We demonstrate that the magnetic susceptibility of strongly alternating antiferromagnetic spin-1/2 chains is an entanglement witness. Specifically, magnetic susceptibility of copper nitrate (CN) measured in 1963 (Berger et al., Phys. Rev. 132, 1057 (1963)) cannot be described without presence of entanglement. A detailed analysis of the spin correlations in CN as obtained from neutron scattering experiments (Xu et al., Phys. Rev. Lett. 84, 4465 (2000)) provides microscopic support for this interpretation. We present a quantitative analysis resulting in the critical temperature of 5K in both, completely independent, experiments below which entanglement exists.
We investigate the scheme for controlling information characterized by Von-Neumann entropy and the stationary state entanglement characterized by concurrence of two solid state qubits in the collective dephasing channel. It is shown that the local maximal value of the stationary state concurrence always corresponds to the local minimal value of information. We also propose a scheme for remotely controlling the entanglement of two solid state qubits against the collective dephasing. This idea may open a door to remotely suppress the detrimental effects of decoherence.
A basic problem of quantum communication is to generate entangled states between distant sites. Using entanglement swapping, we are able to generate an entangled state of the desired distance from connecting many short distance entangled states. We investigate the entanglement swapping of the Valence-Bond Solid state with un-identical local filtering operations. It is found that not only a long distance entangled state can be generated from the VBS state, but also there is a trade-off between the probability and the degree of the entanglement in the resultant state. The results are also genera…
The non-Markovia dynamics of quantum evolution plays an important role in open quantum sytem. However, how to quantify non-Markovian behavior and what can be obtained from non- Markovianity are still open questions, especially in complex solid systems. Here we address the problem of quantifying non-Markovianity with entanglement in a genuine noisy solid state system at room temperature. We observed the non-Markovianity of quantum evolution with entanglement. By prolonging entanglement with dynamical decoupling, we can reveal the non-Markovianity usually concealed in the environment and obtain …
The Valence-Bond-Solid (VBS) states are in general ground states for certain gapped models. We consider the entanglement of VBS states on a two-dimensional Cayley tree. We show that the entropy of the reduced density operator does not depend on the whole size of the Cayley tree. We also show that asymptotically, the entropy is liearly proportional to the number of singlet states cut by the reduced density operator of the VBS state.
We show how to create maximal entanglement between spectrally distinct solid-state emitters embedded in a waveguide interferometer. By revealing the rich underlying structure of multi-photon scattering in emitters, we show that a two-photon input state can generate deterministic maximal entanglement even for emitters with significantly different transition energies and line-widths. The optimal frequency of the input is determined by two competing processes: which-path erasure and interaction strength. We find that smaller spectral overlap can be overcome with higher photon numbers, and quasi-m…
Here we demonstrate generating and storing entanglement in a solid state spin-wave quantum memory with on-demand read out using the process of rephased amplified spontaneous emission (RASE). Amplified spontaneous emission (ASE), resulting from an inverted ensemble of Pr$^{3+}$ ions doped into a Y$_2$SiO$_5$ crystal, generates entanglement between collective states of the praseodymium ensemble and the output light. The ensemble is then rephased using a four-level photon echo technique. Entanglement between the ASE and its echo is confirmed and the inseparability violation preserved when the RAS…
The generation and distribution of entanglement are key resources in quantum repeater schemes. Temporally multiplexed systems offer time-bin encoding of quantum information which provides robustness against decoherence in fibers, crucial in long distance communication. Here we demonstrate the direct generation of entanglement in time between a photon and a collective spin excitation in a rare earth ion doped ensemble. We analyze the entanglement by mapping the atomic excitation onto a photonic qubit and by using time-bin qubits analyzers implemented with another doped crystal using the atomic …
Quantum entanglement, the essential resource for quantum information processing, has rich dynamics under different environments. Probing different entanglement dynamics typically requires exquisite control of complicated system-environment coupling in real experimental systems. Here, by a simple control of the effective solid-state spin bath in a diamond sample, we observe rich entanglement dynamics, including the conventional asymptotic decay as well as the entanglement sudden death, a term coined for the phenomenon of complete disappearance of entanglement after a short finite time interval.…
Future quantum networks will enable the distribution of entanglement between distant locations and allow applications in quantum communication, quantum sensing and distributed quantum computation. At the core of this network lies the ability of generating and storing entanglement at remote, interconnected quantum nodes. While remote physical systems of various nature have been successfully entangled, none of these realisations encompassed all of the requirements for network operation, such as telecom-compatibility and multimode operation. Here we report the demonstration of heralded entangleme…
The potential impact of future quantum networks hinges on high-quality quantum entanglement shared between network nodes. Unavoidable real-world imperfections necessitate means to improve remote entanglement by local quantum operations. Here we realize entanglement distillation on a quantum network primitive of distant electron-nuclear two-qubit nodes. We demonstrate the heralded generation of two copies of a remote entangled state through single-photon-mediated entangling of the electrons and robust storage in the nuclear spins. After applying local two-qubit gates, single-shot measurements h…
Entanglement between photons at telecommunication wavelengths and long-lived quantum memories is one of the fundamental requirements of long-distance quantum communication. Quantum memories featuring on-demand read-out and multimode operation are additional precious assets that will benefit the communication rate. In this work we report the first demonstration of entanglement between a telecom photon and a collective spin excitation in a multimode solid-state quantum memory. Photon pairs are generated through widely non-degenerate parametric down-conversion, featuring energy-time entanglement …
Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However this entanglement may appear a mere mathematical artifact of the typical symmetrization procedure of many-body wave function in solid state physics. Here we show that this entanglement is physical demonstrating the principles of its extraction from a typical solid state system by scattering two particles off the system. Moreover we show how to simulate this process using present-day optical lattices technology. Thi…
Multipartite entanglement, measured by the geometric entanglement(GE), is discussed for integer spin Valance-Bond-Solid (VBS) state respectively with periodic boundary condition(PBC) and open boundary condition(OBC) in this paper. The optimization in the definition of geometric entanglement can be reduced greatly by exploring the symmetry of VBS state, and then the fully separable state can be determined explicitly. Numerical evaluation for GE by the random simulation is also implemented in order to demonstrate the validity of the reductions. Our calculations show that GE is saturated by a fin…
We experimentally demonstrate room-temperature storage of quantum entanglement using two nuclear spins weakly coupled to the electronic spin carried by a single nitrogen-vacancy center in diamond. We realize universal quantum gate control over the three-qubit spin system and produce entangled states encoded within the decoherence-free subspace of the two nuclear spins. By injecting arbitrary collective noise, we demonstrate that the decoherence-free entangled state has coherence time longer than that of other entangled states by an order of magnitude in our experiment.
Quantum systems unfold diversified correlations which have no classical counterparts. These quantum correlations have various different facets. Quantum entanglement, as the most well known measure of quantum correlations, plays essential roles in quantum information processing. However, it has recently been pointed out that quantum entanglement cannot describe all the nonclassicality in the correlations. Thus the study of quantum correlations in separable states attracts widely attentions. Herein, we experimentally investigate the quantum correlations of separable thermal states in terms of qu…
Entanglement, as a key resource for modern quantum technologies, is extremely fragile due to the decoherence. Here, we show that a quantum autoencoder, which is trained to compress a particular set of quantum entangled states into a subspace that is robust to decoherence, can be employed to preserve entanglement. The training process is based on a hybrid quantum-classical approach to improve the efficiency in building the autoencoder and reduce the experimental errors during the optimization. Using nitrogen-vacancy centers in diamond, we demonstrate that the entangled states between the electr…
In this paper we study how to preserve entanglement and nonlocality under dephasing produced by classical noise with large low-frequency components, as $1/f$ noise, by Dynamical Decoupling techniques. We first show that quantifiers of entanglement and nonlocality satisfy a closed relation valid for two independent qubits locally coupled to a generic environment under pure dephasing and starting from a general class of initial states. This result allows to assess the efficiency of pulse-based dynamical decoupling for protecting nonlocal quantum correlations between two qubits subject to pure-de…
Here we evaluate the many-body entanglement properties of a generalized SU(n) valence bond solid state on a chain. Our results follow from a derivation of the transfer matrix of the system which, in combination with symmetry properties, allows for a new, elegant and straightforward evaluation of different entanglement measures. In particular, the geometric entanglement per block, correlation length, von Neumann and Rényi entropies of a block, localizable entanglement and entanglement length are obtained in a very simple way. All our results are in agreement with previous derivations for the SU…
Precise parameter estimation plays a central role in science and technology. The statistical error in estimation can be decreased by repeating measurement, leading to that the resultant uncertainty of the estimated parameter is proportional to the square root of the number of repetitions in accordance with the central limit theorem. Quantum parameter estimation, an emerging field of quantum technology, aims to use quantum resources to yield higher statistical precision than classical approaches. Here, we report the first room-temperature implementation of entanglement-enhanced phase estimation…
Entangling quantum systems with different characteristics through the exchange of photons is a prerequisite for building future quantum networks. Proving the presence of entanglement between quantum memories for light working at different wavelengths furthers this goal. Here, we report on a series of experiments with a thulium-doped crystal, serving as a quantum memory for 794 nm photons, an erbium-doped fibre, serving as a quantum memory for telecommunication-wavelength photons at 1535 nm, and a source of photon pairs created via spontaneous parametric down-conversion. Characterizing the phot…
We analyze and compare three different schemes that can be used to generate entanglement between spin qubits in optically-active single solid-state quantum systems. Each scheme is based on first generating entanglement between the spin degree of freedom and either the photon number, the time bin, or the polarization degree of freedom of photons emitted by the systems. We compute the time evolution of the entanglement generation process by decomposing the dynamics of a Markovian master equation into a set of propagation superoperators conditioned on the cumulative detector photon count. We then…
We show how to implement quantum transport, generate entangled state and achieve spatial entanglement distribution via topological Thouless pumping in one-dimensional disordered lattices. We introduce the on-site disorders to suppress the high-order resonant tunneling (which cause wavepacket dispersion) and realize dispersionless Thouless pumping. The interplay between the on-site disorders and the band topology enables robust unidirectional transport. We also demonstrate how to prepare spatially entangled two-particle NOON state via Hong-Ou-Mandel interference assisted by the Thouless pumping…
In this paper we provide the analytical derivation of the global geometric entanglement per block for the valence bond solid ground state of the spin-1 AKLT chain. In particular, we show that this quantity saturates exponentially fast to a constant when the sizes of the blocks are sufficiently large. Our result provides the first known example of an analytical calculation of the geometric entanglement for a gapped quantum many-body system in one dimension and far away from a quantum critical point.
In a recent paper, Liu et al. [Nat. Commun. 6:6726 (2015)] claim to perform the first room temperature entanglement-enhanced phase measurement in a solid-state system. We argue here that this claim is incorrect: their measurement is not enhanced because of the entanglement in their system, but instead the enhancement comes from the fact that the phase shift is applied twice to their state.
Entanglement is the quintessential quantum phenomenon and a necessary ingredient in most emerging quantum technologies, including quantum repeaters, quantum information processing (QIP) and the strongest forms of quantum cryptography. Spin ensembles, such as those in liquid state nuclear magnetic resonance, have been powerful in the development of quantum control methods, however, these demonstrations contained no entanglement and ultimately constitute classical simulations of quantum algorithms. Here we report the on-demand generation of entanglement between an ensemble of electron and nuclea…
We study entanglement degradation of two non-interacting qubits subject to independent baths with broadband spectra typical of solid state nanodevices. We obtain the analytic form of the concurrence in the presence of adiabatic noise for classes of entangled initial states presently achievable in experiments. We find that adiabatic (low frequency) noise affects entanglement reduction analogously to pure dephasing noise. Due to quantum (high frequency) noise, entanglement is totally lost in a state-dependent finite time. The possibility to implement on-chip both local and entangling operations …
Purdue University（普渡大学）；Max Planck Institute of Quantum Optics（马克斯·普朗克量子光学研究所）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与工程中心）；Virginia Tech（弗吉尼亚理工大学）；Northwestern University（西北大学）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；Stanford University（斯坦福大学）
We present a proposal for the experimental observation of energy-time entanglement of quasi-particles in mesoscopic physics. This type of entanglement arises whenever correlated particles are produced at the same time and this time is uncertain in the sense of quantum uncertainty, as has been largely used in photonics. We discuss its feasibility for electron-hole pairs. In particular, we argue that the recently fabricated 2DEG-2DHG junctions, irradiated with a continuous laser, behave as "entanglers" for energy-time entanglement.
Generating robust entanglement among solid-state spins is key for applications in quantum information processing and precision sensing. We show here a dissipative approach to generate such entanglement among the hyperfine coupled electron nuclear spins using the rapid optical decay of electronic excited states. The combined dark state interference effects of the optical and microwave driving fields in the presence of spontaneous emission from the short-lived excited state leads to a dissipative formation of an entangled steady state. We show that the dissipative entanglement is generated for a…
We investigate the von Neumann entropy of a block of subsystem for the valence-bond solid (VBS) state with general open boundary conditions. We show that the effect of the boundary on the von Neumann entropy decays exponentially fast in the distance between the subsystem considered and the boundary sites. Further, we show that as the size of the subsystem increases, its von Neumann entropy exponentially approaches the summation of the von Neumann entropies of the two ends, the exponent being related to the size. In contrast to critical systems, where boundary effects to the von Neumann entropy…
We show that magnetic susceptibility can reveal spin entanglement between individual constituents of a solid, while magnetisation describes their local properties. We then show that these two thermodynamical quantities satisfy complementary relation in the quantum-mechanical sense. It describes sharing of (quantum) information in the solid between spin entanglement and local properties of its individual constituents. Magnetic susceptibility is shown to be a macroscopic spin entanglement witness that can be applied without complete knowledge of the specific model (Hamiltonian) of the solid.
We study entanglement in Valence-Bond-Solid state. It describes the ground state of Affleck, Kennedy, Lieb and Tasaki quantum spin chain. The AKLT model has a gap and open boundary conditions. We calculate an entropy of a subsystem (continuous block of spins). It quantifies the entanglement of this block with the rest of the ground state. We prove that the entanglement approaches a constant value exponentially fast as the size of the subsystem increases. Actually we proved that the density matrix of the continuous block of spins depends only on the length of the block, but not on the total siz…
Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in …
We demonstrate that the presence of entanglement in macroscopic bodies (e.g. solids) in thermodynamical equilibrium could be revealed by measuring heat-capacity. The idea is that if the system were in a separable state, then for certain Hamiltonians heat capacity would not tend asymptotically to zero as the temperature approaches absolute zero. Since this would contradict the third law of thermodynamics, one concludes that the system must contain entanglement. The separable bounds are obtained by minimization of the heat capacity over separable states and using its universal low-temperature be…
Implementations of solid state quantum optics provide us with devices where qubits are placed at fixed positions in photonic or plasmonic one dimensional waveguides. We show that solely by controlling the position of the qubits and with the help of a coherent driving, collective spontaneous decay may be engineered to yield an entangled mesoscopic steady-state. Our scheme relies on the realization of pure superradiant Dicke models by a destructive interference that cancels dipole-dipole interactions in one-dimension.
We investigate the time evolution of entanglement under various models of decoherence: A general heuristic model based on local relaxation and dephasing times, and two microscopic models describing decoherence of electron spin qubits in quantum dots due to the hyperfine interaction with the nuclei. For each of the decoherence models, we investigate and compare how long the entanglement can be detected. We also introduce filtered witness operators, which extend the available detection time, and investigate this detection time for various multipartite entangled states. By comparing the time requ…
Quantum communication between remote superconducting systems is being studied intensively to increase the number of integrated superconducting qubits and to realize a distributed quantum computer. Since optical photons must be used for communication outside a dilution refrigerator, the direct conversion of microwave photons to optical photons has been widely investigated. However, the direct conversion approach suffers from added photon noise, heating due to a strong optical pump, and the requirement for large cooperativity. Instead, for quantum communication between superconducting qubits, we…
We show that two identical solid-state qubits can be made fully entangled (starting from completely mixed state) with probability 1/4 just measuring them by a detector, equally coupled to the qubits. This happens in the case of repeated strong (projective) measurements as well as in a more realistic case of weak continuous measurement. In the latter case the entangled state can be identified by a flat spectrum of the detector shot noise, while the non-entangled state (probability 3/4) leads to a spectral peak at the Rabi frequency with the maximum peak-to-pedestal ratio of 32/3.
Control over electron-spin states, such as coherent manipulation, filtering and measurement promises access to new technologies in conventional as well as in quantum computation and quantum communication. In this paper, we review recent theoretical proposal of using electron spins in quantum confined structures as qubits. We also present a theoretical proposal for testing Bell's inequality in nano-electronics devices. We show that the entanglement of two electron spins can be detected in the spin filter effect in the nanostructure semiconductor / ferromagnetic semiconductor / semiconductor jun…
Bell-inequality checks constitute a probe of entanglement -- given a source of entangled particles, their violation are a signature of the non-local nature of quantum mechanics. Here, we study a solid state device producing pairs of entangled electrons, a superconductor emitting Cooper pairs properly split into the two arms of a normal-metallic fork with the help of appropriate filters. We formulate Bell-type inequalities in terms of current-current cross-correlators, the natural quantities measured in mesoscopic physics; their violation provides evidence that this device indeed is a source of…
Solid-state spin arrays are being engineered in varied systems, including gated coupled quantum dots and interacting dopants in semiconductor structures. Beyond quantum computation, these arrays are useful integrated analog simulators for many-body models. As entanglement between individual spins is extremely short ranged in these models, one has to measure the entanglement entropy of a block in order to truly verify their many-body entangled nature. Remarkably, the characteristic scaling of entanglement entropy, predicted by conformal field theory, has never been measured. Here we show that w…
The development of sources delivering non-classical states of light is one of the main needs for applications of optical quantum information science. Here, we demonstrate the generation of non-classical states of light using strong-laser fields driving a solid-state system, by using the process of high-order harmonic generation, where an electron tunnels out of the parent site and, later on, recombines on it emitting high-order harmonic radiation, at the expense of affecting the driving laser field. Since in solid-state systems the recombination of the electron can be delocalized along the mat…
We probe the bulk geometry of the Wegner Wilson Flow (WWF) in the context of many-body localization, by addressing efficiency and bulk entanglement growth measures through approximating upper bounds on the boundary entanglement entropy. We connect these upper bounds to the Fubini-Study metric and clarify how a central quantity, the information fluctuation complexity, distinguishes bulk unitary rotation from entanglement production. We also give a short new proof of the small incremental entangling theorem in the absence of ancillas, achieving a dimension-independent, universal factor of $c= 2$…
A theoretical model for high-order harmonic generation (HHG) in bulk solids is considered. Our approach treats laser-induced inter- and intraband currents on an equal footing. The sum of these currents is the source of the high-order harmonic radiation, and does not depend on the particular electromagnetic gauge we choose to describe the process. On the other hand, as it is shown using analytic and numerical calculations, the distinction between intra- and interband dynamics is gauge dependent, implying that the interpretation of the process of HHG using these terms requires carefulness.
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales. In particular, an approximate variant of holographic quantum error correcting code emerges at low energy for critical systems. This implies that two operators that are largely separated in scales behave as if they are spatially separated operators, in the sense that they obey a Lieb-Robinson type locality bound under a time evolution generated bya local Hami…
We create a multi-partite entangled state by storing a single photon in a crystal that contains many large atomic ensembles with distinct resonance frequencies. The photon is re-emitted at a well-defined time due to an interference effect analogous to multi-slit diffraction. We derive a lower bound for the number of entangled ensembles based on the contrast of the interference and the single-photon character of the input, and we experimentally demonstrate entanglement between over two hundred ensembles, each containing a billion atoms. In addition, we illustrate the fact that each individual e…
Boundary impurities are known to dramatically alter certain bulk properties of 1+1 dimensional strongly correlated systems. The entanglement entropy of a zero temperature Luttinger liquid bisected by a single impurity is computed using a novel finite size scaling/bosonization scheme. For a Luttinger liquid of length 2L and UV cut off, e, the boundary impurity correction (δS) to the bulk logarithmic entanglement entropy (S_{ent} ~ ln(L/e)) scales as δS ~ y ln(L/e), where y is the renormalized impurity coupling constant. In this way, the bulk entanglement entropy within a region is related to sc…
We investigate entanglement properties in the ground state of the open/periodic SU($n$) generalized valence-bond-solid state consisting of representations of SU($n$). We obtain exact expression for the reduced density matrix of a block of contiguous spins and explicitly evaluate the von Neumann and the Rényi entropies. We discover that the Rényi entropy is independent of the parameter $α$ in the limit of large block sizes and its value $2 \log n$ coincides with that of von Neumann entropy. We also find the direct relation between the reduced density matrix of the subsystem and edge states for …
We consider a quantum mechanical model for the high-order harmonic generation in bulk solids. The bandgap is assumed to be considerably larger than the exciting photon energy. Using dipole approximation, the dynamical equations for different initial Bloch states are decoupled in the velocity gauge. Although there is no quantum mechanical interference between the time evolution of different initial states, the complete harmonic radiation results from the interference of fields emitted by all the initial (valence band) states. In particular, this interference is shown to be responsible for the s…
In this chapter we review the use of spins in optically-active InAs quantum dots as the key physical building block for constructing a quantum repeater, with a particular focus on recent results demonstrating entanglement between a quantum memory (electron spin qubit) and a flying qubit (polarization- or frequency-encoded photonic qubit). This is a first step towards demonstrating entanglement between distant quantum memories (realized with quantum dots), which in turn is a milestone in the roadmap for building a functional quantum repeater. We also place this experimental work in context by p…
