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Photonics Research

Limitations of teleporting a qubit via a two-mode squeezed state

Seok Hyung Lie, Hyunseok Jeong

Published Apr 15, 2019• 14 citations
Publisher

Abstract

Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a “hybrid” approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment. The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.

DOI
10.1364/prj.7.0000a7

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Recently, a teleportation scheme using a two-mode squeezed state to teleport a photonic qubit, so called a “hybrid” approach, has been suggested and experimentally demonstrated as a candidate to overcome the limitations of all-optical quantum information processing. We find, however, that there exists the upper bound of fidelity when teleporting a photonic qubit via a two-mode squeezed channel under a lossy environment. The increase of photon loss decreases this bound, and teleportation better than this limit is impossible even when the squeezing degree of the teleportation channel becomes infinity. Our result indicates that the hybrid scheme can be valid for fault-tolerant quantum computing only when the photon loss rate can be suppressed under a certain limit.
It was shown that using multiphoton qubits, a nearly deterministic Bell-state measurement can be performed with linear optics and on-off photodetectors [Phys. Rev. Lett. 114, 113603 (2015)]. However, multiphoton qubits are generally more fragile than single-photon qubits under a lossy environment. In this paper, we propose and analyze a scheme to teleport multiphoton-qubit information using hybrid entanglement with a loss-tolerant carrier qubit. We consider three candidates for the carrier qubit: a coherent-state qubit, a single-photon polarization qubit, and a vacuum-and-single-photon qubit. We find that teleportation with the vacuum-and-single-photon qubit tolerates about 10 times greater photon losses than with the multiphoton qubit of the photon number $N\ensuremath{\ge}4$ in the high fidelity regime ($F\ensuremath{\ge}90%$). The coherent-state qubit encoding may be even better than the vacuum-and-single-photon qubit as the carrier when its amplitude is as small as $\ensuremath{\alpha}<0.78$. We further point out that the fidelity of the teleported state by our scheme is determined by loss in the carrier qubit while the success probability depends on loss only in the multiphoton qubit to be teleported. Our study implies that the hybrid architecture may complement the weaknesses of each qubit encoding.
We compare single-photon qubits and hybrid qubits as information carriers through quantum teleportation using a Gaussian continuous-variable channel. A hybrid qubit in our study is in the form of entanglement between a coherent state and a single photon. We find that hybrid qubits outperform photonic qubits when coherent amplitudes of the hybrid qubits are as low as $\ensuremath{\alpha}\ensuremath{\lesssim}1$, while single-photon qubits yield better results for larger amplitudes. We analyze further the effect of photon losses and observe that the overall character of teleportation for different qubits remains the same although the teleportation fidelities are degraded by photon losses. Our work provides a comparative look at practical quantum information processing with different types of qubits.
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 enables transferring quantum states by leveraging entanglement. The distribution of entangled states is challenged by decoherence, which degrades the teleportation performance. Continuous-variable teleportation with coherent-state qubits has gained particular interest because it can provide better performance than discrete-variable teleportation with polarization-encoded qubits and is more resilient to decoherence. However, most existing schemes employ a specific configuration of coherent-state qubits, namely Schrödinger cat states, and assume symmetric photon-loss channels. This work explores the teleportation of qubits based on coherent states through asymmetric quantum channels impaired by photon loss. First, we characterize the teleportation protocol for arbitrary coherent-state qubit configurations considering asymmetric and photon-loss channels. Then, we present case studies under both ideal entanglement distribution and lossy conditions. Results reveal a trade-off between state distinguishability and teleportation fidelity, providing insight into the optimal design of coherent-state qubits in practical teleportation protocols.
The teleportation of two-mode continuous variables was performed by using two two-mode squeezed vacuum states served as quantum channel.The average fidelity and the probability density were calculated for teleportation of a two-mode squeezed vacuum state.The results indicate that increased squeezing of teleported state will lead to a loss of fidelity.The probability density of measuring result consists of the product of two bivariate normed density functions,and it shows that when the average fidelity goes up,the probability of obtaining large measurement value also increases.