Entanglement Swapping and Swapped Entanglement

The Bell basis is a distinctive set of maximally entangled two-particle quantum states that forms the foundation for many quantum protocols such as teleportation, dense coding and entanglement swapping. While the generation, manipulation, and measurement of two-level quantum states is well understood, the same is not true in higher dimensions. Here we present the experimental generation of a complete set of Bell states in a four-dimensional Hilbert space, comprising of 16 orthogonal entangled Bell-like states encoded in the orbital angular momentum of photons. The states are created by the application of generalized high-dimensional Pauli gates on an initial entangled state. Our results pave the way for the application of high-dimensional quantum states in complex quantum protocols such as quantum dense coding.

Einstein-Podolsky-Rosen (EPR)-entangled state light field at a telecommunication wavelength of 1.5 μm is an important quantum source for realizing the continuous variable quantum information processing and some quantum protocols over optical fiber channel. When the EPR-entangled state light field is distributed over the optical fiber channel, the disentanglement is always present because the the EPR entangled state interacts with the fiber channel. It affects the performance of quantum information processing. In this paper, we theoretically calculate the positive partial transposition (PPT) of the entangled state distributed over the optical fiber channel in the single-channel and dual-channel distribution scheme, respectively. Three types of initial entangled light field are considered and analyzed, they being an initial EPR entangled state, an EPR entangled state with asymmetric quadratures, and an EPR entangled state with asymmetric modes. Furthermore, the influence of the extra noise in the optical fiber on the transmission distance of EPR entangled state over the optical fiber channel is investigated. In the single-channel scheme or dual-channel scheme, the extra noise in the optical fiber channel leads the entangled state light field to be disentangled, and the transmission distance of EPR entangled state over the optical fiber channel to decrease rapidly with the increase of the extra noise. For maintaining the robustness of EPR entangled states in lossy optical fiber channels, the dual-channel scheme has more stringent requirements for the correlation quadrature symmetry and purity of the initial entangled state than the single-channel scheme. In the single fiber noise channel scheme, the maximum transmission distance and the robustness of the EPR entangled states with asymmetric modes are not sensitive to the asymmetry between modes. The change of asymmetry between modes does not lead to being disentangled. The maximum transmission distance does not change either. However, the decrease of asymmetry between modes results in the disentanglement in the double fiber noise channels’ scheme. The maximum transmission distance is reduced and the sudden death occurs to the entanglement. The present results will lay a foundation for continuous variables quantum information processing based on optical fiber, such as realizing continuous variables quantum communication over optical fiber and constructing metropolitan quantum network over optical fiber.

In this paper, we propose an explicit scheme to fully recover a multiple-qubit state subject to a phase damping noise. We establish the theoretical framework and the operational procedure to restore an unknown initial quantum state for an N-qubit model interacting with either individual baths or a common bath. We give an explicit construction of the random unitary (RU) Kraus decomposition for an N-qubit model interacting with a common bath. We also demonstrate how to use only one unitary reversal operation to restore an arbitrary state with phase damping noise. In principle, the initial state can always be recovered with a success probability of 1. Interestingly, we found that non-RU decomposition can also be used to restore some particular entangled states. This may open a new path to restore a quantum state beyond the standard RU scheme.

We introduce a simple experimentally realisable protocol for manipulating entanglement in mixed states of two polarisation-entangled qubits and show how concentration is achievable. We discuss a second protocol based on entanglement swapping with mixed states and show how the shared entanglement between distant parties can be improved.

In this paper, we have investigated the entanglement dynamics between two identical two-level atoms in the framework of two-photon double Jaynes-Cummings model taking into account the detuning between atoms and twice cavities frequencies and Kerr nonlinearities in both cavities. We have carried out the temporal dependence of the atom-atom negativity for Bell's initial entangled atomic states. The results show that these parameters have great impact on the amplitudes of the atom-atom entanglement oscillations and that presence of detuning and Kerr nonlinearity lead to stabilization of entanglement for all Bell-types initial atomic states. For a certain initial atomic entangled states, there is an entanglement sudden death effect between the two atoms. The detuning and Kerr medium in the cavities can prevent the undesirable entanglement sudden death from occurring.

Based on the exactly analytic solution obtained of the intensity-dependent Jaynes–Cummings model for a certain class of initial entangled mixed states, we explore the time evolution of the entanglement between two atoms, initially non-locally correlated and separately interacting with two distinct cavities. The results show that entanglement sudden death is dependent on the different initial states of atoms, and the length of the time interval for the zero entanglement is invariant for a certain class of initial mixed states.

Entanglement swapping for Bell states and Greenberger–Horne–Zeilinger states in qubit systems

We investigate the time evolution of entanglement of various entangled states of a two-qubit system exposed to either thermal or squeezed reservoirs. We show that, except for the vacuum reservoir, the sudden-death of entanglement always exists in the thermal and squeezed reservoirs. We present explicit expression for the sudden-death time of entanglement for various entangled states. We find that the sudden-death of entanglement results from the portion of the double excitation component in the initial entangled state. In this sense, the maximally entangled states of a two-qubit system that do not have the double excitation component is more robust against the quantum fluctuations of the vacuum reservoir.

Taming decoherence is a critical issue in quantum information science. We here investigate amplitude-damping decoherence suppression of two-qubit entangled states by weak quantum measurements. It is shown that the weak measurements can effectively suppress the decoherence for different initial entangled states. More interestingly, we show that the weak measurements have different effects on the entanglement protection for two entangled states which are equivalent under a local unitary operation. This result implies that the entanglement protection effect could be modulated according to different demands.

One scheme that aids in this distribution is entanglement concentration. This converts a large number of less entangled pairs into a smaller number of more entangled pairs using only local operations @3#. The concentrated pairs can then be used to perform the communication protocol faithfully. One such protocol, quantum teleportation @2#, exploits priorly shared entanglement to transfer an unknown ~or even partially unknown @4#! quantum state to a distant location. Teleporting one particle of an entangled pair results in the exchange of entangled partners across a distance, a process known as ‘‘entanglement swapping’’ @2,5#. Two of the particles that become entangled have not directly interacted at any stage, and, therefore, the swapping can be used as a means of entanglement distribution. Both teleportation and entanglement swapping have been experimentally demonstrated @6,7#, in the domain of microscopic systems. Demonstrations of such schemes with macroscopic objects would be of fundamental interest. An increasingly controllable macroscopic quantum system is a Bose-Einstein condensed state of a trapped dilute gas @8#. Bose condensates have already been used to demonstrate quantum features, such as superposition, in the macroscopic domain @9#. More recently, there have also been suggestions for creating specific types of entangled atomic beams, and multiparticle entangled states from Bose condensates @10#. In this paper, we propose a method for achieving entanglement swapping, using techniques that are experimentally feasible. This opens up the possibility of entanglement-aided communications using Bose condensates. We also show that a theoretical proposal for entanglement concentration by entanglement swapping, @11#, may be implemented, using exactly the same measurements. We begin by presenting a general entanglement swapping protocol for Bose condensates. We consider four condensates labeled by the modes a,b,c, and d ~see Fig. 1!. Modes a and b are entangled with a total number of n atoms uc ab& 15 ( p50 n

In Ref. 1 , we proposed a multiparty quantum secret sharing QSS protocol based on Bell-state entanglement swapping. Our multiparty protocol is a general one, that is, it contains both the three-party n=3 case and its generalization to a more-party n 4 case. Recently, in Ref. 2 the authors first pointed out some advantages of our protocol, such as dense coding, easy implementation, high efficiency, etc. Then they claimed that if our protocol is attacked by the so-called participant attack, the protocol is insecure. In fact, our multiparty n 3 QSS protocol is secure against any outsiders’ or insider’s eavesdropping. Only the generalized protocol i.e., the n 4 QSS protocol is insecure under the specific dishonest insiders’ attack as shown in Ref. 2 . Nonetheless, this leak in the generalized protocol can be easily fixed and accordingly the advantage of high efficiency in our protocol can be retained. We will explain these as follows. In Ref. 1 , when we simply generalized our three-party protocol to a n n 4 -party one, we changed the original qubit distribution method due to our carelessness. The original distribution method is that Alice prepares the qubits and distributes them to her two agents. When generalizing, we changed the qubit distribution in such a way that each party sends a qubit to the next party. It is this change which leads to the insecurity under the special attack case 2 . The comment 2 aims essentially at this change. That is, the two dishonest parties who each initially shares an e-bit with the sender can let one of them share both the two e-bits and the other one shares none by exchanging their qubits and cheating. In this case, the protocol is insecure. It is a minor leak in our protocol. If the change about qubit distribution is removed during the generalization, that is, the same qubit distributions as that in the three-party case are maintained when generalizing, then the security of the n n 4 -party protocol can still be assured. The reason is as follows. When the sender distributes two qubits to an agent one by one, if the sender does not tell the agent the orderings of the two qubits, the agent cannot distinguish their orderings for the two qubits are identical. In this case, the two agents who share entanglements with the sender cannot assure that only one of them can definitively share the entanglements with the sender by exchanging their qubits. To be explicit, let us take the four-party case as an example: Alice prepares four photon Einstein-Podolsky-Rosen EPR pairs A2,B1 , B2,C1 , C2,D1 , and D2,A1 . She sends two photons B1,B2 to Bob, C1,C2 to Charlie, and D1, D2 to Dick. In this case, Alice shares the EPR pair A2, B1 with Bob and the EPR pair A1, D2 with Dick. Note that each sharer Bob, Charlie, Dick cannot differentiate his two photons since their two photons are identical. In this case, Bob or Dick cannot correctly let only one sharer say, Bob hereafter share two EPR pairs by exchanging their photons. Obviously, with probability 1/2 Bob may send the photon B1 to Dick. Also with probability 1/2, Dick may send the photon D1 to Bob. In either case, the goal of deterministically letting Bob share two EPR pairs with Alice cannot be realized via the exchange. Consequently, the so-called participant attack is invalid. Hence the leak in our generalized protocol can be easily fixed and accordingly the advantage of high efficiency the authors of Ref. 2 admitted is retained. Incidentally, the modification in Ref. 2 can fix the leak of our protocol also, however, it decreases the efficiency of the protocol.

Cryptanalysis and improvement of a DSQC using four-particle entangled state and entanglement swapping

The dynamics of entanglement and quantum discord between two identical qubits strongly interacting with a common single mode leaky cavity field have been investigated beyond the rotating wave approximation (RWA) by using recently derived Lindblad type quantum optical master equation [F. Beaudoin, J.M. Gambetta, A. Blais, Phys. Rev. A {\bf 84}, 043832 (2011)] that can describe the losses of the cavity field in a strong atom-field coupling regime. Contrary to previous investigations of the same model in the dissipative regime by using the standard Lindblad quantum optical master equation in a strong-coupling regime, the atom-field steady states are found to be cavity decay rate independent and have a very simple structure determined solely by the overlap of initial atomic state with the subradiant state which is valid for all coupling regimes. Non-RWA dynamics are found to have remarkable effects on the steady state quantum discord and entanglement that cannot be achieved under RWA conditions, for instance, they can induce steady state entanglement even for the initial states that have no overlap with the subradiant state. Moreover, the non-RWA dynamics are found to reverse the initial state dependence of steady state entanglement and quantum discord contrary to the RWA case.

Quantum network is a promising platform for numerous quantum applications, including distributed quantum computing, secure communication, and improved sensing. Implementing entanglement distribution between remote quantum nodes plays a vital role in realizing the quantum network's capabilities, and it requires effective remote entanglement distribution protocols. To meet this requirement, we propose two strategies, namely connection-oriented and connectionless, to achieve end-to-end entanglement distribution inspired by the designs of classical communication. For the connection-oriented strategy, an exclusive quantum connection is pre-established between the source and destination nodes. For the connectionless strategy, entanglement swapping is performed hop-by-hop tentatively. In this way, the best-effort service is provided for the source node to establish long-distance entanglement with the destination node. Analogous to classical communication, the proposed strategies have their advantages and disadvantages. Our simulation results show that the connectionless strategy is more efficient and robust than the connection-oriented strategy in terms of throughput. However, the connection-oriented strategy provides reliable end-to-end entanglement distribution but at the expense of higher overhead. Moreover, the application scenarios of these two strategies are discussed. This work paves the road for designing end-to-end entanglement distribution protocols in quantum networks.

Summary form only given. We consider quantum teleportation and entanglement swapping for systems of arbitrary spin j /spl ges/ 1/2. Spin quantum teleportation and entanglement swapping enable quantum state transfer between distant material systems, as well as being important for quantum network operations built on qubit elements. We identify an appropriate entangled resource state for high-fidelity spin quantum teleportation, and, in the case of spin entanglement swapping, develop a measurement scheme that yields the largest entanglement between the two output states. We present teleportation fidelity for moderate photon numbers and finite displacements. We show that the fidelity for teleportation of coherent spin states can be significantly improved using an alternative scheme of final rotations. Also the fidelity is not maximised for a maximally entangled entanglement resource, which is unusual in quantum teleportation. This teleportation scheme also exhibits entanglement swapping for moderate photon numbers. In contrast with the case for the fidelity, the final entanglement is maximised when the entanglement resource is maximally entangled.