Continuous-variable Entanglement Swapping Research Articles

利用连续变量纠缠交换增强罗兰C台链时间同步的方案研究

利用连续变量纠缠交换增强罗兰C台链时间同步的方案研究

Non-Gaussian swapping of entangled resources

We investigate the continuous-variable entanglement swapping protocol in a non-Gaussian setting, with non- Gaussian states employed either as entangled inputs and/or as swapping resources. The quality of the swapping protocol is assessed in terms of the teleportation fidelity achievable when using the swapped states as shared entangled resources in a teleportation protocol. We thus introduce a two-step cascaded quantum communication scheme that includes a swapping protocol followed by a teleportation protocol. The swapping protocol is fed by a general class of tunable non-Gaussian states, the squeezed Bell states, which, by means of controllable free parameters, allows for a continuous morphing from Gaussian twin beams up to maximally non-Gaussian squeezed number states. In the realistic instance, taking into account the effects of losses and imperfections, we show that as the input two-mode squeezing increases, optimized non-Gaussian swapping resources allow for a monotonically increasing enhancement of the fidelity compared to the corresponding Gaussian setting. This result implies that the use of non-Gaussian resources is necessary to guarantee the success of continuous-variable entanglement swapping in the presence of decoherence.

Continuous-variable quantum homomorphic signature

Quantum cryptography is believed to be unconditionally secure because its security is ensured by physical laws rather than computational complexity. According to spectrum characteristic, quantum information can be classified into two categories, namely discrete variables and continuous variables. Continuous-variable quantum protocols have gained much attention for their ability to transmit more information with lower cost. To verify the identities of different data sources in a quantum network, we propose a continuous-variable quantum homomorphic signature scheme. It is based on continuous-variable entanglement swapping and provides additive and subtractive homomorphism. Security analysis shows the proposed scheme is secure against replay, forgery and repudiation. Even under nonideal conditions, it supports effective verification within a certain verification threshold.

Deterministically Entangling Two Remote Atomic Ensembles via Light-Atom Mixed Entanglement Swapping.

Entanglement of two distant macroscopic objects is a key element for implementing large-scale quantum networks consisting of quantum channels and quantum nodes. Entanglement swapping can entangle two spatially separated quantum systems without direct interaction. Here we propose a scheme of deterministically entangling two remote atomic ensembles via continuous-variable entanglement swapping between two independent quantum systems involving light and atoms. Each of two stationary atomic ensembles placed at two remote nodes in a quantum network is prepared to a mixed entangled state of light and atoms respectively. Then, the entanglement swapping is unconditionally implemented between the two prepared quantum systems by means of the balanced homodyne detection of light and the feedback of the measured results. Finally, the established entanglement between two macroscopic atomic ensembles is verified by the inseparability criterion of correlation variances between two anti-Stokes optical beams respectively coming from the two atomic ensembles.

Entangling two distant non‐interacting microwave modes

A protocol able to prepare two remote and initially uncorrelated microwave modes in an entangled stationary state, which is certifiable using only local optical homodyne measurements id proposed. The protocol is an extension of continuous variable entanglement swapping, and exploits two hybrid quadripartite opto‐electro‐mechanical systems in which a nanomechanical resonator acts as a quantum interface able to entangle optical and microwave fields. The proposed protocol allows to circumvent the problems associated with the fragility of microwave photons with respect to thermal noise and may represent a fundamental tool for the realization of quantum networks connecting distant solid‐state and superconducting qubits, which are typically manipulated with microwave fields. The certifying measurements on the optical modes guarantee the success of entanglement swapping without the need of performing explicit measurements on the distant microwave fields.

Gaussian-modulated coherent-state measurement-device-independent quantum key distribution

Measurement-device-independent quantum key distribution (MDI-QKD), leaving the detection procedure to the third partner and thus being immune to all detector side-channel attacks, is very promising for the construction of high-security quantum information networks. We propose a scheme to implement MDI-QKD, but with continuous variables instead of discrete ones, i.e., with the source of Gaussian-modulated coherent states, based on the principle of continuous-variable entanglement swapping. This protocol not only can be implemented with current telecom components but also has high key rates compared to its discrete counterpart; thus it will be highly compatible with quantum networks.

Unity gain and nonunity gain quantum teleportation

We investigate continuous variable quantum teleportation. We discuss the methods presently used to characterize teleportation in this regime, and propose an extension of the measures proposed by Grangier and Grosshans , and Ralph and Lam . This new measure, the gain normalized conditional variance product M, turns out to be highly significant for continuous variable entanglement swapping procedures, which we examine using a necessary and sufficient criterion for entanglement. We elaborate on our recent experimental continuous variable quantum teleportation results , demonstrating success over a wide range of teleportation gains. We analyze our results using fidelity; signal transfer, and the conditional variance product; and a measure derived in this paper, the gain normalized conditional variance product.

Experiment towards continuous-variable entanglement swapping: Highly correlated four-partite quantum state

We present a protocol for performing entanglement swapping with intense pulsed beams. In a first step, the generation of amplitude correlations between two systems that have never interacted directly is demonstrated. This is verified in direct detection with electronic modulation of the detected photocurrents. The measured correlations are better than expected from a classical reconstruction scheme. In an entanglement swapping process, a four-partite entangled state is generated. We prove experimentally that the amplitudes of the four optical modes are quantum correlated 3 dB below shot noise, which is consistent with the presence of genuine four-party entanglement.

Quantum Communication with Continuous Variables

Many quantum communication schemes rely on the resource of entanglement. For example, quantum teleportation is the transfer of arbitrary quantum states through a classical communication channel using shared entanglement. Entanglement, however, is in general not easy to produce on demand. The bottom line of this work is that a particular kind of entanglement, namely that based on continuous quantum variables, can be created relatively easily. Only squeezers and beam splitters are required to entangle arbitrarily many electromagnetic modes. Similarly, other relevant operations in quantum communication protocols become feasible in the continuous-variable setting. For instance, measurements in the maximally entangled basis of arbitrarily many modes can be accomplished via linear optics and efficient homodyne detections. In the first two chapters, some basics of quantum optics and quantum information theory are presented. These results are then needed in Chapter III, where we characterize continuous-variable entanglement and show how to make it. The members of a family of multi-mode states are found to be truly multi-party entangled with respect to all their modes. These states also violate multi-party inequalities imposed by local realism, as we demonstrate for some members of the family. Further, we discuss how to measure and verify multi-party continuous-variable entanglement. Various quantum communication protocols based on the continuous-variable entangled states are discussed and developed in Chapter IV. These include the teleportation of entanglement (entanglement swapping) as a test for genuine quantum teleportation. It is shown how to optimize the performance of continuous-variable entanglement swapping. We highlight the similarities and differences between continuous-variable entanglement swapping and entanglement swapping with discrete variables. Chapter IV also contains a few remarks on quantum dense coding, quantum error correction, and entanglement distillation with continuous variables, and in addition a review of quantum cryptographic schemes based on continuous variables. Finally, in Chapter V, we consider a multi-party generalization of quantum teleportation. This so-called telecloning means that arbitrary quantum states are transferred not only to a single receiver, but to several. However, due to the quantum mechanical no-cloning theorem, arbitrary quantum states cannot be perfectly copied. We present a protocol that enables telecloning of arbitrary coherent states with the optimal quality allowed by quantum theory. The entangled states needed in this scheme are again producible with squeezed light and beam splitters. Although the telecloning scheme may also be used for "local'' cloning of coherent states, we show that cloning coherent states locally can be achieved in an optimal fashion without entanglement. It only requires a phase-insensitive amplifier and beam splitters.

Continuous variable entanglement swapping in a thermal environment

With the application of a Wigner function description of a two-mode squeezed state, we study a protocol of continuous variable entanglement swapping in a noisy quantum channel. Assuming that the two initial entangled states are coupled with the same environment, we analyse the quantum state emerging from the swapping and obtain the inseparable condition for the output correlation. It is found that there is more noise resulting from the entanglement swapping than from the direct transmission, no matter what values of displacement gain are chosen.

Wigner function description of continuous variable entanglement swapping

We discuss the continuous variable entanglement swapping using the Wigner function. The sufficient inseparability criterion for continuous variable systems is used to analyse the quantum correlation. Perfect teleportation can be obtained by increasing the degree of squeezing on the entanglement source. Entanglement swapping occurs for any nonzero squeezing in both of the two initial sources if optimal gain is obtained.

Broadband teleportation

Quantum teleportation of an unknown broadband electromagnetic field is investigated. The continuous-variable teleportation protocol by Braunstein and Kimble [Phys. Rev. Lett. {\bf 80}, 869 (1998)] for teleporting the quantum state of a single mode of the electromagnetic field is generalized for the case of a multimode field with finite bandwith. We discuss criteria for continuous-variable teleportation with various sets of input states and apply them to the teleportation of broadband fields. We first consider as a set of input fields (from which an independent state preparer draws the inputs to be teleported) arbitrary pure Gaussian states with unknown coherent amplitude (squeezed or coherent states). This set of input states, further restricted to an alphabet of coherent states, was used in the experiment by Furusawa {\it et al.} [Science {\bf 282}, 706 (1998)]. It requires unit-gain teleportation for optimizing the teleportation fidelity. In our broadband scheme, the excess noise added through unit-gain teleportation due to the finite degree of the squeezed-state entanglement is just twice the (entanglement) source's squeezing spectrum for its ``quiet quadrature.'' The teleportation of one half of an entangled state (two-mode squeezed vacuum state), i.e., ``entanglement swapping,'' and its verification are optimized under a certain nonunit gain condition. We will also give a broadband description of this continuous-variable entanglement swapping based on the single-mode scheme by van Loock and Braunstein [Phys. Rev. A {\bf 61}, 10302 (2000)]

Entanglement quantification and purification in continuous-variable systems

We develop theoretical and numerical tools for the quantification of entanglement in systems with continuous degrees of freedom. Continuous variable entanglement swapping is introduced and based on this idea we develop methods of entanglement purification for continuous variable systems. The success of these entanglement purification methods is then assessed using these tools.

Unconditional teleportation of continuous-variable entanglement

We give a protocol and criteria for demonstrating unconditional teleportation of continuous-variable entanglement (i.e., entanglement swapping). The initial entangled states are produced with squeezed light and linear optics. We show that any nonzero entanglement (any nonzero squeezing) in both of two entanglement sources is sufficient for entanglement swapping to occur. In fact, realization of continuous-variable entanglement swapping is possible using only two single-mode squeezed states.