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arXiv:1705.10056 · Physical Review A

Optimal continuous-variable teleportation under energy constraint

Jaehak Lee, Jiyong Park, Hyunchul Nha

Published May 24, 2017• 4 citations
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Abstract

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.

DOI
10.1103/physreva.95.052343

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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.
Continuous-variable (CV) teleportation is a fundamental protocol in quantum information science. A number of experiments have been designed to simulate ideal teleportation under realistic conditions. In this paper, we detail an analytical approach for determining optimal input states for quantifying the performance of CV unidirectional and bidirectional teleportation. The metric that we consider for quantifying performance is the energy-constrained channel fidelity between ideal teleportation and its experimental implementation, and along with this, our focus is on determining optimal input states for distinguishing the ideal process from the experimental one. We prove that, under certain energy constraints, the optimal input state in unidirectional as well as bidirectional teleportation is a finite entangled superposition of twin-Fock states saturating the energy constraint. Moreover, we also prove that, under the same constraints, the optimal states are unique; that is, there is no other optimal finite entangled superposition of twin-Fock states.
Non-Gaussian operations have been shown to enhance the fidelity of continuous-variable quantum teleportation. However, a disadvantage of these non-Gaussian operations is that they are probabilistic in nature. In this article we study the trade-off between teleportation fidelity and success probability for optimal performance of the teleportation protocol. To this end, we first derive a unified expression for the Wigner characteristic function describing three non-Gaussian states: photon-subtracted, photon-added, and photon-catalyzed two-mode squeezed vacuum states. We then utilize it to obtain the fidelity of teleportation for input coherent and squeezed vacuum states using the aforementioned non-Gaussian resource states. We optimize the product of the relative enhancement in fidelity and the probability of state preparation by tuning the transmissivity of the beam splitters involved in implementing non-Gaussian operations. This leads to a scenario that can be effectively implemented in a laboratory to enhance fidelity. It turns out that among all the non-Gaussian resource states considered, the symmetric one-photon-subtracted two-mode squeezed vacuum state is the most advantageous. We provide the associated optimal squeezing and beam splitter transmissivity values for the non-Gaussian resource states considered, which will be of significant interest to the experimental community. We also consider the effect of imperfect photon detectors on teleportation fidelity. Further, we expect the derived Wigner characteristic function to be useful in state characterization and other quantum information processing protocols.
Continuous variable quantum teleportation provides a path to the long-distance transmission of quantum states. Photon-varying non-Gaussian operations have been shown to improve the fidelity of quantum teleportation when integrated into the protocol. However, for a given type of non-Gaussian operation, the achievable fidelity varies with the parameters associated with the operation. Previous work only focused on particular settings of the parameters, over which an optimization was missing. The potential of such operations is not fully uncovered. Given a fixed non-Gaussian operation, the achievable fidelity also varies with input states. An operation that increases the fidelity for teleporting one class of states might do the contrary for other classes of states. A performance metric, upon which an operation is optimized, suitable for different input states, is also missing. In this work, we build a framework for photon-varying non-Gaussian operations for multimode states, upon which we propose a performance metric suitable for arbitrary teleportation input states. We then apply the new metric to evaluate different types of non-Gaussian operations. Starting from simple multiphoton photon subtraction and photon addition, we find that increasing the number of ancillary photons involved in the operation does not guarantee performance improvement. We then investigate a generalization of the operations mentioned above, finding that operations that approximate a particular form provide the best improvement. The results provided here will be valuable for real-world implementations of quantum teleportation networks and applications that harness the non-Gaussianity of quantum states. Published by the American Physical Society 2024
We investigate continuous variable quantum teleportation using non-Gaussian states of the radiation field as entangled resources. We compare the performance of different classes of degaussified resources, including two-mode photon-added and two-mode photon-subtracted squeezed states. We then introduce a class of two-mode squeezed Bell-like states with one-parameter dependence for optimization. These states interpolate between and include as subcases different classes of degaussified resources. We show that optimized squeezed Bell-like resources yield a remarkable improvement in the fidelity of teleportation both for coherent and nonclassical input states. The investigation reveals that the optimal non-Gaussian resources for continuous variable teleportation are those that most closely realize the simultaneous maximization of the content of entanglement, the degree of affinity with the two-mode squeezed vacuum, and the, suitably measured, amount of non-Gaussianity.
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.