This paper continues research initiated in quant-ph/0201022 . The main subject here is the so-called Edmonds' problem of deciding if a given linear subspace of square matrices contains a nonsingular matrix . We present a deterministic polynomial time algorithm to solve this problem for linear subspaces satisfying a special matroids motivated property, called in the paper the Edmonds-Rado property . This property is shown to be very closely related to the separability of bipartite mixed states . One of the main tools used in the paper is the Quantum Permanent introduced in quant-ph/0201022 .
We present a deterministic entanglement purification protocol (EPP) working for currently available experiment technique. In this protocol, we resort to the robust time-bin entanglement to purify the polarization entanglement determinately, which is quite different from the previous EPPs. After purification, one can obtain a completely pure maximally entangled pair with the success probability of 100%, in principle. As the maximal polarization entanglement is of vice importance in long-distance quantum communication, this protocol may have a wide application.
We present an efficient entanglement purification protocol with hyperentanglement in which additional spatial entanglement is utilized to purify the two-particle polarization-entangled state. The bit-flip error and phase-flip error can be corrected and eliminated in one step. Two remote parties can obtainmaximally entangled polarization states deterministically and only passive linear optics are employed. We also discuss the protocol with practical quantum source and noisy channel.
Deterministic extraction of Bell pairs from a finite number of partially entangled pairs is discussed. We derive the maximum number of Bell pairs that can be obtained with probability 1 by local operations and classical communication. It is proved that the optimal deterministic concentration needs only a two-pair collective manipulation in each step, and that a collective manipulation of all entangled pairs is not necessary. Finally, this scheme reveals an entanglement measure for the deterministic concentration.
We show a deterministic secure direct communication protocol using single qubit in mixed state. The security of this protocol is based on the security proof of BB84 protocol. It can be realized with current technologies.
We prove that sufficiently many copies of a bipartite entangled pure state can always be transformed into some copies of another one with certainty by local quantum operations and classical communication. The efficiency of such a transformation is characterized by deterministic entanglement exchange rate, and it is proved to be always positive and bounded from top by the infimum of the ratios of Renyi's entropies of source state and target state. A careful analysis shows that the deterministic entanglement exchange rate cannot be increased even in the presence of catalysts. As an application, …
We propose a protocol for deterministic communication that does not make use of entanglement. It exploits nonorthogonal states in a two-way quantum channel attaining significant improvement of security and efficiency over already known cryptographic protocols. The presented scheme, being deterministic, can be devoted to direct communication as well as to key distribution, and its experimental realization is feasible with present day technology.
We present a one-step deterministic entanglement purification protocol with linear optics and postselection. Compared with the Simon-Pan protocol (Phys. Rev. Lett. 89, 257901 (2002)), this one-step protocol has some advantages. First, it can get a maximally entangled pair with only one step, not only improve the fidelity of less-entangled photon pairs by performing the protocol repeatedly. Second, it works in a deterministic way, not a probabilistic one, which will reduce a great deal of entanglement resources. Third, it does not require the polarization state be entangled, only spatial entang…
We outline a proof that teleportation with a single particle is in principle just as reliable as with two particles. We thereby hope to dispel the skepticism surrounding single-photon entanglement as a valid resource in quantum information. A deterministic Bell state analyzer is proposed which uses only classical resources, namely coherent states, a Kerr non-linearity, and a two-level atom.
We propose a scheme that employs dissipation to deterministically generate entanglement in an ensemble of strongly interacting Rydberg atoms. With a combination of microwave driving between different Rydberg levels and a resonant laser coupling to a short lived atomic state, the ensemble can be driven towards a dark steady state that entangles all atoms. The long-range resonant dipole-dipole interaction between different Rydberg states extends the entanglement beyond the van der Walls interaction range with perspectives for entangling large and distant ensembles.
By exactly solving the underlying Schödinger equation we show that one and the same resonant cavity can be used as a catalyst to maximally entangle atoms of two nonidentical groups. The generation scheme is realistic and advantageous in the sense that it is deterministic, efficient, scalable and immune from decoherence effects.
Hybrid matter-photon entanglement is the building block for quantum networks. It is very favorable if the entanglement can be prepared with a high probability. In this paper, we report the deterministic creation of entanglement between an atomic ensemble and a single photon by harnessing Rydberg blockade. We design a scheme that creates entanglement between a single photon's temporal modes and the Rydberg levels that host a collective excitation, using a process of cyclical retrieving and patching. The hybrid entanglement is tested via retrieving the atomic excitation as a second photon and pe…
The development of efficient network nodes is a key element for the realisation of quantum networks which promise great capabilities as distributed quantum computing or provable secure communication. We report the realisation of a quantum network node using a trapped ion inside a fiber-based Fabry-Perot cavity. We show the generation of deterministic entanglement at a high fidelity of $ 91.2(2) $\,\% between a trapped Yb--ion and a photon emitted into the resonator mode. We achieve a success probability for generation and detection of entanglement for a single shot of $ 2.5 \cdot 10^{-3}$ resu…
Entanglement swapping, the process to entangle two particles without coupling them in any way, is one of the most striking manifestations of the quantum-mechanical nonlocal characteristic. Besides fundamental interest, this process has applications in complex entanglement manipulation and quantum communication. Here we report a high-fidelity, unconditional entanglement swapping experiment in a superconducting circuit. The measured concurrence characterizing the qubit-qubit entanglement produced by swapping is above 0.75, confirming most of the entanglement of one qubit with its partner is dete…
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
Promising access to high-speed quantum networks relies on the creation of high-dimensional entangled memories that provide quantum communication with higher capacity of noisy quantum channels, thereby reducing the transmission time of information. Yet, the distribution of multidimensional entanglement between remote memory nodes is still faintly investigated. We propose an experimentally feasible protocol of deterministic generation of high-dimensional entanglement between distant multi-level atoms confined in high-finesse optical cavities and driven by laser pulses. Three-dimensional entangle…
Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed entangled state with a higher fidelity probabilistically by consuming quantum resources exponentially, here we present a deterministic EPP with hyperentanglement. Using this protocl, the two parties can, in principle, obtain deterministically maximally entangled pure states in polarization without destroying any less-entangled photon pair, which will improve …
A necessary and sufficient condition of the possibility of a deterministic local operations and classical communication (LOCC) transformation of three-qubit pure states is given. The condition shows that the three-qubit pure states are a partially ordered set parametrized by five well-known entanglement parameters and a novel parameter; the five are the concurrences $C_{AB}$, $C_{AC}$, $C_{BC}$, the tangle $τ_{ABC}$ and the fifth parameter $J_{5}$ of Ref. [18], while the other new one is the entanglement charge $Q_{e}$. The order of the partially ordered set is defined by the possibility of a …
We propose an efficient quantum repeater architecture with mesoscopic atomic ensembles, where the Rydberg blockade is employed for deterministic local entanglement generation, entanglement swapping and entanglement purification. Compared with conventional atomic-ensemble-based quantum repeater, the entanglement distribution rate is improved by up to two orders of magnitude with the help of the deterministic Rydberg gate. This new quantum repeater scheme is robust and fast, and thus opens up a new way for practical long-distance quantum communication.
We have prepared the internal states of two trapped ions in both the Bell-like singlet and triplet entangled states. In contrast to all other experiments with entangled states of either massive particles or photons, we do this in a deterministic fashion, producing entangled states on demand without selection. The deterministic production of entangled states is a crucial prerequisite for large-scale quantum computation.
It is crucial for physical realization of quantum information networks to first establish entanglement among multiple space-separated quantum memories and then at a user-controlled moment to transfer the stored entanglement to quantum channels for distribution and conveyance of information. Here we present an experimental demonstration on generation, storage and transfer of deterministic quantum entanglement among three spatially separated atomic ensembles. The off-line prepared multipartite entanglement of optical modes is mapped into three distant atomic ensembles to establish entanglement o…
Entanglement purification is to distill high-quality entangled states from low-quality entangled states. It is a key step in quantum repeaters, determines the efficiency and communication rates of quantum communication protocols, and is hence of central importance in long-distance communications and quantum networks. In this work, we report the first experimental demonstration of deterministic entanglement purification using polarization and spatial mode hyperentanglement. After purification, the fidelity of polarization entanglement arises from $0.268\pm0.002$ to $0.989\pm0.001$. Assisted wit…
We propose a method for generating maximally entangled states of N two-level trapped ions. The method is deterministic and independent of the number of ions in the trap. It involves a controlled-NOT acting simultaneously on all the ions through a dispersive interaction. We explore the potential application of our scheme for high precision frequency standards.
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 propose a method to generate arbitrary symmetric states of N qubits, which can be easily associated with their entanglement classes. It is particularly suited to quantum optics systems like trapped ions or superconducting circuits. We encode each qubit in two metastable levels of the system and use a bosonic quantum bus for creating the states. The method is deterministic and relies on a sequence of selective unitary gates upon the qubits within the system coherence time.
A scheme is proposed to entangle two systems that have not interacted by using an ancillary particle in a Mach-Zehnder interferometer, by making a suitable post--selection of the particle followed by a conditional feedback on one of the subsystems to be entangled. For a strong interaction, the process works deterministically. For a weaker interaction only the probability of success is reduced, but the output continues to be a maximally entangled state.
Entangled continuous variable (CV) Gaussian states with different wavelengths plays a central role in recent CV-based approaches to quantum network, quantum information processing and quantum metrology. Typically, experiments demonstrating CV entanglement exploit the optical parametric frequency down conversion. Due to the probabilistic nature of photon pair generation, the entanglement involving the post-selection of photonic qubits is limited to at most three colors. Here We theoretically present a scheme for the deterministic generation of entanglement among bright multicolor CV Gaussian st…
We discuss the role of nonclassicality of quantum states as a necessary resource in deterministic generation of multipartite entangled states. In particular for three bilinearly coupled modes of the electromagnetic field, tuning of the coupling constants between the parties allows the total system to evolve into both Bell and GHZ states only when one of the parties is initially prepared in a nonclassical state. A superposition resource is then converted into an entanglement resource.
A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts 2-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity $F=0.889\pm0.010$ by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum enta…
We have implemented a universal quantum logic gate between qubits stored in the spin state of a pair of trapped calcium 40 ions. An initial product state was driven to a maximally entangled state deterministically, with 83% fidelity. We present a general approach to quantum state tomography which achieves good robustness to experimental noise and drift, and use it to measure the spin state of the ions. We find the entanglement of formation is 0.54.
The role of entanglement and quantum correlations in complex physical systems and quantum information processing devices has become a topic of intense study in the past two decades. In this work we present new tools for learning about entanglement and quantum correlations in dynamical systems where the quantum states are mixed and the eigenvalue spectrum is highly degenerate. We apply these results to the Deterministic quantum computing with one qubit (DQC1) computation model and show that the states generated in a DQC1 circuit have an eigenvalue structure that makes them difficult to entangle…
Measurement-based heralded entanglement schemes have served as the primary link between physically separated qubits in most quantum information platforms. However, the impossibility of performing a deterministic Bell measurement with linear optics bounds the success rate of the standard protocols to at most 50%, which means that the entanglement of the unheralded state is zero. Here we show that the ability to perform feedback during the measurement process enables unit success probability in a single shot. Our primary feedback protocol, based on photon counting retains the same robustness as …
Quantum entanglement is a key resource for quantum computation and quantum communication \cite{Nielsen2010}. Scaling to large quantum communication or computation networks further requires the deterministic generation of multi-qubit entanglement \cite{Gottesman1999,Duan2001,Jiang2007}. The deterministic entanglement of two remote qubits has recently been demonstrated with microwave photons \cite{Kurpiers2018,Axline2018,Campagne2018,Leung2019,Zhong2019}, optical photons \cite{Humphreys2018} and surface acoustic wave phonons \cite{Bienfait2019}. However, the deterministic generation and transmis…
Quantum entanglement of mechanical systems emerges when distinct objects move with such a high degree of correlation that they can no longer be described separately. Although quantum mechanics presumably applies to objects of all sizes, directly observing entanglement becomes challenging as masses increase, requiring measurement and control with a vanishingly small error. Here, using pulsed electromechanics, we deterministically entangle two mechanical drumheads with masses of 70 pg. Through nearly quantum-limited measurements of the position and momentum quadratures of both drums, we perform …
We propose a deterministic and scalable scheme to construct a two-qubit controlled-NOT (CNOT) gate and realize entanglement swapping between photonic qubits using a quantum-dot (QD) spin in a double-sided optical microcavity. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive and heralded way. We assess the feasibility of the scheme and show that the scheme can work in both the weak coupling and the strong coupling regimes. The scheme opens promising perspectives for long-distance photonic quantum communication and distributed quantu…
Certain quantum information tasks require entanglement of assistance, namely a reduction of a tripartite entangled state to a bipartite entangled state via local measurements. We establish that 'concurrence of assistance' (CoA) identifies capabilities and limitations to producing pure bipartite entangled states from pure tripartite entangled states and prove that CoA is an entanglement monotone for $(2\times2\times n)$-dimensional pure states. Moreover, if the CoA for the pure tripartite state is at least as large as the concurrence of the desired pure bipartite state, then the former may be t…
Large-scale quantum networks promise to enable secure communication, distributed quantum computing, enhanced sensing and fundamental tests of quantum mechanics through the distribution of entanglement across nodes. Moving beyond current two-node networks requires the rate of entanglement generation between nodes to exceed their decoherence rates. Beyond this critical threshold, intrinsically probabilistic entangling protocols can be subsumed into a powerful building block that deterministically provides remote entangled links at pre-specified times. Here we surpass this threshold using diamond…
We develop a one-step scheme for generating multiparticle entangled states between two cold atomic clouds in distant cavities coupled by an optical fiber. We show that, through suitably choosing the intensities and detunings of the fields and precisely tuning the time evolution of the system, multiparticle entanglement between the separated atomic clouds can be engineered deterministically, in which quantum manipulations are insensitive to the states of the cavity and losses of the fiber. The experimental feasibility of this scheme is analyzed based on recent experimental advances in the reali…
A novel secure communication protocol is presented, based on an entangled pair of qubits and allowing asymptotically secure key distribution and quasi-secure direct communication. Since the information is transferred in a deterministic manner, no qubits have to be discarded. The transmission of information is instantaneous, i.e. the information can be decoded during the transmission. The security against arbitrary eavesdropping attacks is provided. In case of eavesdropping attacks with full information gain, the detection rate is 50% per control transmission. The experimental realization of th…
The ability to deterministically generate genuine multi-partite entanglement is fundamental for the advancement of quantum information science. We show that the interaction between entangled twin beams of light and an atomic ensemble under conditions for electromagnetically induced transparency leads to the generation of genuine hybrid tri-partite entanglement between the two input fields and the atomic ensemble. In such a configuration, the system is driven through dissipation to a steady state given by the hybrid entangled state. To show the presence of the genuine hybrid entanglement, we in…
We present an efficient scheme for the controlled generation of pure two-qubit states possessing {\em any} desired degree of entanglement and a {\em prescribed} symmetry in two cavity QED based systems, namely, cold trapped ions and flying atoms. This is achieved via on-resonance ion/atom-cavity couplings which are time-dependent and asymmetric, leading to a trapping vacuum state condition which does not arise for identical couplings. A duality in the role of the coupling ratio yields states with a given concurrence but opposing symmetries. The experimental feasibility of the proposed scheme i…
Entanglement between a single photon and a matter qubit is an indispensable resource for quantum repeater and quantum networks. With atomic ensembles, the entanglement creation probability is typically very low to inhibit high-order events. In this paper, we propose and experimentally realize a scheme which creates atom-photon entanglement with an intrinsic efficiency of 50%. We make use of Rydberg blockade to generate two collective excitations, lying in separate internal states. By introducing the momentum degree of freedom for the excitations, and interfering them via Raman coupling, we ent…
As two valuable quantum resources, Einstein-Podolsky-Rosen entanglement and steering play important roles in quantum-enhanced communication protocols. Distributing such quantum resources among multiple remote users in a network is a crucial precondition underlying various quantum tasks. We experimentally demonstrate the deterministic distribution of two- and three-mode Gaussian entanglement and steering by transmitting separable states in a network consisting of a quantum server and multiple users. In our experiment, entangled states are not prepared solely by the quantum server, but are creat…
In the solid-state circuit QED system and based on the homodyne measurement in dispersive regime, we demonstrate that a homodyne-current-based feedback can create and stabilize highly entangled two-qubit states in the presence of moderate noisy environment. Particularly, we present an extended analysis for the current-based Markovian feedback, which leads to an improved filtered-current-based feedback scheme. We show that this is essential for us to achieve the desirable control effect in present system.
Quantum computing promises to provide exponential speed-ups to certain classes of problems. In many such algorithms, a classical vector $\mathbf{b}$ is encoded in the amplitudes of a quantum state $\left |b \right >$. However, efficiently preparing $\left |b \right >$ is known to be a difficult problem because an arbitrary state of $Q$ qubits generally requires approximately $2^Q$ entangling gates, which results in significant decoherence on today's Noisy Intermediate Scale Quantum (NISQ) computers. We present a deterministic (nonvariational) algorithm that allows one to flexibly reduce the qu…
Blind quantum computation (BQC) provides an efficient method for the client who does not have enough sophisticated technology and knowledge to perform universal quantum computation. The single-server BQC protocol requires the client to have some minimum quantum ability, while the double-server BQC protocol makes the client's device completely classical, resorting to the pure and clean Bell-state shared by two servers. In this paper, we provide a deterministic entanglement distillation protocol in a practical noisy environment for the double-server BQC protocol. This protocol can obtain the pur…
Distributed variational quantum computing with deterministic entanglement tuning
Korea Institute of Science and Technology (KIST)（韩国科学技术院）；Kyung Hee University（庆熙大学）；Korea University of Science and Technology（韩国科学技术院）；Korea Institute for Advanced Study（韩国高等研究院）；Korea University（高丽大学）
A deterministic direct quantum communication protocol by using swapping quantum entanglement and local unitary operations is proposed in this paper. A set of ordered EPR pairs in one of the four Bell states is used. For each pair, each of the two legitimate users owns a photon of the entangled pair via quantum channel. The pairs are divided into two types of group, i.e., the checking groups and the encoding-decoding groups. In the checking groups, taking advantage of the swapping quantum entanglement and Alice's (the message sender's) public announcement, the eavesdropping can be detected prov…
We present a general theoretical framework for both deterministic and probabilistic entanglement transformations of bipartite pure states achieved via local operations and classical communication. This framework unifies and greatly simplifies previous works. A necessary condition for ``pure contraction'' transformations is given. Finally, constructive protocols to achieve both probabilistic and deterministic entanglement transformations are presented.
A photonic cluster state with a tree-type entanglement structure constitutes an efficient resource for quantum error correction of photon loss. But the generation of a tree cluster state with an arbitrary size is notoriously difficult. Here, we propose a protocol to deterministically generate photonic tree states of arbitrary size by using only a single quantum emitter. Photonic entanglement is established through both emission and re-scattering from the same emitter, enabling fast and resource-efficient entanglement generation. The same protocol can also be extended to generate more general t…
Entanglement-swapping measurements for deterministic entanglement distribution
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所，巴塞罗那科技研究所）；Department of Electronic Systems, Aalborg University（奥尔堡大学电子系统系）；School of Electrical Engineering, Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院电气工程学院）；ICREA - Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究高级学院）
Deterministic entanglement of neutral cold atoms can be achieved by combining several already available techniques like the creation/dissociation of neutral diatomic molecules, manipulating atoms with micro fabricated structures (atom chips) and detecting single atoms with almost 100% efficiency. Manipulating this entanglement with integrated/linear atom optics will open a new perspective for quantum information processing with neutral atoms.
We demonstrate the first deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal an entanglement fidelity of $F=0.58\pm0.04$, which is above the entanglement threshold of $F=0.5$, without any correction for atom loss, and $F=0.71\pm0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.
We propose a simple interaction protocol to be implemented on a scalable quantum network, in which the quantum nodes consist of qubit systems confined in cavities. The nodes are deterministically coupled by transmission and reflection of a single photon, which is disentangled from the qubits at the end of the coupling operation. This single photon can generate an entangling controlled phase (C-PHASE) gate between any selected number of qubits in the network. Our multi-qubit gate reaches a much higher fidelity compared to schemes concatenating one-qubit and two-qubit gates; thus it forms an eff…
We present a deterministic secure direct communication scheme via entanglement swapping, where a set of ordered maximally entangled three-particle states (GHZ states), initially shared by three spatially separated parties, Alice, Bob and Charlie, functions as a quantum information channel. After ensuring the safety of the quantum channel, Alice and Bob apply a series local operations on their respective particles according to the tripartite stipulation and the secret message they both want to send to Charlie. By three Alice, Bob and Charlie's Bell measurement results, Charlie is able to infer …
