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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Quantum noise and probabilistic teleportation

Arun Kumar Pati, Pankaj Agrawal

Published May 16, 2003• 1 citation
Publisher

Abstract

In the presence of quantum noise a perfect EPR pair becomes imperfect and may be described by a non-maximally entangled pair. With non-maximally entangled state as a resource one cannot teleport an unknown state faithfully. Typically, one has to perform either local filtering or entanglement concentration and then follow the standard teleportation method. In this talk, we will present a new protocol that uses neither local filtering nor entanglement concentration to teleport an unknown state. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity but with a probability that is less than unit. Ours is a generalized quantum teleportation protocol that encompasses probabilistic as well as deterministic teleportation scenarios. We describe the probabilistic teleportation in terms of quantum operations and give explicit expressions for success and failure probabilities. This may have practical value in real experiments, and even may be tested with current technology.

DOI
10.1117/12.497241

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In the presence of quantum noise a perfect EPR pair becomes imperfect and may be described by a non-maximally entangled pair. With non-maximally entangled state as a resource one cannot teleport an unknown state faithfully. Typically, one has to perform either local filtering or entanglement concentration and then follow the standard teleportation method. In this talk, we will present a new protocol that uses neither local filtering nor entanglement concentration to teleport an unknown state. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity but with a probability that is less than unit. Ours is a generalized quantum teleportation protocol that encompasses probabilistic as well as deterministic teleportation scenarios. We describe the probabilistic teleportation in terms of quantum operations and give explicit expressions for success and failure probabilities. This may have practical value in real experiments, and even may be tested with current technology.
We consider a generalized quantum teleportation protocol for an unknown qubit using non-maximally entangled state as a shared resource. Without recourse to local filtering or entanglement concentration, using standard Bell-state measurement and classical communication one cannot teleport the state with unit fidelity and unit probability. We show that using non-maximally entangled measurements one can teleport an unknown state with unit fidelity albeit with reduced probability. We also give a generalized protocol for entanglement swapping using non-maximally entangled states. I.
We describe a new protocol where, by using a non-maximally entangled basis as the measurement basis, one can use a general pure entangled state as a resource for quantum teleportation. Using this protocol one can teleport a state with unit fidelity though less than unit probability. We also use the more natural language of quantum operations to describe this probabilistic teleportation. We also provide success and failure probabilities for this protocol. This scheme could be of use in real experiments which may be tested in the near future.
We extend the research program initiated in [Phys. Rev. A 92, 012338 (2015)] from noisy deterministic teleportation protocols to noisy probabilistic (conditional) protocols. Our main goal now is to study how we can increase the fidelity of the teleported state in the presence of noise by working with probabilistic protocols. We work with several scenarios involving the most common types of noise in realistic implementations of quantum communication tasks and find many cases where adding more noise to the probabilistic protocol increases considerably the fidelity of the teleported state, without decreasing the probability of a successful run of the protocol. Also, there are cases where the entanglement of the channel connecting Alice and Bob leading to the greatest fidelity is not maximal. Moreover, there exist cases where the optimal fidelity for the probabilistic protocols are greater than the maximal fidelity (2/3)(2/3)(2/3) achievable by using only classical resources, while the optimal ones for the deterministic protocols under the same conditions lie below this limit. This result clearly illustrates that in some cases we can only get a truly quantum teleportation if we use probabilistic instead of deterministic protocols.
Quantum teleportation, a cornerstone of quantum information science, enables the transfer of an unknown quantum state from one location to another without physically moving the state itself. Its efficacy is primarily quantified by fidelity, a measure of how closely the teleported state resembles the original. Achieving high-fidelity teleportation is paramount for practical applications in quantum communication and computation. This paper explores the intricate relationship between non-locality, the no-cloning theorem, and the pursuit of high-fidelity quantum teleportation. We introduce the concept of "unclonable non-locality" to describe scenarios where the inherent non-local correlations of entangled states are leveraged in a manner that inherently resists illicit copying, thereby enhancing the integrity and security of the teleportation process. We review current state-of-the-art teleportation protocols, analyzing their fidelity limitations and the impact of various noise models, such as those arising from Bell-diagonal resource states and local amplitude-damping channels. Our framework emphasizes that protocols exhibiting identical average fidelities can conceal distinct statistical behaviors and asymmetries introduced by local noise, stressing the need for a comprehensive statistical assessment beyond simple average fidelity. We propose methods for constructing and utilizing entangled resources that maximize non-local correlations while inherently enforcing the no-cloning principle, thereby offering a robust pathway to deterministic, high-fidelity quantum state transfer. The discussion highlights the potential for designing tailored teleportation benchmarks based on prior importance functions, unifying moment-based criteria and threshold-based success probabilities into a single figure of merit, and clarifying the role of entanglement strength in certifying high-fidelity teleportation. We also acknowledge the ethical implications associated with the development of powerful quantum technologies that could have significant societal impacts.
Achieving near-unity fidelity of Quantum Teleportation (QT) in a noisy environment is an essential requirement for its real-world applications. Towards this goal, we devise a distinctive protocol based on the timing of the sender Alice's Bell-basis measurement, synchronous with the suitably engineered structure of noise in the receiver Bob's wing, without requiring any knowledge or manipulation of Alice's local noise. For this purpose, to finally obtain the teleported states by performing the required unitary operations, Bob has to retain his qubits for only two particular Bell-basis outcomes communicated by Alice, whose corresponding reduced states have no dependence on the noise parameters in Alice's wing. Such postselection is crucial for enhancing the fidelity of the teleported state towards its ideal limit, while ensuring its full independence of Alice's noise. We formulate the specifics of our protocol in terms of a generic two-level quantum system, subjected to a general non-Markovian spin-boson model for dephasing noise. The proposed scheme is illustrated by using any pure maximally/non-maximally entangled state as well as a Werner-type mixed state as resource. In particular, using resource states having small values of entanglement measure, we show that the high fidelity of QT is achievable in the presence of noise. Further, using our scheme, considering even the local regime of Werner states, wherein the Bell-CHSH inequalities are not violated, we show that the QT fidelity in the presence of noise can be appreciably high.
Two simple schemes for probabilistic teleportation of an arbitrary unknown two-particle state using a non-maximally entangled EPR pair and a non-maximally entangled GHZ state as quantum channels are proposed. After receiving Alice's Bell state measurement results, Bob performs a collective unitary transformation on his inherent particles without introducing the auxiliary qubit. The original state can be probabilistically teleported. Meanwhile, quantum circuits for realization of successful teleportation are also presented.