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arXiv:2208.07495 · Scientific Reports

Teleportation of hybrid entangled states with continuous-variable entanglement

Mingjian He, Robert Malaney

Published Oct 13, 2022• 12 citations
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Abstract

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.

DOI
10.1038/s41598-022-21283-4

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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 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 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] .
Hybrid entanglement swapping supports the teleportation of any arbitrary states, regardless of whether the quantum information in the state is encoded in Discrete Variables (DV) or Continuous Variables (CV). In this work, we study the CV teleportation channel created between two ground receivers via direct lossy-distribution from a low-Earth-orbit (LEO) satellite. Such a flexible teleportation protocol has the potential to interconnect a global array of quantum-enabled devices regardless of the different intrinsic technology upon which the devices are built. However, past studies of hybrid entanglement swapping have not accounted for channel transmission loss. Here we derive the general framework for teleporting an arbitrary input mode over a lossy CV teleportation channel. We investigate the specific case where the input modes are part of DV states entangled in the photon number basis, then identify the optimal teleportation strategy. Our results show that, relative to DV photon-number entanglement sourced directly from the satellite, there are circumstances where our teleported DV states retain higher entanglement quality. We discuss the implications of our new results in the context of generating a global network of ultra-secure communications between different quantum-enabled devices which possess line-of-sight connections to LEO satellites. Specifically, we illustrate the impact the teleportation process has on the key rates from a Quantum Key Distribution protocol.
Quantum teleportation, a transfer protocol of quantum states, is the essence of many sophisticated quantum information protocols. There have been two complementary approaches to optical quantum teleportation: discrete variables (DVs) and continuous variables (CVs). However, both approaches have pros and cons. Here we take a “hybrid” approach to overcome the current limitations: CV quantum teleportation of DVs. This approach enabled the first realization of deterministic quantum teleportation of photonic qubits without post-selection. We also applied the hybrid scheme to several experiments, including entanglement swapping between DVs and CVs, conditional CV teleportation of single photons, and CV teleportation of qutrits. We are now aiming at universal, scalable, and fault-tolerant quantum computing based on these hybrid technologies.
Quantum teleportation allows for the transfer of arbitrary, in principle, unknown quantum states from a sender to a spatially distant receiver, who share an entangled state and can communicate classically. It is the essence of many sophisticated protocols for quantum communication and computation. In order to realize flying qubits in these schemes, photons are an optimal choice. However, teleporting a photonic qubit has been limited due to experimental inefficiencies and restrictions. Major disadvantages have been the probabilistic nature of both entangled resource states and linear-optics Bell-state measurements (BSM), as well as the need for post-selecting the successful events by destroying the teleported qubit. Here, all the above limitations are overcome through a totally distinct, “hybrid” approach: continuous-variable (CV) quantum teleportation of a discrete-variable, photonic qubit. The strength of CV teleportation lies in the on-demand availability of the quadrature-entangled states and the completeness of a BSM in the quadrature bases using linear optics and homodyne detections; this enables fully deterministic, unconditional teleportation of photonic qubits. We implement this kind of “hybrid” teleportation by utilizing a very recent, advanced technology: a broadband CV teleporter and a narrow-band qubit compatible with the teleporter.
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.