Preparing remote states for genuine quantum networks

Quantum networks are complex systems comprising quantum channels, repeaters, and end nodes. Remote state preparation (RSP) offers a unique advantage within these networks: it allows a sender (Alice) to remotely prepare the state of a receiver's (Bob's) qubit. This is particularly useful when Bob lacks the capability to implement a desired target operator locally. RSP provides advantages over quantum teleportation, which requires Bell-state measurements to transmit an unknown qubit, whereas RSP only necessitates local measurements on Alice's particle. This efficiency makes RSP highly suitable for various quantum networking applications. RSP finds utility in creating deterministic single-photon states, preparing single-photon hybrid entanglement, and initializing atomic quantum memory for quantum communication. It plays a crucial role in quantum memory applications, such as memory-assisted measurement-device-independent quantum key distribution and space-borne quantum memories for global quantum networking. Furthermore, RSP is vital in client-server blind quantum computation and is intrinsically linked to measurement-based quantum information processes like one-way quantum computing and entanglement-enabled networks. One-way quantum computing uses measurements on a highly entangled cluster state to produce computational results, while entanglement-enabled networks extend this functionality for complex networking tasks. Given the inherent noise and imperfections in experimental RSP implementations, determining whether a practical RSP in a quantum network truly surpasses any classical approach is of paramount importance. A genuine quantum network, as defined in this paper, possesses quantum functionality for preparing and transmitting quantum information that transcends classical predictions. Existing verification methods relying on quantum discord or RSP benchmarks fall short; they are based on theoretical assumptions that don't always hold in practice, where classical physics may account for experimental imperfections. This necessitates a new approach for confirming truly quantum RSP implementations.

The paper extensively reviews the existing literature on remote state preparation (RSP), highlighting its role in various quantum information processing tasks and quantum networking applications. It emphasizes the limitations of using quantum discord as a sufficient criterion for identifying genuinely quantum RSP implementations due to the inability of existing methods to account for noise and imperfections in practical scenarios. The authors cite several key papers demonstrating RSP's applications in quantum memory initialization, quantum key distribution, and blind quantum computation. This literature review establishes the need for a new method that can definitively determine the quantum advantage offered by RSP in practical implementations within quantum networks.

The core of the methodology lies in the introduction and experimental validation of a novel quantum resource termed 'RSP capability.' This resource assesses the quantum advantage of remote state preparation (RSP) in networks by considering both static and dynamic resources. The researchers developed a general classical RSP model that operates without Einstein-Podolsky-Rosen (EPR) entangled pairs or qubit unitaries. This model serves as a benchmark against which the quantum performance of the RSP process can be compared. The experimental setup uses a bidirectionally pumped down-conversion source within a polarization Sagnac interferometer (PSI) to generate polarization-entangled photon pairs. These pairs serve as the foundation for the RSP protocol. The researchers meticulously detail the implementation of the RSP protocol, including Alice's operations (applying a unitary transformation U and performing a measurement) and Bob's potential correction operations based on Alice's measurement results. They also considered a heralded version of the RSP where Bob's correction is not always necessary. To quantify the RSP process, the researchers employ the quantum operations formalism, representing the processes through experimentally measurable process matrices. These matrices capture the effects of the entire hardware and resources involved. The classical RSP model is used to create a corresponding classical process matrix. The difference between the experimental process matrix and the best possible classical process matrix reveals whether the RSP process exhibits quantum advantages. Three criteria are established to quantify RSP capability: 1. **RSP Composition (α):** Quantifies the proportion of a classical process within an experimental process. A higher α indicates a stronger classical component. 2. **RSP Robustness (β):** Measures the minimum amount of noise required to render an experimental process classical. A higher β value indicates more robustness to noise. 3. **Average-State-Fidelity Criterion:** Compares the average state fidelity of the experimental RSP to the maximum achievable fidelity using classical methods. A fidelity above the classical limit signifies a quantum advantage. These criteria are formulated as semidefinite programming (SDP) problems, which are solved numerically to obtain the RSP capability. The experimental demonstration utilizes high-fidelity EPR-pair sources, and the researchers carefully account for experimental imperfections and noise. They analyze RSP capability under different conditions, including noise contamination via both incoherent mixtures and Werner states, providing a comprehensive assessment of the quantum resource.

The key findings of this research revolve around the introduction and experimental validation of 'RSP capability' as a crucial resource for demonstrating the quantum advantage of remote state preparation (RSP) in quantum networks. This work provides strong evidence refuting the sufficiency of existing methods and metrics, such as quantum discord, in characterizing genuinely quantum RSP processes. The experimental results demonstrate a clear transition between classical and nonclassical RSP behavior based on the quality of the entangled photon pairs. High-fidelity entangled photon pairs display significant RSP capability, satisfying the three defined criteria for nonclassicality (high RSP composition α, high RSP robustness β, and average state fidelity exceeding the classical limit). However, when noise is introduced, either through incoherent mixing or using Werner states, the RSP capability diminishes. Significantly, the study finds that even when the entangled photon pairs exhibit quantum discord (a measure of quantum correlations), the corresponding RSP process may still be perfectly emulated by the classical model, highlighting the inadequacy of quantum discord as a sole indicator of quantum advantage in RSP. The researchers present experimental measurements of the RSP capability (α, β, and average state fidelity) for various photon pair states under different noise conditions. These results strongly support their theoretical framework and demonstrate that RSP capability, not quantum discord, is the decisive factor in distinguishing genuinely quantum RSP processes from their classical counterparts. The quantitative analysis using process matrices, together with the SDP optimization, offers a rigorous approach to determine the quantum advantage of RSP in various scenarios. The experimental demonstration emphasizes the importance of considering both static and dynamic resources (e.g., EPR pairs, quantum channels, and correction operations) for accurately evaluating RSP performance. The high consistency between theoretical predictions and experimental findings strengthens the reliability and validity of the proposed RSP capability metric.

The findings of this research significantly advance the understanding and characterization of remote state preparation (RSP) in quantum networks. The introduction of the RSP capability metric addresses a critical gap in the field, providing a more comprehensive and experimentally accessible method for evaluating the quantum advantage of RSP over classical methods. The experimental validation strongly supports the theoretical framework, showing a clear correlation between photon pair quality, noise levels, and the presence of RSP capability. The demonstration that quantum discord is insufficient to guarantee nonclassical RSP underscores the importance of moving beyond simple correlation measures to accurately quantify quantum resources in complex networked scenarios. The study's rigorous methodology, using process matrices and semidefinite programming, enhances the reliability and precision of the RSP capability assessment. The research's impact extends beyond RSP, suggesting potential applications in characterizing other measurement-based quantum information processing techniques.

This paper introduces RSP capability, a novel quantum resource essential for genuine quantum networks utilizing RSP. It demonstrates that RSP capability, unlike quantum discord, accurately distinguishes nonclassical RSP from classical emulation, even considering experimental imperfections and noise. Experimental results using entangled photon pairs confirm this, showing that achieving nonclassical RSP is crucial for applications where classical simulations are unacceptable. Future work could explore the implications of RSP capability in various quantum networking applications, particularly those involving quantum memory and quantum key distribution, exploring trade-offs between performance metrics like link availability, range, and loss.

While the experimental setup demonstrates the effectiveness of the proposed method, several limitations exist. The experiments focus on a specific type of entangled photon pair source and RSP implementation. Extending the findings to other quantum systems, different types of entanglement, and more complex network topologies would further strengthen the generality of the RSP capability metric. The computational complexity of the semidefinite programming used to calculate RSP capability might pose a challenge for larger, more complex quantum networks. Furthermore, the classical model used for comparison assumes a specific type of classical strategy, and other classical strategies might yield different results.