Quantum teleportation should surpass maximum fidelity thresholds possible with local measurements and classical communications. Benchmarks have been established when states are drawn from a uniform distribution of qubits or coherent states of harmonic oscillators. These are not applicable when there is prior knowledge about the input that skews the distribution. We determine the highest mean fidelity achievable for teleportation of states without using entanglement but drawn from a non-uniform prior distribution, specifically a von Mises - Fisher distribution. Using Bayesian methods, we derive benchmark functions for single qubit teleportation that utilize projective measurement on specific axes on the Bloch sphere. We demonstrate that similar results can be achieved with a coherent spin positive operator-valued measure (POVM), based upon heterodyne detection. These methods are then used to derive corresponding benchmarks for teleporting multi-qubit systems that we model as spin coherent states, covering the full range of particle number $N\in [1, \infty)$. The results show that fidelity thresholds to declare quantum advantage can be significantly higher than is typically assumed with uniform distribution.
Quantum teleportation should surpass maximum fidelity thresholds possible with local measurements and classical communications. Benchmarks have been established when states are drawn from a uniform distribution of qubits or coherent states of harmonic oscillators. These are not applicable when there is prior knowledge about the input that skews the distribution. We determine the highest mean fidelity achievable for teleportation of states without using entanglement but drawn from a non-uniform prior distribution, specifically a von Mises - Fisher distribution. Using Bayesian methods, we derive benchmark functions for single qubit teleportation that utilize projective measurement on specific axes on the Bloch sphere. We demonstrate that similar results can be achieved with a coherent spin positive operator-valued measure (POVM), based upon heterodyne detection. These methods are then used to derive corresponding benchmarks for teleporting multi-qubit systems that we model as spin coherent states, covering the full range of particle number N∈[1,∞). The results show that fidelity thresholds to declare quantum advantage can be significantly higher than is typically assumed with uniform distribution.
In this work, we introduce a comprehensive statistical framework for assessing single-qubit quantum teleportation performance beyond the conventional average-fidelity benchmark. At first, we derive a closed-form expression for the full probability density function of actual teleportation fidelities and apply it to both classical measure-and-prepare schemes and standard quantum teleportation, considering two relevant noise models: Bell-diagonal resource states and local amplitude-damping channels. These results reveal that protocols with identical average fidelities can exhibit markedly different statistical behaviors, and that relying solely on average fidelity can mask inherent asymmetries introduced by local noise, potentially leading to spurious conclusions of symmetry. Secondly, we introduce a certification method based on prior importance functions (e.g., Beta distributions), which unifies moment-based criteria and threshold-based success probabilities into a single figure of merit. Applying this framework, we show that certifying high-fidelity teleportation requires increasingly stronger entanglement or non-locality, and we clarify that the so-called ``fighting noise with noise'' effect arises from the chosen prior importance function rather than representing a genuine advantage. Our approach thus provides versatile tools for tailored, application-specific teleportation benchmarks.
Prior information about an input state can be utilized to enhance the efficiency of quantum teleportation, which we quantify using the first two moments of fidelity. The input knowledge is introduced by relaxing the uniformity assumption in the distribution of the input state and considering nonuniform distributions, namely, the polar cap and von Mises--Fisher densities. For these distributions, we show that the average fidelity increases depending on the shared resource state between the sender and the receiver, while the deviation decreases with the increase of information content about the input ensemble, thereby establishing its role as a resource. Our comparative study between these two distributions reveals that for the same amount of information content about inputs, although the average fidelity yield is the same for both, the polar cap distribution is better as it offers a smaller deviation. Moreover, we contrast the resource of prior information with other resources involved in the protocol such as shared entanglement and classical communication. Specifically, we observe that unlike a uniform distribution, the amount of classical communication required to fulfill the task decreases with the increase of information available for inputs. We also investigate the role of prior information in higher- (three-)dimensional teleportation and report the characteristics of the dimensional advantage in prior information-based teleportation.
Quantum technology promises revolutionary advantages in information processing and transmission compared to classical technology; however, determining which specific resources are needed to surpass the capabilities of classical machines often remains a nontrivial problem. To address such a problem, one first needs to establish the best classical solutions, which set benchmarks that must be beaten by any implementation claiming to harness quantum features for an enhanced performance. Here we introduce and develop a self-contained formalism to obtain the ultimate, generally probabilistic benchmarks for quantum information protocols including teleportation and approximate cloning, with arbitrary ensembles of input states generated by a group action, so-called Gilmore-Perelomov coherent states. This allows us to construct explicit fidelity thresholds for the transmission of multimode Gaussian and non-Gaussian states of continuous-variable systems, as well as qubit and qudit pure states drawn according to nonuniform distributions on the Bloch hypersphere, which accurately model the current laboratory facilities. The performance of deterministic classical procedures such as square-root measurement strategies is further compared with the optimal probabilistic benchmarks, and the state-of-the-art performance of experimental quantum implementations against our newly derived thresholds is discussed. This work provides a comprehensive collection of directly useful criteria for the reliable certification of quantum communication technologies.
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.
We investigate whether it is possible to teleport the coherence of an unknown quantum state from Alice to Bob by communicating a smaller number of classical bits in comparison to what is required for teleporting an unknown quantum state. We find that we cannot achieve perfect teleportation of coherence with one bit of classical communication for an arbitrary qubit. However, we find that if the qubit is partially known, i.e., chosen from the equatorial and polar circles of the Bloch sphere, then teleportation of coherence is possible with the transfer of one cbit of information when we have maximally entangled states as a shared resource. In the case of the resource being a nonmaximally entangled state, we can teleport the coherence with a certain probability of success. In a general teleportation protocol for coherence, we derive a compact formula for the final state at Bob's laboratory in terms of the composition of the completely positive maps corresponding to the shared resource state and a joint positive operator-valued measure (POVM) performed by Alice on her qubit and the unknown state. Using this formula, we show that teleportation of the coherence of a partially known state with real matrix elements is perfectly possible with the help of a maximally entangled state as a resource. Furthermore, we explore the teleportation of coherence with Werner states and show that even when Werner states become separable, the amount of teleported coherence is nonzero, implying the possibility of teleportation of coherence without entanglement.
We investigate quantum teleportation through dissipative channels and calculate teleportation fidelity as a function of damping rates. It is found that the average fidelity of teleportation and the range of states to be teleported depend on the type and rate of the damping in the channel. Using the fully entangled fraction, we derive two bounds on the damping rates of the channels: one is to beat the classical limit and the second is to guarantee the nonexistence of any other copy with better fidelity. The effect of the initially distributed maximally entangled state on the process is presented; the concurrence and the fully entangled fraction of the shared states are discussed. We intend to show that prior information on the dissipative channel and the range of qubit states to be teleported is helpful for the evaluation of the success of teleportation, where success is defined as surpassing the fidelity limit imposed by the fidelity of the 1-to-2 optimal cloning machine for the specific range of qubits.