arXiv subjects

Yanning Jia

Publications and source records attributed to Yanning Jia.

6 recordsLinked to original sources

arXiv2026

Semidefinite-programming hierarchies for classically simulable state families

Identifying whether a state family admits an irreducible quantum advantage is a fundamental task in quantum resource theory and quantum information processing. Here we study classically simulable state families, namely those residing within the convex hull of pairwise commuting families and therefore admitting a classical explanation. We develop a complete semidefinite-programming (SDP) hierarchy characterizing the set of classically simulable state families in arbitrary finite dimension. The key step is to reformulate classical simulability as a feasibility problem over deterministic response functions and auxiliary positive-operator-valued measures (POVMs) simulable by rank-one projective measurements. We establish a complete SDP hierarchy for rank-one projectively simulable POVMs and transfer the resulting characterization to state families, yielding both primal feasibility tests and dual affine witnesses certifying failure of classical simulability. Applying the hierarchy to state families mixed with depolarizing noise gives computable upper bounds on the critical classical visibility, which are matched by explicit classical simulations in several symmetric examples. These results provide a systematic convex-optimization framework for certifying classical simulability of quantum state families.

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arXiv2026

Geometric Construction of Optimal Teleportation Witnesses

Not all entangled states are useful for quantum teleportation. We present a geometric method to construct optimal teleportation witnesses, which provide operational necessary and sufficient criteria for identifying the teleportation usefulness of arbitrary two-qudit entangled states. Specifically, by developing a two-layer iterative cutting-plane algorithm to solve the shortest distance problem from the target state $\rho$ to the convex set $S$ of useless states, we obtain the projection point $\sigma^* \in S$ and then construct the optimal teleportation witness from the projection geometry. Moreover, the shortest distance $D(\rho)$ obtained during this construction also serves as a necessary and sufficient criterion for usefulness. We apply our method to identify the teleportation usefulness of three classes of entangled states.

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arXiv2026

Semi-device-independent certification of high-dimensional quantum channels

Certifying high-dimensional quantum channels is essential for ensuring the reliability of quantum communication protocols. Existing certification schemes often rely on fully trusted internal devices, which is difficult to achieve in realistic scenarios. Here, we 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, our approach exploits the Choi-Jamio{\l}kowski 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.

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arXiv2025

A General Framework for Constructing Local Hidden-state Models to Determine the Steerability

Not all entangled states can exhibit quantum steering, and determining whether a given entangled state is steerable is a crucial problem in quantum information theory. The main challenge lies in verifying the existence of a local hidden-state (LHS) model capable of reproducing all post-measurement assemblages generated by arbitrary measurements. To address this, we propose a machine learning-based framework that employs batch sampling of measurements and gradient-based optimization to construct an optimal LHS model. We validate our method by analyzing the steerability of two-qubit Werner and two-qutrit isotropic states. For Werner states, our approach saturates the analytical visibility bounds under three Pauli measurements, arbitrary projective measurements (PVMs), and arbitrary positive operator-valued measurements (POVMs). For isotropic states, we achieve the known analytical bounds under arbitrary PVMs. We further investigate the steerability of this class of states under arbitrary POVMs, and our results suggest that POVMs can offer an advantage over PVMs in revealing the steerability of such states.

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arXiv2025

Measuring network quantum steerability utilizing artificial neural networks

Network quantum steering plays a pivotal role in quantum information science, enabling robust certification of quantum correlations in scenarios with asymmetric trust assumptions among network parties. The intricate nature of quantum networks, however, poses significant challenges for the detection and quantification of steering. In this work, we develop a neural network-based method for measuring network quantum steerability, which can be generalized to arbitrary quantum networks and naturally applied to standard steering scenarios. Our method provides an effective framework for steerability analysis, demonstrating remarkable accuracy and efficiency in standard bipartite and multipartite steering scenarios. Numerical simulations involving isotropic states and noisy GHZ states yield results that are consistent with established findings in these respective scenarios. Furthermore, we demonstrate its utility in the bilocal network steering scenario, where an untrusted central party shares two-qubit isotropic states of different visibilities, $\nu$ and $\omega$, with trusted endpoint parties and performs a single Bell state measurement. Through explicit construction of a network local hidden state model derived from numerical results and incorporation of the entanglement properties of network assemblages, we analytically demonstrate that the network steering thresholds are determined by the curve $\nu \omega = {1}/{3}$ under the corresponding configuration.

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arXiv2024

Characterizing the set of quantum correlations in prepare-and-measure quantum chain-shaped networks

We introduce a hierarchy of tests satisfied by any probability distribution $P$ that represents the quantum correlations generated in prepare-and-measure (P\&M) quantum chain-shaped networks, assuming only the inner-product information of the non-orthogonal quantum states. The P\&M quantum chain-shaped networks involve multiple measurement parties, each measurement party potentially having multiple sequential receivers. Specifically, we adapt the original NPA-hierarchy by incorporating a finite number of linear and positive semi-definite constraints to characterize the quantum correlations in P\&M quantum chain-shaped networks. These constraints in each hierarchy are derived from sequential measurement operators and the inner-product matrix of the non-orthogonal quantum states. We apply the adapted NPA-hierarchy to tackle some quantum information tasks, including sequential quantum random access codes (QRACs) and randomness certification. First, we derive the optimal trade-off between the two sequential receivers in the $2 \to 1$ sequential QRACs. Furthermore, we have investigated semi-device-independent randomness certification in the double violation region of $2 \to 1$ sequential QRACs. Second, considering the presence of eavesdropper (Eve) in actual communication, we show how much global and local randomness can be certified using the optimal trade-off of $2 \to 1$ sequential QRACs. Additionally, we quantify the amount of local and global randomness that can be certified from the complete probabilities generated by the two sequential receivers. We conclude that utilizing the complete set of probabilities certifies more local and global randomness than relying solely on the optimal trade-off relationship.

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