Knill-Laflamme-Milburn Research Articles

Deterministic Conversion of Hyperentangled States with Error‐Heralded Quantum Units

AbstractIn the paper, the possibility of two complete conversions is investigated, one is from the two‐photon hyperentangled Knill–Laflamme–Milburn (KLM) state to hyperentangled Bell states, the other is from three‐photon KLM state to the hyperentangled Greenberger–Horne–Zeilinger states, for photonic systems hyper‐encoded in polarization and spatial degrees of freedom assisted by error‐heralded quantum units (EHQUs). The system inhomogeneity and/or the imperfect photon scattering often restrict the performance of effective conversions of two types of hyperentangled states, and result in the reductions of the fidelity and the efficiency in tangible quantum information technologies. The polarization EHQU and spatial EHQU are two critical tools for actualizing two hyperentangled conversions in a heralded way, as the errors stemming from the system inhomogeneity and practically imperfect scattering are converted into efficacious responses of the detectors in our protocols. Thus, the fidelities of these conversion cases keep unchanged and have close to unity fidelities, which deepen the understanding of the properties of hyperentanglement.

Decoherence-free-subspace-based deterministic conversions for entangled states with heralded robust-fidelity quantum gates.

The decoherence-free subspace (DFS) serves as a protective shield against certain types of environmental noise, allowing the system to remain coherent for extended periods of time. In this paper, we propose two protocols, i.e., one converts two-logic-qubit Knill-Laflamme-Milburn (KLM) state to two-logic-qubit Bell states, and the other converts three-logic-qubit KLM state to three-logic-qubit Greenberger-Horne-Zeilinger states, through cavity-assisted interaction in DFS. Especially, our innovative protocols achieve their objectives in a heralded way, thus enhancing experimental accessibility. Moreover, single photon detectors are incorporated into the setup, which can predict potential failures and ensure seamless interaction between the nitrogen-vacancy center and photons. Rigorous analyses and evaluations of two schemes demonstrate their abilities to achieve near-unit fidelities in principle and exceptional efficiencies. Further, our protocols offer progressive solutions to the challenges posed by decoherence, providing a pathway towards practical quantum technologies.

Complete conversion of KLM entanglement to GHZ entanglement with error-detected quantum devices

Quantum entanglement plays a crucial role in quantum information technologies. In the paper, we propose two schemes to convert from two-photon Knill–Laflamme–Milburn (KLM) entangled states to Bell states and three-photon KLM state to Greenberger–Horne–Zeilinger states based on error-detected quantum devices (EDQDs), which employ the interaction between a quantum-dot-cavity system and a photon. Moreover, the quantum circuits of EDQDs applied in the conversion processes make our schemes carry out faithfully, as the practical photon-scattering deviations are changed into heralded-failure detections. Analyses show that conversion cases have unity fidelities and high efficiencies, which encourage us to appreciate deeply fundamental properties of entanglement.

Engineering Knill–Laflamme–Milburn Entanglement via Dissipation and Coherent Population Trapping in Rydberg Atoms

We present a scheme for dissipatively preparing bipartite Knill–Laflamme–Milburn (KLM) entangled state in a neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the coherent population trapping, is actively exploited to engineer a steady KLM state from an arbitrary initial state. Instead of commonly used antiblockade dynamics of two Rydberg atoms, we particularly utilize the Rydberg–Rydberg interaction as the pumping source to drive the undesired states so that it is unnecessary to satisfy a certain relation with laser detuning. The numerical simulation of the master equation signifies that both the fidelity and the purity above 98% is available with the current feasible parameters, and the corresponding steady-state fidelity is robust to the variations of the dynamical parameters.

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement in Decoherence‐Free Subspace

AbstractIn the process of quantum information processing, decoherence effect caused by the coupling between system and its environment will no doubt lead to the error of quantum information stored in the system. To decrease the influence of decoherence effect, decoherence‐free subspace (DFS) is introduced. In this work, several schemes to convert the polarized‐entangled Knill–Laflamme–Milburn (KLM) states into Greenberger–Horne–Zeilinger (GHZ) states in DFS by using the weak cross‐Kerr nonlinearity are proposed. Numerical analysis shows that the proposed schemes have high fidelity and success probability. Due to the unique applications of multi‐qubit quantum entangled states in quantum information processing and the robust feature of DFS, the proposed schemes may play positive roles in the future development of quantum communication and quantum information processing tasks.

Fast and dephasing-tolerant preparation of steady Knill-Laflamme-Milburn states via dissipative Rydberg pumping

We propose a fast and dephasing-tolerant scheme for the preparation of steady Knill-Laflamme-Milburn (KLM) state between a pair of Rydberg atoms by dissipation. In this scheme, arbitrary initial state can be engineered to the KLM state with high fidelity (99.24%). Compared to most schemes based on Rydberg dissipation dynamics, the time to prepare steady state can be significantly reduced in our scheme $(80 \ensuremath{\mu}\mathrm{s})$ due to the use of strong resonant dipole-dipole interactions. In addition, the scheme can effectively suppress the dephasing error of the Rydberg atoms caused by interatomic distance fluctuations, which may severely disrupt the desired systematic dynamics. Thus the present scheme is of interest and deserves further experimental investigation to enrich the dissipation dynamics based on the Rydberg atoms.

Conversion of Knill–Laflamme–Milburn Entanglement to Greenberger–Horne–Zeilinger Entanglement

AbstractSchemes for converting photonic polarized‐entangled Knill–Laflamme–Milburn (KLM) states to Greenberger–Horne–Zeilinger (GHZ) states are proposed using weak cross‐Kerr nonlinearity and X‐quadrature homodyne measurement. Analyses show that the two‐qubit (Bell state) and three‐qubit conversion cases have very high fidelities and close‐to‐unity probabilities. The conversion processes are robust against photon loss. The schemes linking these two entangled states may be helpful to the study of quantum information processing based on them.

Rydberg-atom-based controlled arbitrary-phase gate and its applications

Controlled-phase (CP) gates with an arbitrary phase, which play an irreplaceable role in quantum computation and quantum information processing, are constructed between two neutral-atom qubits by using the Rydberg antiblockade regime. The phases needed for the CP gates are induced by the collective excitation of the pair of atoms. Numerical simulations show that high-fidelity CP gates can be obtained. In addition, the optimization of the scheme is given to enhance the robustness against the control error. As applications, we study in detail the preparation of n-qubit Knill–Laflamme–Milburn (KLM) states and a cluster state based on the Rydberg CP gates. The high-fidelity KLM states and cluster state can be obtained with the current physical parameters.

Accelerated and Noise‐Resistant Protocol of Dissipation‐Based Knill–Laflamme–Milburn State Generation with Lyapunov Control

AbstractA protocol to generate steady Knill–Laflamme–Milburn (KLM) states of two Rydberg atoms with dissipation and Lyapunov control is proposed. Herein, combining with the quantum Zeno dynamics and the Rydberg antiblockade, a unique and steady solution of the master equation of the system is obtained, which satisfies the definition of KLM states. Furthermore, to polish the convergence rate, well‐designed additional coherent control (ACC) fields with Lyapunov control are added into the traditional dissipation process. Numerical simulation reveals that the steady target state generation is prominently accelerated and the protocol is robust against the stochastic noise errors caused by laser fields. It is hoped that the work may provide an alternative protocol to polish the generation of entanglement.

Generation and concentration of two-photon partially entangled Knill–Laflamme–Milburn state

The protocol for the compact generation of the two-photon four-dimensional spatial-mode partially entangled Knill–Laflamme–Milburn (KLM) state is proposed. The two-photon entanglement shared among four spatially distinct optical modes can be generated from three concurrent spontaneous parametric down-conversion processes by using the multiple quasi-phase-matching technique. The scheme for the concentration of the two-photon four-dimensional spatial-mode partially entangled KLM state is also proposed. By using quantum non-destructive detection and local operation, the two-photon maximally entangled KLM state can be obtained and used as an entangled quantum channel in quantum communication.

Mutual Conversions Between Knill–Laflamme–Milburn and W States

AbstractHerein, two proposals are speculated to realize mutual conversions between Knill–Laflamme–Milburn (KLM) and W entangled states via X homodyne measurement (HM). By one of these proposals three‐qubit mutual conversions can be realized between these two photonic polarization entangled states. The other can be generalized to convert an arbitrary‐qubit KLM state to a W state adopting a control‐NOT gate. With the increasing number of qubits, the utilization ratio of photons in the second proposal would be close to unity. Analyses of the three‐qubit mutual conversions show that the proposal has a low error rate and high utilization ratio of photons. Moreover, the fidelity can also be very high even in consideration of decoherence. The P homodyne measurement is analyzed as well to improve the precision. The proposals, especially the second one, are expected to be helpful to reveal the relationship between these two robust multiple‐qubit entanglements.

Channel fidelities for high-fidelity approach in KLM scheme

We study channel fidelity for the high-fidelity approach in the Knill-Laflamme-Milburn (KLM) scheme. We examine an optimal channel fidelity f_{opt} and identify the corresponding KLM ancilla state. In the limit of large n, where 2n is the number of the ancilla qubits, we find f_{opt}=1-{\pi^{2} \over 6n^{2}}+{2\pi^{2} \over 9n^{3}}. We see that as n increases f_{opt} approaches to 1 slightly faster than f=1-{2 \over n^{2}} which is the channel fidelity computed by Franson et. al. in the limit of large n. We also compute the channel fidelity for the ancilla state that gives a lower bound of success probability of quantum teleportation.

Lower bounds of success probabilities for high-fidelity approach in KLM scheme

In the Knill–Laflamme–Milburn (KLM) scheme, the success probability of quantum teleportation is given by [Formula: see text], where [Formula: see text] is the number of the ancilla qubits. For the high-fidelity approach in the KLM scheme, the success probability averaged for all input states is approximately given by [Formula: see text] for large [Formula: see text]. We give an exact lower bound of the success probability and show how the corresponding ancilla state is settled for the high-fidelity approach for arbitrary [Formula: see text].

Multiphoton Knill-Laflamme-Milburn states generated by nonlinear optics

The Knill-Laflamme-Milburn (KLM) entangled state, proposed by Knill et al. in Nature409, 46 (2001)NATUAS0028-083610.1038/35051009, has unique advantages for linear optics quantum information processing tasks, because it is able to decrease the error rate. In this paper, we propose scalable schemes to generate the multi-qubit KLM entangled states with single-photon resources and weak cross-Kerr nonlinearity theoretically. We first construct the two-qubit KLM state, through which the three- and other n-qubit KLM states are generated. For the schemes using weak cross-Kerr nonlinearity, P homodyne measurement has a higher success rate than X homodyne measurement but with narrow applications since |αeiθ⟩ and |αe−iθ⟩ are distinguished from each other, which is undesirable for most of the entanglement generation schemes. To avoid this disadvantage, Jin et al. [Phys. Rev. A75, 054302 (2007)PLRAAN1050-294710.1103/PhysRevA.75.054302] introduced the coherent state superposition (CSS), c(|α⟩+|−α⟩), to generate a Greenberger-Horne-Zeilinger state but with a rapid oscillation term, which needs to be ignored. Through designing the optical path uniquely and choosing the phase of cross-Kerr nonlinearity suitably, our P homodyne measurement and CSS probe mode-based schemes to generate the KLM state avoid the needless term. The present scalable schemes have high total success probabilities, high fidelities even in consideration of decoherence, and may find potential applications in the future with the further development of nonlinear optics.

Engineering steady Knill-Laflamme-Milburn state of Rydberg atoms by dissipation.

The Knill-Laflamme-Milburn (KLM) states have been proved to be a useful resource for quantum information processing [Nature409, 46 (2001)]. For atomic KLM states, several schemes have been put forward based on the time-dependent unitary dynamics, but the dissipative generation of these states has not been reported. This work discusses the possibility for creating different forms of bipartite KLM states in neutral atom system, where the spontaneous emission of excited Rydberg states, combined with the Rydberg antiblockade mechanism, is actively exploited to engineer a steady KLM state from an arbitrary initial state. The numerical simulation of the master equation signifies that a fidelity above 99% is available with the current experimental parameters.

Measurement-induced nonclassical states from a coherent state heralded by Knill–Laflamme–Milburn-type interference

We theoretically generate nonclassical states from coherent state heralded by Knill-Laflamme-Milburn (KLM)-type SU(3) interference. Injecting a coherent state in signal mode and two single-photon sources in other two auxiliary modes of SU(3) interferometry, a broad class of useful nonclassical states are obtained in the output signal port after making two single-photon-counting measurements in the two output auxiliary modes. The nonclassical properties, in terms of anti-bunching effect and squeezing effect as well as the negativity of the Wigner function, are studied in detail by adjusting the interaction parameters. The results show that the input coherent state can be transformed into non-Gaussian states with higher nonclassicality after measurement induction. The maximum squeezing of our generated states can be arrived at about 1.9 dB.

Photons as qubits

We review the physical principles behind measurement-based quantum information processing with optical fields. The original Knill–Laflamme–Milburn (KLM) scheme, based on single-photon states, is explained, as well as extensions of the scheme inspired by the idea of cluster state quantum computing, which dramatically reduce the resources required for implementation. A careful analysis of the intrinsic error sources in optical cluster state methods indicates that fault-tolerant quantum gates are feasible given developments in current technology. The main impediment to progress is the lack of single-photon sources and we briefly review what kinds of sources are needed. We conclude with a discussion of phase-shift coherent state codes and discuss a possible implementation in circuit quantum electrodynamics.

Unity fidelity multiple teleportation using partially entangled states

We show that the multiple teleportation protocol (MTP) given in reference (J Modławska and A Grudka 2008 Phys. Rev. Lett. 100 110503) is not restricted to the Knill–Laflamme–Milburn (KLM) framework. Rather, we show that MTP can be implemented using any teleportation scheme. We also present two new MTPs which, under certain situations, are more efficient than the original one, requiring half of the number of its teleportations to achieve at least the same probability of success (). One of the protocols, however, uses less entanglement than the others yielding, surprisingly, the greatest .

Adaptive quantum teleportation

We consider multiple teleportation in the Knill-Laflamme-Milburn (KLM) scheme. We introduce adaptive teleportation, i.e., such that the choice of entangled state used in the next teleportation depends on the results of the measurements performed during the previous teleportations. We show that adaptive teleportation enables an increase in the probability of faithful multiple teleportation in the KLM scheme. In particular if a qubit is to be teleported more than once then it is better to use nonmaximally entangled states than maximally entangled ones in order to achieve the highest probability of faithful teleportation.

Knill-Laflamme-Milburn Quantum Computation with Bosonic Atoms

A Knill-Laflamme-Milburn (KLM) type quantum computation with bosonic neutral atoms or bosonic ions is suggested. Crucially, as opposite to other quantum computation schemes involving atoms (ions), no controlled interactions between atoms (ions) involving their internal levels are required. Versus photonic KLM computation, this scheme has the advantage that single-atom (ion) sources are more natural than single-photon sources, and single-atom (ion) detectors are far more efficient than single-photon ones.