used for generating entanglement and for practical applications are not isolated from the environment, and are hence susceptible to noise. Entanglement in more than one degree of freedom between two systems, known as hyperentanglement, is known to have certain advantages, including robustness against noise over conventional entangled states. Quantum illumination, imaging and communication schemes that involve sending one photon from a pair of entangled photons and retaining the other photon usually involve exposing only the signal photon to environmental noise. Th…
Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carriers. We solve a practically relevant problem of finding an optimal initial encoding to distribute entangled polarized qubits though communication lines with polarization dependent losses and extra depolarizing noise. The longest entanglement lifetime is shown to be attainable wit…
We propose how to achieve nonreciprocal quantum entanglement of light and motion and reveal its counterintuitive robustness against random losses. We find that by splitting the counterpropagating lights of a spinning resonator via the Sagnac effect, photons and phonons can be entangled strongly in a chosen direction but fully uncorrelated in the other. This makes it possible both to realize quantum nonreciprocity even in the absence of any classical nonreciprocity and also to achieve significant entanglement revival against backscattering losses in practical devices. Our work provides a way to…
We examined the possibility of recovering the losses of entanglement and the non-local advantage by using the local symmetric operations. The improvement efficiency may be increased by applying the symmetric operations on both qubits. The recovering process of both phenomenon is exhibited clearly when only one qubit is accelerated and the symmetric operations is applied on both qubits. It is shown that, for large acceleration, the non-local coherent advantage may be re-birthed by using these symmetric operations.
We study the diffraction of two maximally entangled qubits encoded into spatial modes of light with orbital angular momenta $\pm \hbar l_0$, on angular apertures. Exploiting the uncertainty relation between angular position and momentum, we quantify the diffraction-induced entanglement loss, for different $l_0$, as a function of the angular uncertainty $Δϕ$ induced by the apertures. We demonstrate that the degradation of entanglement follows a universal law parametrised by the product $l_0Δϕ$ alone.} {We study the diffraction of two photonic qubits, which are initially maximally entangled in t…
Improving Entanglement Resilience in Quantum Memories with Error-Detection-Based Distillation
School of Electrical Engineering, Korea University（韩国大学电气工程学院）；Quantum Network Research Center, Korea Institute of Science and Technology Information（韩国科学技术信息研究院量子网络研究中心）
For entangled states of light both the amount of entanglement and the sensitivity to noise generally increase with the number of photons in the state. The entanglement-sensitivity tradeoff is investigated for a particular set of states, multi-dimensional entangled coherent states. Those states possess an arbitrarily large amount of entanglement $E$ provided the number of photons is at least of order $2^{2E}$. We calculate how fast that entanglement decays due to photon absorption losses and how much entanglement is left. We find that for very small losses the amount of entanglement lost is equ…
We address the dynamics induced by collective atomic recoil in a Bose-Einstein condensate in presence of radiation losses and atomic decoherence. In particular, we focus on the linear regime of the lasing mechanism, and analyze the effects of losses and decoherence on the generation of entanglement. The dynamics is that of three bosons, two atomic modes interacting with a single-mode radiation field, coupled with a bath of oscillators. The resulting three-mode dissipative Master equation is solved analytically in terms of the Wigner function. We examine in details the two complementary limits …
We study the effects of losses on the entanglement created between two separate atomic gases by optical probing and homodyne detection of the transmitted light. The system is well-described in the Gaussian state formulation. Analytical results quantifying the degree of entanglement between the two gases are derived and compared with the entanglement in a pair of light pulses generated by an EPR source. For low (high) transmission losses the highest degree of entanglement is obtained by probing with squeezed (antisqueezed) light. In an asymmetric setup where light is only sent one way through t…
Coherent information quantifies the achievable rate of the reliable quantum information transmission through a communication channel. Use of the correlated quantum states instead of the factorized ones may result in an increase in the coherent information, a phenomenon known as superadditivity. However, even for simple physical models of channels it is rather difficult to detect the superadditivity and find the advantageous multipartite states. Here we consider the case of polarization dependent losses and propose some physically motivated multipartite entangled states which outperform all fac…
Entanglement in bipartite continuous-variable systems is investigated in the presence of partial losses, such as those introduced by a realistic quantum communication channel, e.g. by propagation in an optical fiber. We find that entanglement can vanish completely for partial losses, in a situa- tion reminiscent of so-called entanglement sudden death. Even states with extreme squeezing may become separable after propagation in lossy channels. Having in mind the potential applications of such entangled light beams to optical communications, we investigate the conditions under which entanglement…
We consider a Bell-like inequality performed using various instances of multi-photon entangled states to demonstrate that losses occurring after the unitary transformations used in the nonlocality test can be counteracted by enhancing the "size" of such entangled states. In turn, this feature can be used to overcome detection inefficiencies affecting the test itself: a slight increase in the size of such states, pushing them towards a more "macroscopic" form of entanglement, significantly improves the state robustness against detection inefficiency, thus easing the closing of the detection loo…
We study the nonlocal properties of two-qubit maximally-entangled and N-qubit Greenberger-Horne-Zeilinger states under local decoherence. We show that the (non)resilience of entanglement under local depolarization or dephasing is not necessarily equivalent to the (non)resilience of Bell-inequality violations. Apart from entanglement and Bell-inequality violations, we consider also nonlocality as quantified by the nonlocal content of correlations, and provide several examples of anomalous behaviors, both in the bipartite and multipartite cases. In addition, we study the practical implications o…
The influence of losses in the transmission of continuous-variable entangled light through linear devices such as optical fibers is studied, with special emphasis on Gaussian states. Upper bounds on entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement and thus do not show the drastic decrease of entanglement with increasing mean photon number, as does the distance measure. In particular, it shows that losses give rise to entanglement saturation, which principally limi…
A parametric down-conversion (PDC) source can be used as either a triggered single photon source or an entangled photon source in quantum key distribution (QKD). The triggering PDC QKD has already been studied in the literature. On the other hand, a model and a post-processing protocol for the entanglement PDC QKD are still missing. In this paper, we fill in this important gap by proposing such a model and a post-processing protocol for the entanglement PDC QKD. Although the PDC model is proposed to study the entanglement-based QKD, we emphasize that our generic model may also be useful for ot…
Understanding the distribution of quantum entanglement over many parties is a fundamental challenge of quantum physics and is of practical relevance for several applications in the field of quantum information. Here we use methods from quantum metrology to microscopically characterize the entanglement structure of multimode continuous-variable states in all possible multi-partitions and in all reduced distributions. From experimentally measured covariance matrices of Gaussian states with 2, 3, and 4 photonic modes with controllable losses, we extract the metrological sensitivity as well as an …
Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the ent…
Several emerging quantum technologies, including quantum networks, modular and fusion-based quantum computing, rely crucially on the ability to perform photonic Bell state measurements. Therefore, photon losses and the 50\% success probablity upper bound of Bell state measurements pose a critical limitation to photonic quantum technologies. Here, we develop protocols that overcome these two key challenges through logical encoding of photonic qubits. Our approach uses a tree graph state logical encoding, which can be produced deterministically with a few quantum emitters, and achieves near-dete…
We present a detailed theoretical analysis for the distillation of one copy of a mixed two-mode continuous-variable entangled state using beamsplitters and coherent photon-detection techniques, including conventional on-off detectors and photon number resolving detectors. The initial Gaussian mixed-entangled states are generated by transmitting a two-mode squeezed state through a lossy bosonic channel, corresponding to the primary source of errors in current approaches to optical quantum communication. We provide explicit formulas to calculate the entanglement in terms of logarithmic negativit…
Entangled quantum states, such as N00N states, are of major importance for quantum technologies due to their quantum-enhanced performance. At the same time, their quantum correlations are relatively vulnerable when they are subjected to imperfections. Therefore, it is crucial to determine under which circumstances their distinct quantum features can be exploited. In this paper, we study the entanglement property of noisy N00N states. This class of states is a generalization of N00N states including various attenuation effects, such as mixing, constant or fluctuating losses, and dephasing. To v…
The experimental verification of quantum features, such as entanglement, at large scales is extremely challenging because of environment-induced decoherence. Indeed, measurement techniques for demonstrating the quantumness of multiparticle systems in the presence of losses are difficult to define and, if not sufficiently accurate, they provide wrong conclusions. We present a Bell test where one photon of an entangled pair is amplified and then detected by threshold detectors, whose signals undergo postselection. The amplification is performed by a classical machine, which produces a fully sepa…
We discuss the generation of a macroscopic entangled state in a single atom cavity-QED system. The three-level atom in a cascade configuration interacts dispersively with two classical coherent fields inside a doubly resonant cavity. We show that a macroscopic entangled state between these two cavity modes can be generated under large detuning conditions. The entanglement persists even under the presence of cavity losses.
We develop a theory and accompanying mathematical model for quantum communication via any number of intermediate entanglement swapping operations and solve numerically for up to three intermediate entanglement swapping operations. Our model yields two-photon interference visibilities post-selected on photon counts at the intermediate entanglement-swapping stations. Realistic experimental conditions are accommodated through parametric down-conversion rate, photon-counter efficiencies and dark-count rates, and instrument and transmission losses. We calculate achievable quantum communication dist…
The influence of losses in the interferometric generation and the transmission of continuous-variable entangled light is studied, with special emphasis on Gaussian states. Based on the theory of quantum-state transformation at absorbing dielectric devices, the amount of entanglement is quantified by means of the relative-entropy measure. Upper bounds of entanglement and the distance to the set of separable Gaussian states are calculated. Compared with the distance measure, the bounds can substantially overestimate the entanglement. In particular, they do not show the drastic decrease of entang…
We consider the creation of polarization entangled light from parametric down- conversion driven by an intense pulsed pump inside a cavity. The multi-photon states produced are close approximations to singlet states of two very large spins. A criterion is derived to quantify the entanglement of such states. We study the dynamics of the system in the presence of losses and other imperfections, concluding that the creation of strongly entangled states with photon numbers up to a million seems achievable.
Multi-photon states from parametric down-conversion can be entangled both in polarization and photon number. Maximal high-dimensional entanglement can be concentrated from these states via photon counting. This makes them natural candidates for quantum key distribution, where the presence of more than one photon per detection interval has up to now been considered as undesirable. We propose a simple multi-photon protocol for the case of low losses and point out the robustness of the entanglement under photon loss.
We adopt the beam splitter model for losses to analyse the performance of a recent compact continuous-variable entanglement distillation protocol [Phys. Rev. Lett. 108, 060502, (2012)] implemented using realistic quantum memories. We show that the decoherence undergone by a two-mode squeezed state while stored in a quantum memory can strongly modify the results of the preparatory step of the protocol. We find that the well-known method for locally increasing entanglement, phonon subtraction, may not result in entanglement gain when losses are taken into account. Thus, we investigate the critic…
We theoretically investigate the entanglement dynamics in photonic Mott insulators in the presence of particle losses and dephasing. We explore two configurations where entanglement is generated following the injection or extraction of a photon in the central site of a chain of cavity resonators. We study the entanglement negativity of two-site reduced density matrices as a function of time and inter-site distance. Our findings show that in spite of particle losses the quantum entanglement propagation exhibits a ballistic character with propagation speeds related to the differerent quasipartic…
Noise can be considered the natural enemy of quantum information. An often implied benefit of high-dimensional entanglement is its increased resilience to noise. However, manifesting this potential in an experimentally meaningful fashion is challenging and has never been done before. In infinite dimensional spaces, discretisation is inevitable and renders the effective dimension of quantum states a tunable parameter. Owing to advances in experimental techniques and theoretical tools, we demonstrate an increased resistance to noise by identifying two pathways to exploit high-dimensional entangl…
We discuss the conclusions that can be drawn on a recent experimental micro-macro entanglement test [F. De Martini, F. Sciarrino, and C. Vitelli, Phys. Rev. Lett. 100, 253601 (2008). The system under investigation is generated through optical parametric amplification of one photon belonging to an entangled pair. The adopted entanglement criterion makes it possible to infer the presence of entanglement before losses, that occur on the macrostate, under a specific assumption. In particular, an a priori knowledge of the system that generates the micro-macro pair is necessary to exclude a class of…
Based on correlations of coherently displaced photon-numbers, we derive entanglement criteria for the purpose to verify non-Gaussian entanglement. Our construction method enables us to verify bipartite and multipartite entanglement of complex states of light. An important advantage of our technique is that the certified entanglement even persists in the presence of arbitrarily high, constant losses. We exploit experimental correlation schemes for the two-mode and multimode scenarios, which allow us to directly measure the desired observables. To detect entanglement of a given state, a genetic …
We apply spin-squeezing techniques to identify and quantify highly multi-partite photonic entanglement in polarization-squeezed light. We consider a practical single-mode scenario, and find that Wineland-criterion polarization squeezing implies entanglement of a macroscopic fraction of the total photons. A Glauber-theory computation of the observable N-photon density matrix, with N up to 100, finds that N-partite entanglement is observable despite losses and without post-selection. We estimate that existing detectors could observe $\sim1000$-partite entanglement from a few dB of polarization s…
We propose a hybrid approach to the experimental assessment of the genuine quantum features of a general system consisting of microscopic and macroscopic parts. We infer entanglement by combining dichotomic measurements on a bidimensional system and phase-space inference through the Wigner distribution associated with the macroscopic component of the state. As a benchmark, we investigate the feasibility of our proposal in a bipartite-entangled state composed of a single-photon and a multiphoton field. Our analysis shows that, under ideal conditions, maximal violation of a Clauser-Horne-Shimony…
Large-scale quantum information processing networks will most probably require the entanglement of distant systems that do not interact directly. This can be done by performing entangling gates between standing information carriers, used as memories or local computational resources, and flying ones, acting as quantum buses. We report the deterministic entanglement of two remote transmon qubits by Raman stimulated emission and absorption of a traveling photon wavepacket. We achieve a Bell state fidelity of 73 %, well explained by losses in the transmission line and decoherence of each qubit.
We predict that the collective excitations of an atomic array become entangled with the light of a high-finesse cavity mode when they are suitably coupled. This entanglement is of Einstein-Podolsky-Rosen type, it is robust against cavity losses and is a stationary property of the coupled system. It is generated when the atomic array is aligned along the cavity axis and driven transversally by a laser, when coherent scattering of photons into the cavity mode is suppressed because of phase-mismatching. We identify the parameter regimes under which entanglement is found and show that these are co…
