We present a finite-size scaling analysis of the entanglement in a two-dimensional arrays of quantum dots modeled by the Hubbard Hamiltonian on a triangular lattice. Using multistage block renormalization group approach, we have found that there is an abrupt jump of the entanglement when a first-order quantum phase transition occurs. At the critical point, the entanglement is constant, independent of the block size.
A system of two or more quantum dots interacting with a dissipative plasmonic nanostructure is investigated in detail by using a cavity quantum electrodynamics approach with a model Hamiltonian. We focus on determining and understanding system configurations that generate multiple bipartite quantum entanglements between the occupation states of the quantum dots. These configurations include allowing for the quantum dots to be asymmetrically coupled to the plasmonic system. Analytical solution of a simplified limit for an arbitrary number of quantum dots and numerical simulations and optimizati…
Multipartite entanglement is indispensable in the implementation of quantum technologies and the fundamental test of quantum mechanics. Here we study how the W state and W-like state may be generated in a quantum-dot array by controlling the coupling between an incident photon and the quantum dots on a waveguide. We also discuss how the coupling may be controlled to observe the sudden death of entanglement. Our work can find potential applications in quantum information processing.
With Hubbard model, the entanglement scaling behavior in a two-dimensional itinerant system is investigated. It has been found that, on the two sides of the critical point denoting an inherent quantum phase transition (QPT), the entanglement follows different scalings with the size just as an order parameter does. This fact reveals the subtle role played by the entanglement in QPT as a fungible physical resource.
The dynamics of the entanglement for coherent excitonic states in the system of two coupled large semiconductor quantum dots ($R/a_{B}\gg 1$) mediated by a single-mode cavity field is investigated. Maximally entangled coherent excitonic states can be generated by cavity field initially prepared in odd coherent state. The entanglement of the excitonic coherent states between two dots reaches maximum when no photon is detected in the cavity. The effects of the zero-temperature environment on the entanglement of excitonic coherent state are also studied using the concurrence for two subsystems of…
Exciton fine-structure splittings within quantum dots introduce phase differences between the two biexciton decay paths that greatly reduce the entanglement of photon pairs generated via biexciton recombination. We analyze this problem in the frequency domain and propose a practicable method to compensate the phase difference by inserting a spatial light modulator, which substantially improves the entanglement of the photon pairs without any loss.
We present a novel approach to look for the existence of maximum entanglement in a system of two identical quantum dots coupled by the Forster process and interacting with a classical laser field. Our approach is not only able to explain the existing treatments, but also provides further detailed insights into the coupled dynamics of quantum dots systems. The result demonstrates that there are two ways for generating maximum entangled states, one associated with far off-resonance interaction, and the other associated with the weak field limit. Moreover, it is shown that exciton decoherence res…
We show how two qubits encoded in the orbital states of two quantum dots can be entangled or disentangled in a controlled way through their interaction with a weak electron current. The transmission/reflection spectrum of each scattered electron, acting as an entanglement mediator between the dots, shows a signature of the dot-dot entangled state. Strikingly, while few scattered carriers produce decoherence of the whole two-dots system, a larger number of electrons injected from one lead with proper energy is able to recover its quantum coherence. Our numerical simulations are based on a real-…
We describe a method for generating entanglement between two spatially separated dipoles coupled to optical micro-cavities. The protocol works even when the dipoles have different resonant frequencies and radiative lifetimes. This method is particularly important for solid-state emitters, such as quantum dots, which suffer from large inhomogeneous broadening. We show that high fidelities can be obtained over a large dipole detuning range without significant loss of efficiency. We analyze the impact of higher order photon number states and cavity resonance mismatch on the performance of the pro…
We study the coherent dynamics of one- and two-electron transport in a linear array of tunnel-coupled quantum dots. We find that this system exhibits a rich variety of coherent phenomena, ranging from electron wavepacket propagation and interference to two-particle bonding and entanglement. Our studies, apart from their relevance to the exploration of quantum dynamics and transport in periodic structures, are also aimed at possible applications in future quantum computation schemes.
Entanglement between quantum dots transmitted via Majorana wire: Insights from the fermionic negativity, concurrence and quantum mutual information
Rzeszów University of Technology（热舒夫理工大学）；University of Opole（奥波莱大学）；A. Mickiewicz University（亚当·密茨凯维奇大学）；M. Curie-Skłodowska University（玛丽亚·居里-斯克沃多夫斯卡大学）
The time evolution of entanglement for excitons in two quantum dots embedded in a single mode cavity is studied in a ``spin-boson'' regime. It is found that although with the dissipation from the boson mode, the excitons in the two quantum dots can be entangled by only modulating their energy bias $ε$ under the influence of external driving magnetic field. Initially, the two excitons are prepared in a pure separate state. When the time-dependent magnetic field is switched on, a highly entangled state is produced and maintained even in a very long time interval. The mechanism may be used to con…
The time dependent quantum Monte Carlo method for fermions is introduced and applied for calculation of entanglement of electrons in one-dimensional quantum dots with several spin-polarized and spin-compensated electron configurations. The rich statistics of wave functions provided by the method allows one to build reduced density matrices for each electron and to quantify the spatial entanglement using measures such as quantum entropy by treating the electrons as identical or distinguishable particles. Our results indicate that the spatial entanglement in parallel-spin configurations is rathe…
Time evolution of entanglement of N quantum dots is analyzed within the spin-1/2 van der Waals (or Lipkin-Meshkov-Glick) XY model. It is shown that, for a single dot initially excited and disentangled from the remaining unexcited dots, the maximum bipartite entanglement can be obtained in the systems of N=2,...,6 dots only.
Studying quantum properties in solid-state systems is a significant avenue for research. In this scenario, double quantum dots (DQDs) appear as a versatile platform for technological breakthroughs in quantum computation and nanotechnology. This work inspects the thermal entanglement and quantum coherence in two-coupled DODs, where the system is exposed to an external stimulus that induces an electronic transition within each subsystem. The results show that the introduction of external stimulus induces a quantum level crossing that relies upon the Coulomb potential changing the degree of quant…
Measurements provide a novel mechanism for generating the entanglement resource necessary for performing scalable quantum computation. Recently, we proposed a method for performing parity measurements in a coupled quantum dot system. In this paper we generalise this scheme and perform a comprehensive analytic and numerical study of environmental factors. We calculate the effects of possible error sources including non-ideal photon detectors, ineffective spin-selective excitation and dot distinguishability (both spatial and spectral). Furthermore, we present an experimental approach for verifyi…
We studied the quantum correlations between the nodes in a quantum neural network built of an array of quantum dots with dipole-dipole interaction. By means of the quasiadiabatic path integral simulation of the density matrix evolution in a presence of the common phonon bath we have shown the coherence in such system can survive up to the liquid nitrogen temperature of 77K and above. The quantum correlations between quantum dots are studied by means of calculation of the entanglement of formation in a pair of quantum dots with the typical dot size of a few nanometers and the interdot distance …
Transport properties of arrays of metallic quantum dots are governed by the distance-dependent exchange coupling between the dots. It is shown that the effective value of the exchange coupling, as measured by the charging energy per dot, depends monotonically on the size of the array. The effect saturates for hexagonal arrays of over 7^5 unit cells. The discussion uses a multi-stage block renormalization group approach applied to the Hubbard Hamiltonian. A first order phase transition occurs upon compression of the lattice and the size dependence is qualitatively different for the two phases.
In this chapter we review the use of semiconductor quantum dots as sources of quantum light. Principally, we focus on resonant two-photon excitation, which is a method that allows for on-demand generation of photon pairs. We explore the advantages of resonant excitation and present a number of measurements that were made in this excitation regime. In particular, we cover the following topics: photon statistics, coherent manipulation of the ground-excited state superposition, and generation of time-bin entangled photon pairs.
We study the dynamics of quantum correlations of two coupled double quantum dots containing two excess electrons. The dissipation is included through the contact with an oscillator bath. We solve the Redfield master equation in order to determine the dynamics of the quantum discord and the entanglement of formation. Based on our results, we find that the quantum discord is more resistant to dissipation than the entanglement of formation for such a system. We observe that this characteristic is related to whether the oscillator bath is common to both qubits or not and to the form of the interac…
The universal quantum computation is obtained when there exists asymmetric anisotropic exchange between electron spins in coupled semiconductor quantum dots. The asymmetric Heisenberg model can be transformed into the isotropic model through the control of two local unitary rotations for the realization of essential quantum gates. The rotations on each qubit are symmetrical and depend on the strength and orientation of asymmetric exchange. The implementation of the axially symmetric local magnetic fields can assist the construction of quantum logic gates in anisotropic coupled quantum dots. Th…
We show that two spatially separated semiconductor quantum dots under resonant and continuous-wave excitation can be strongly entangled in the steady-state, thanks to their radiative coupling by mutual interaction through the normal modes of a photonic crystal dimer. We employ a quantum master equation formalism to quantify the steady-state entanglement by calculating the system {\it negativity}. Calculations are specified to consider realistic semiconductor nanostructure parameters for the photonic crystal dimer-quantum dots coupled system, determined by a guided mode expansion solution of Ma…
In this work, the exchange energy J for a system of two laterally-coupled quantum dots, each one with an electron, is calculated analytically and in a detailed form, considering them as hydrogen-like atoms, under the Heitler-London approach. The atomic orbitals, associated to each quantum dot, are obtained from translation relations, as functions of the Fock-Darwin states. Our results agree with the reported ones by Burkard, Loss and DiVincenzo in their model of quantum gates based on quantum dots, as well as with some recent experimental reports.
Generation of polarization-entangled photons from quantum dots via the biexciton-exciton recombination cascade is complicated by the presence of an energy spitting between the intermediate excitonic levels, which severely degrades the quality of the entangled photon source. In this paper we present a novel, conceptually simple and straightforward proposal for restoring the entanglement of said source by applying a cascade of time-dependent operations on the emitted photons. This is in striking contrast with the techniques usually employed, that act on the quantum emitter itself in order to rem…
We report on the generation of time-bin entangled photon pairs from a semiconductor quantum dot via pulsed resonant biexciton generation. Based on theoretical modeling we optimized the duration of the excitation pulse to minimize the laser-induced dephasing and increase the biexciton-to-background single exciton occupation probability. This results in a high degree of entanglement with a concurrence of up to 0.78(6) and a 0.88(3) overlap with a maximally entangled state. Theoretical simulations also indicate a power dependent nature of the dephasing during the laser excitation that limits the …
Equivalent-neighbor interactions of the conduction-band electron spins of quantum dots in the model of Imamoglu et al. [Phys. Rev. Lett. 83, 4204 (1999)] are analyzed. Analytical solution and its Schmidt decomposition are found and applied to evaluate how much the initially excited dots can be entangled to the remaining dots if all of them are initially disentangled. It is demonstrated that the perfect maximally entangled states (MES) can only be generated in the systems of up to 6 dots with a single dot initially excited. It is also shown that highly entangled states, approximating the MES wi…
We present Monte Carlo wavefunction simulations for quantum computations employing an exchange-coupled array of quantum dots. Employing a combination of experimentally and theoretically available parameters, we find that gate fidelities greater than 98 % may be obtained with current experimental and technological capabilities. Application to an encoded 3 qubit (nine physical qubits) Deutsch-Josza computation indicates that the algorithmic fidelity is more a question of the total time to implement the gates than of the physical complexity of those gates.
We present a proposal for heralded entanglement between two quantum dots via Hong--Ou--Mandel effect. Each of the quantum dots, drived off-resonance by two lasers, can be entangled with the coherent cavity mode. The output photons from the two coherent cavity modes interfering by a beamsplitter, we could entangle the two QDs with nearly unit success probability. Our scheme requires neither direct coupling between qubits nor the detection of single photons. Moreover the quantum dots do not need to have the same frequencies and coupling constants.
We study numerically the production of orbital and spin entangled states in chaotic quantum dots for non-interacting electrons. The introduction of spin-orbit coupling permit us to identify signatures of time-reversal symmetry correlations in the entanglement production previously unnoticed, resembling weak-(anti)localization quantum corrections to the conductance. We find the entanglement to be strongly dependent on spin-orbit coupling, showing universal features for broken time-reversal and spin-rotation symmetries.
We study theoretically the appearance of quantum correlations in two- and three-electron scattering in single and double dots. The key role played by transport resonances into entanglement formation between the single-particle states is shown. Both reflected and transmitted components of the scattered particle wavefunction are used to evaluate the quantum correlations between the incident carrier and the bound particle(s) in the dots. Our investigation provides a guideline for the analysis of decoherence effects due to the Coulomb scattering in semiconductor quantum dots structures.
We give an elementary introduction to the notion of quantum entanglement between distinguishable parties and review a recent proposal about solid state quantum computation with spin-qubits in quantum dots. The indistinguishable character of the electrons whose spins realize the qubits gives rise to further entanglement-like quantum correlations. We summarize recent results concerning this type of quantum correlations of indistinguishable particles.
The production of orbitally entangled electrons in quantum-chaotic dots is investigated from a statistical point of view. The degree of entanglement is quantified through the concurrence and the entanglement of formation. We calculate the complete statistical distributions of the entanglement measures by using random matrix theory. Simple analytical expressions are provided for the concurrence distributions. We identify clear signatures of time-reversal invariance in the production of entanglement at the level of the entanglement-measure distributions, such as the ability of producing maximall…
The development of scalable sources of non-classical light is fundamental to unlock the technological potential of quantum photonics\cite{Kimble:Nat2008}. Among the systems under investigation, semiconductor quantum dots are currently emerging as near-optimal sources of indistinguishable single photons. However, their performances as sources of entangled-photon pairs are in comparison still modest. Experiments on conventional Stranski-Krastanow InGaAs quantum dots have reported non-optimal levels of entanglement and indistinguishability of the emitted photons. For applications such as entangle…
Nonlocal entanglement between two quantum dots can be generated through Majorana fermions. The two Majorana fermions at the ends of an one-dimensional topological superconductor form a nonlocal fermion level, coupling to the occupation states of two quantum dots put close to the two ends, and the entire system will come into an entangled state. After introducing a charging energy by a capacitor, entanglement of the entire system can manifest itself through the nonlocal entanglement between the two quantum dots. That is, when measuring the electron occupations of the quantum dots, the measureme…
Coupling nanocrystals (quantum dots) to a high-$Q$ whispering gallery mode (WGM) of a silica microsphere, can produce a strong coherent interaction between the WGM and the electronic states of the dots. Shifting the resonance frequencies of the dots, for instance by placing the entire system in an electric potential, then allows this interaction to be controlled, permitting entangling interactions between different dots. Thus, this system could potentially be used to implement a quantum computer.
We propose schemes for generating spatially-separated spin entanglement in systems of two quantum dots with onsite Coulomb repulsion weakly coupled to a joint electron reservoir. An enhanced probability for the formation of spin entanglement is found in nonequilibrium situations with one extra electron on each dot, either in the transient state after rapid changes of the gate voltage, or in the steady state with applied bias voltage. In both cases so-called Werner states with spin singlet fidelity exceeding 1/2 are generated, which indicates entanglement.
We investigate coherent single surface-plasmon transport in a metal nanowire strongly coupled to two colloidal quantum dots. Analytical expressions are obtained for the transmission and reflection coefficients by solving the corresponding eigenvalue equation. Remote entanglement of the wave functions of the two quantum dots can be created if the inter-dot distance is equal to a multiple half-wavelength of the surface plasmon. Furthermore, by applying classical laser pulses to the quantum dots, the entangled states can be stored in metastable states which are decoupled from the surface plasmons…
Entropic entanglement measures of a two-dimensional system of two Coulombically interacting particles confined in an anisotropic harmonic potential are discussed in dependence on the anisotropy and the interaction strength. The harmonic approximation appears exact in the strong interaction limit, allowing determination of the asymptotic expression for the linear entropy. Entanglement properties are dramatically influenced by the anisotropy of the confining potential in the strong-correlation regime.
We investigate how decoherence affects the entanglement established between two quantum dots in micro cavities, and propose a tomographic scheme able to measure the entangled state. The scheme we consider establishes the entanglement via the exchange and measurement of a photon. Making the realistic assumption of noise dominated by pure-dephasing processes, we find that the photon must be exchanged and measured on timescales shorter than the quantum dots' characteristic dephasing time for appreciable levels of entanglement to be achieved. The tomographic scheme is able to reconstruct the full …
Singlet-triplet states in double quantum dots are promising realizations of qubits, and capacitive coupling can be used to create entanglement between these qubits. We propose an entangling three-qubit gate of singlet-triplet qubits in a triangular setup. Our simulations using a realistic microscopic model show that a maximally entangled Greenberger-Horne-Zeilinger state can be generated as the qubits are evolved under exchange. Furthermore, our analysis for the gate operation can be used to extract the actual experimental pulse sequence needed to realize this.
We investigate the competition between pair entanglement of two spin qubits in double quantum dots attached to leads with various topologies and the separate entanglement of each spin with nearby electrodes. Universal behavior of entanglement is demonstrated in dependence on the mutual interactions between the spin qubits, the coupling to their environment, temperature and magnetic field. As a consequence of quantum phase transition an abrupt switch between fully entangled and unentangled states takes place when the dots are coupled in parallel.
We study entanglement of charge qubits in a vertical tunnel-coupled double quantum dot containing two interacting electrons. Exact diagonalization is used to compute the negativity characterizing entanglement. We find that entanglement can be efficiently generated and controlled by sidegate voltages, and describe how it can be detected. For large enough tunnel coupling, the negativity shows a pronounced maximum at an intermediate interaction strength within the Wigner molecule regime.
We propose how to generate genuine multipartite entanglement of electron spin qubits in a chain of quantum dots using the naturally available single-qubit rotations and two-qubit Heisenberg exchange interaction in the system. We show that the minimum number of required operations to generate entangled states of the GHZ-, cluster and W-type scales linearly with the number of qubits and estimate the fidelities of the generated entangled cluster states. As the required single and two-qubit operations have recently been realized, our proposed scheme opens the way for experimental investigation of …
Adiabatic passage of two correlated electrons in three coupled quantum dots is shown to provide a robust and controlled way of distilling, transporting and detecting spin entanglement, as well as of measuring the rate of spin disentanglement. Employing tunable interdot coupling the scheme creates, from an unentangled two-electron state, a superposition of spatially separated singlet and triplet states. A single measurement of a dot population (charge) collapses the wave function to either of these states, realizing entanglement to charge conversion. The scheme is robust, with the efficiency cl…
We propose a quantum dot architecture for enabling universal quantum information processing. Quantum registers, consisting of arrays of vertically stacked self-assembled semiconductor quantum dots, are connected by chains of in-plane self-assembled dots. We propose an entanglement distributor, a device for producing and distributing maximally entangled qubits on demand, communicated through in-plane dot chains. This enables the transmission of entanglement to spatially separated register stacks, providing a resource for the realisation of a sizeable quantum processor built from coupled registe…
Generation and control of quantum entanglement are studied in an equivalent-neighbor system of spatially-separated semiconductor quantum dots coupled by a single-mode cavity field. Generation of genuinely multipartite entanglement of qubit states realized by conduction-band electron-spin states in quantum dots is discussed. A protocol for quantum teleportation of electron-spin states via cavity decay is briefly described.
Quantum gates that temporarily increase singlet-triplet splitting in order to swap electronic spins in coupled quantum dots, lead inevitably to a finite double-occupancy probability for both dots. By solving the time-dependent Schrödinger equation for a coupled dot model, we demonstrate that this does not necessarily lead to quantum computation errors. Instead, the coupled dot ground state evolves quasi-adiabatically for typical system parameters so that the double-occupancy probability at the completion of swapping is negligibly small. We introduce a measure of entanglement which explicitly t…
We present a detailed analysis of the electronic and optical properties of two-electron quantum dots with a two-dimensional Gaussian confinement potential. We study the effects of Coulomb impurities and the possibility of manipulate the entanglement of the electrons by controlling the confinement potential parameters. The degree of entanglement becomes highly modulated by both the location and charge screening of the impurity atom, resulting two regimes: one of low entanglement and other of high entanglement, with both of them mainly determined by the magnitude of the charge. It is shown that …
We present a solid state thermal machine based on quantum dots to generate steady-state entanglement between distant spins. Unlike previous approaches our system is controlled by experimentally feasible steady state currents manipulated by dc voltages. By analyzing the Liouvillian eigenspectrum as a function of the control parameters, we show that our device operates over a large voltage region. As an extension, the proposed device also works as an entanglement thermal machine under a temperature gradient that can even give rise to entanglement at zero voltage bias. Finally, we highlight a pos…
Entanglement-based quantum key distribution promises enhanced robustness against eavesdropping and compatibility with future quantum networks. Among other sources, semiconductor quantum dots can generate polarization-entangled photon pairs with near-unity entanglement fidelity and a multi-photon emission probability close to zero even at maximum brightness. These properties have been demonstrated under resonant two-photon excitation (TPE) and at operation temperatures between 4 and 8 K. However, source blinking is often reported under TPE conditions, limiting the maximum achievable photon rate…
We show that two initially non-resonant quantum dots may be brought into resonance by the application of a single detuned laser. This allows for control of the inter-dot interactions and the generation of highly entangled excitonic states on the picosecond timescale. Along with arbitrary single qubit manipulations, this system would be sufficient for the demonstration of a prototype excitonic quantum computer.
A scheme for probabilistic entanglement generation between two distant single electron doped quantum dots, each placed in a high-Q microcavity, by detecting strong coherent light which has interacted dispersively with both subsystems and experienced Faraday rotation due to the spin selective trion transitions is discussed. In order to assess the applicability of the scheme for distant entanglement generation between atomic qubits proposed by T.D. Ladd et al. [New J. Phys. 8, 184 (2006)] to two distant quantum dots, one needs to understand the limitations imposed by hyperfine interactions of th…
The measurable degree of entanglement from a quantum dot via the biexciton-exciton cascade depends crucially on the bright exciton fine-structure splitting and on the detection time resolution. Here, we propose an optical approach with fast rotating waveplates to erase this fine-structure splitting and therefore obtain a high degree of entanglement with near-unity efficiency. Our optical approach is possible with current technology and is also compatible with any quantum dot showing fine-structure splitting.
We discuss entanglement generation in a closed system of one or two atomic quantum dots (qubits) coupled via Raman transitions to a pool of cold interacting bosons. The system exhibits rich entanglement dynamics, which we analyze in detail in an exact quantum mechanical treatment of the problem. The bipartite setup of only one atomic quantum dot coupled to a pool of bosons turns out to be equivalent to two qubits which easily get entangled being initially in a product state. We show that both the number of bosons in the pool and the boson-boson interaction crucially affect the entanglement cha…
We present a model of quantum teleportation protocol based on one-dimensional quantum dots system. Three quantum dots with three electrons are used to perform teleportation, the unknown qubit is encoded using one electron spin on quantum dot A, the other two dots B and C are coupled to form a mixed space-spin entangled state. By choosing the Hamiltonian for the mixed space-spin entangled system, we can filter the space (spin) entanglement to obtain pure spin (space) entanglement and after a Bell measurement, the unknown qubit is transfered to quantum dot B. Selecting an appropriate Hamiltonian…
