The continuous-variable (CV) quantum state of light allows for the teleportation of a discrete-variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource state is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold. In this paper, we present a nondeterministic teleportation protocol that combines a Gaussian CV resource state with a modified form of the Bell state measurement that accommodates significantly improved DV-qubit fidelity over a wide range of channel losses. Beyond this improvement, we also show how the use of non-Gaussian operations on the CV resource state can lead to a DV-qubit fidelity approaching unity for any channel loss.
The continuous-variable (CV) quantum state of light allows for the teleportation of a discrete-variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource state is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold. In this paper, we present a nondeterministic teleportation protocol that combines a Gaussian CV resource state with a modified form of the Bell state measurement that accommodates significantly improved DV-qubit fidelity over a wide range of channel losses. Beyond this improvement, we also show how the use of non-Gaussian operations on the CV resource state can lead to a DV-qubit fidelity approaching unity for any channel loss.
Hybrid entanglement between discrete-variable (DV) and continuous-variable (CV) quantum systems is an essential resource for heterogeneous quantum networks. Our previous work showed that in lossy channels the teleportation of DV qubits, via CV-entangled states, can be significantly improved by a new protocol defined by a modified Bell state measurement at the sender. This work explores whether a new, similarly modified, CV-based teleportation protocol can lead to improvement in the transfer of hybrid entangled states. To set the scene, we first determine the performance of such a modified protocol in teleporting CV-only qubits, showing that significant improvement over traditional CV-based teleportation is obtained. We then explore similar modifications in the teleportation of a specific hybrid entangled state showing that significant improvement over traditional CV-based teleportation is again found. For a given channel loss, we find teleporting the DV qubit of the hybrid entangled state can always achieve higher fidelity than teleporting the CV qubit. We then explore the use of various non-Gaussian operations in our modified teleportation protocol, finding that, at a cost of lower success probability, quantum scissors provides the most improvement in the loss tolerance. Our new results emphasize that in lossy conditions, the quantum measurements undertaken at the sender can have a surprising and dramatic impact on CV-based teleportation.
The wave-particle duality of light has led to two different encodings of optical quantum information. One approach, referred to as the discrete-variable (DV) one, relies on finite dimensional quantum systems, while the other one, referred to as the continuous-variable (CV) one, is based on wave-like states belonging to an infinite dimensional Hilbert space. These two encodings have historically been separated, but recently, new hybrid protocols which aim at combining the advantages of the two encodings have emerged [1] . In that prospect our recent demonstration of the measurement-induced generation of hybrid entanglement between discrete- and continuous-variable quantum states [2] , [3] , located at distant places and connected by a lossy channel, has opened the way to the implementation of hybrid protocols and heterogeneous quantum networks. Following the first protocols based on this resource, such as the remote preparation of continuous-variable qubits [4] , or a violation of an Einstein-Podolsky-Rosen steering inequality [5] , we will here report our latest experimental results on entanglement swapping and quantum teleportation protocols using hybrid entangled states based on different encodings [6] .
The need for high-fidelity quantum teleportation arises in a variety of quantum algorithms and protocols. Unfortunately, conventional continuous-variable teleportation schemes rely on Einstein–Podolsky–Rosen states that yield a fidelity that approaches unity only in the limit of an unphysical amount of squeezing. A new method that utilizes an ensemble of single photon entangled states, qubits, to teleport continuous variable (CV) states with fidelity approaching unity with finite resources was recently proposed by Andersen and Ralph [Phys. Rev. Lett.111, 050504 (2013)]. We extend these ideas to consider the general case of using maximally entangled d-level states, qudits, to teleport a CV state and discuss how the corresponding results are affected. In particular, we find that, by using qudits with dimension greater than two, we can achieve a higher fidelity with comparable resources.
Quantum teleportation is one of the crucial protocols in quantum information processing. It is important to accomplish an efficient teleportation under practical conditions, aiming at a higher fidelity desirably using fewer resources. The continuous-variable (CV) version of quantum teleportation was first proposed using a Gaussian state as a quantum resource, while other attempts were also made to improve performance by applying non-Gaussian operations. We investigate the CV teleportation to find its ultimate fidelity under energy constraint identifying an optimal quantum state. For this purpose, we present a formalism to evaluate teleportation fidelity as an expectation value of an operator. Using this formalism, we prove that the optimal state must be a form of photon-number entangled states. We further show that Gaussian states are near optimal, while non-Gaussian states make a slight improvement and therefore are rigorously optimal, particularly in the low-energy regime.
A characteristic function (CF) based formalism for the representation of quantum optical operations pertaining to the Continuous Variable (CV) quantum teleportation protocol for general resource and input states is introduced; allowing for modifications of basic CV teleportation; such as lossy homodyne measurements and the presence of thermal noise. The output state CF is given as a product of the CFs of resource and input. The use of non-Gaussian resources is studied by means of a general class of two-mode squeezed Bell-like states that include as special cases Gaussian, non-Gaussian and "degaussified" resources; it is shown that Bell-like resources optimized ("tailored") for maximum fidelity yield a remarkable improvement in fidelity of teleportation for the studied input states. A further generalization is introduced with two-mode squeezed superpositions of Fock states including finite truncations of Gaussian states as special cases; it is shown that the optimization for maximum fidelity reduces these resources to truncated Gaussian states. Another class of non-Gaussian resources is introduced, optimized squeezed cat-like states; their performance is shown to be higher than that of a Gaussian state; but lower than that for the Bell-like states. It is shown that the optimal non-Gaussian resources are those that most closely realize the simultaneous maximization of the entanglement, the affinity with the two-mode squeezed vacuum and the (suitably measured) amount of non-Gaussianity. The teleportation of coherent state inputs is studied using squeezed Bell-like and squeezed cat-like states superimposed over Gaussian modes representing thermal noise; it is shown that the optimized non-Gaussian resources are more robust in the presence of noise then Gaussian resources.
We present a general formalism to describe continuous-variable (CV) quantum teleportation of discrete-variable (DV) states with gain tuning, taking into account experimental imperfections. Here the teleportation output is given by independently transforming each density matrix element of the initial state. This formalism allows us to accurately model various teleportation experiments and to analyze the gain dependence of their respective figures of merit. We apply our formalism to the recent experiment on CV teleportation of qubits [S. Takeda et al., Nature 500, 315 (2013)] and investigate the optimal gain for the transfer fidelity. We also propose and model an experiment for CV teleportation of DV entanglement. It is shown that, provided the experimental losses are within a certain range, DV entanglement can be teleported for any nonzero squeezing by optimally tuning the gain.