Quantum Reliability Boosted by New Certification Method Needing Fewer Trusted Components

Researchers are increasingly focused on verifying the reliability of quantum communication protocols, and certifying high-dimensional quantum channels represents a crucial step in this process. Mengyan Li, Yanning Jia from Beijing University of Posts and Telecommunications, and Fenzhuo Guo, et al. present a novel semi-device-independent framework that certifies channel properties directly from experimental data, relaxing the need for fully trusted internal devices. This work is significant because it leverages the Choi-Jamiołkowski isomorphism and incorporates structural constraints to rigorously assess channel characteristics, initially certifying entanglement dimensionality via a newly introduced witness and subsequently quantifying entanglement fidelity using semidefinite programming. By reproducing established benchmarks and successfully applying the method to common noise channels, the authors demonstrate a robust and practical approach to channel certification. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Researchers propose a semi-device-independent framework for certifying channel properties directly from observed statistics, assuming only that the system dimension is known. By explicitly incorporating the full set of structural constraints inherent to Choi states, their approach advances the field. Certifying entanglement dimensionality and fidelity via Choi-Jamiołkowski isomorphism and semidefinite programming Scientists exploit the Choi-Jamio lkowski isomorphism for rigorous certification of quantum channels. The entanglement dimensionality of quantum channels is first certified by introducing a witness and numerically determining its Schmidt-number-dependent bounds. This certification method reproduces known analytical benchmarks and is applied to dephasing and depolarizing noise channels, thereby confirming its validity. To provide a more complete assessment of channel performance, the entanglement fidelity of quantum channels is also certified using a hierarchy of semidefinite programming relaxations based on localizing matrices. Lower bounds on the entanglement fidelity are obtained that are compatible with either the full set of observed statistics or a single witness value. Quantum communication is a central pillar of quantum information science, enabling fundamentally new modes of information transfer that surpass classical limits in security, efficiency, and functionality. In practice, quantum communication tasks are implemented through specific protocols, each relying on the physical process governing the transmission of quantum states from a sender to a receiver, typically in the presence of noise and environmental interactions. Such processes are mathematically described by quantum channels, which represent the most general evolutions permitted by quantum mechanics for open quantum systems. Understanding and assessing these channels is therefore essential for evaluating the performance and fundamental limits of quantum communication protocols. Traditionally, quantum channels have been characterised using quantum process tomography, which aims to fully reconstruct the channel’s process matrix from tomographic data. Although powerful in principle, quantum process tomography suffers from exponential resource scaling with system dimension and requires precise control and trust in all internal devices. To overcome these limitations, measurement-device-independent and device-independent certification schemes have been developed. In measurement-device-independent schemes, quantum channels are certified while relaxing assumptions about the measurement devices, whereas in device-independent schemes, channel properties are inferred solely from Bell-like correlations, removing assumptions about all internal device structures. Experimental demonstrations on several physical platforms have confirmed the practical feasibility of these schemes. To date, the above measurement-device-independent and device-independent schemes are mainly focused on qubit systems. High-dimensional quantum systems have advantages in enhancing communication capacity, increasing noise resilience, and enabling more complex information processing tasks. Recent efforts have begun to extend channel certification schemes beyond qubit systems. In this direction, Mallick et al. introduced methods based on moments of generalised positive maps to certify the entanglement dimensionality, as quantified by Schmidt number, of quantum channels. More recently, another study proposed entanglement dimensionality witnesses to estimate the minimal entanglement dimensionality preserved during transmission. While both works establish an important foundation for high-dimensional channel certification via the Choi-Jamio lkowski isomorphism, which maps a quantum channel to an associated bipartite state commonly referred to as the Choi state, they do not explicitly incorporate the partial-trace constraint intrinsic to Choi states. As a consequence, the certifiable entanglement dimensionality may not be stringent enough. Furthermore, these schemes rely on fully trusted internal devices, which limits their practical applicability in quantum communication tasks. In this work, researchers certify high-dimensional quantum channels in a semi-device-independent scenario, where only the system dimension d is assumed to be known, while all other aspects of the preparation and measurement devices are left unspecified. Channel properties are inferred directly from the observed prepare-and-measure statistics, and the partial-trace constraint intrinsic to Choi states is explicitly enforced to ensure consistency with a valid quantum channel description. Within this framework, they first certify the entanglement dimensionality of quantum channels by introducing a witness inspired by the average success probability of quantum random access codes. Through numerical optimisation over Choi states that explicitly incorporate both structural and Schmidt number constraints, they derive Schmidt-number-dependent bounds for this witness, which recover known analytical benchmarks from a previous study in specific cases. They further apply their method to dephasing and depolarizing noise channels, thereby establishing a direct relation between noise parameters and certifiable entanglement dimensionality. Nevertheless, entanglement dimensionality alone does not provide a complete description of channel performance. In particular, even when two channels share the same entanglement dimensionality, the strength of the entanglement they preserve may differ substantially. To capture this aspect, they go beyond entanglement dimensionality and develop a method for certifying entanglement fidelity directly from observed statistics. To this end, they construct a hierarchy of semidefinite programming relaxations based on localizing matrices, which provide systematic lower bounds on the entanglement fidelity compatible with the full set of observed statistics. Finally, they show that the entanglement fidelity can also be certified by incorporating the observed witness value as a constraint within the semidefinite programming hierarchy. Researchers consider the semi-device-independent prepare-and-measure scenario involving two parties, A and B, who are connected only through a quantum channel. Generally, A prepares states denoted by ρx, where x = (x1, . , xn) with xi ∈[d] := {1, 2, . , d}. B performs measurements described by positive operator valued measure elements Mb|y, with y ∈[n] and b ∈[d], satisfying Mb|y ⪰0 and P b Mb|y = IB. The conditional probability distribution observed in the experiment is therefore P(b|x, y) = Tr Λ(ρx)Mb|y, where Λ denotes the quantum channel from A to B. Let Md represent the set of complex matrices of dimension d×d. A quantum channel is a linear map Λ: Md 7→Md that is completely positive and trace preserving. Complete positivity requires that (idk ⊗Λ)(X) ⪰0 for all k ∈N and all positive semidefinite operators X, where idk denotes the identity map acting on Mk. This condition guarantees that Λ preserves positivity when acting on a subsystem of an arbitrary larger composite system. Trace preservation further requires that Tr[Λ(ρ)] = Tr[ρ] for all density operators ρ. For the certification of quantum channels, it is often convenient to employ the Choi-Jamio lkowski isomorphism, which maps a channel Λ to its associated Choi state ΦΛ = (id ⊗Λ) |Φ+ d ⟩⟨Φ+ d |, where |Φ+ d ⟩= (1/ √ d) Pd i=1 |i, i⟩is a d-dimensional maximally entangled state. The map Λ 7→ΦΛ is linear and injective, and its image is fully characterised by simple structural constraints. First, ΦΛ ⪰0, TrB(ΦΛ) = IA/d, ρx ⪰0, Tr(ρx) = 1, Mb|y ⪰0, X b Mb|y = IB, where the transpose on ρx is omitted for notational simplicity, which does not affect the Results since the state preparation device is treated as unspecified. Moreover, Sr denotes the set of bipartite states with Schmidt number at most r, namely Sr:= {σAB: SN(σAB) ≤r}. The ASP compatible with channels of Schmidt number at most r is upper bounded by βQ n,d,r. Consequently, if the experimentally observed ASP violates this bound, i.e. , αn,d βQ n,d,r, then the underlying channel Λ must necessarily satisfy SN(Λ) r. Entanglement fidelity bounds for low-dimensional channels match analytical predictions Numerical bounds on the entanglement fidelity of two-dimensional channels were established for dimensions d = 3, 4, 5, and Schmidt numbers ranging from 1 to d. The research demonstrates that, for d = 3, 4, and 5, the computed bounds βQ 2,d,r coincide, to within a precision of approximately 10−8, with established analytical benchmarks βL 2,d and βQ 2,d when the Schmidt number is either 1 or equal to the channel dimension d. This agreement validates the numerical optimisation process and confirms the accurate enforcement of the Schmidt number constraints. Comparison of the computed bounds with known benchmarks reveals a tight and reliable lower bound on βQ 2,d,r, indicating the effectiveness of the methodology. Both the generalised Doherty-Parrilo-Spedalieri hierarchy and the generalised reduction map criterion yielded nearly identical numerical results across all tested cases, suggesting that both relaxations adequately capture the relevant Schmidt number constraints. The optimisation became uninformative without the partial-trace constraint, resulting in a trivial bound of 1 irrespective of the values of r and d, thereby highlighting the necessity of this condition for meaningful certification. For dimensions d = 6 and 7, the generalised reduction map criterion was adopted as the Schmidt number constraint due to computational limitations of the generalised DPS hierarchy, which becomes impractical for d 5 given standard computing resources. Illustrative examples for these higher dimensions were presented, building upon the previously established numerical results. The study considered dephasing and depolarizing channels as paradigmatic noise models, relevant to realistic experimental settings where perfect communication is not guaranteed, to assess the practical relevance of the findings. Certifying High-Dimensional Entanglement via Observed Statistics and Choi State Structure Scientists have developed a semi-device-independent framework for certifying the properties of high-dimensional quantum channels using only observed statistics and knowledge of the system dimension. This approach rigorously certifies channels by incorporating structural constraints inherent to Choi states and exploiting the Choi-Jamiołkowski isomorphism. The research introduces a witness to certify entanglement dimensionality, establishing Schmidt-number-dependent bounds that align with known analytical benchmarks when applied to dephasing and depolarizing noise channels. Furthermore, the entanglement fidelity of channels is certified through a hierarchy of semidefinite programming relaxations, yielding lower bounds based on observed statistics or a single witness value. Numerical results demonstrate that the entanglement fidelity varies continuously with observed statistics, differing from the threshold-like behaviour of entanglement dimensionality. This work extends existing methods, which typically focus on dimensionality certification and rely on fully trusted internal devices, by simultaneously certifying both dimensionality and fidelity without such assumptions. The authors acknowledge that certifying entanglement fidelity often requires higher levels within the semidefinite programming hierarchy to achieve convergence, potentially due to limitations in the hierarchy or the inherent complexity of fidelity certification. Future research may focus on refining the semidefinite programming hierarchy to improve convergence for entanglement fidelity or exploring alternative methods for its efficient certification. This advancement provides a more comprehensive assessment of channel performance, enhancing its applicability to practical quantum communication tasks by quantifying the strength of entanglement preserved by a channel, even among those with similar dimensionality. 👉 More information 🗞 Semi-device-independent certification of high-dimensional quantum channels 🧠 ArXiv: https://arxiv.org/abs/2602.07823 Tags: