arXiv subjects

Tianshi Yu

Publications and source records attributed to Tianshi Yu.

9 recordsLinked to original sources

arXiv2026

No-Go Theorems for Quantum Transport Metrics from Fixed Cost Operators

Coupling-based quantum optimal transport generalizes classical optimal transport by representing transport plans as bipartite states with prescribed marginals and evaluating their cost as the expectation of a fixed Hermitian operator. Friedland et al. [Phys. Rev. Lett. 129, 110402 (2022)] conjectured that the square root of the optimal cost associated with the SWAP projector is a metric in every dimension and that this property persists for nearby quantum cost matrices. Miller [arXiv:2607.07764] disproved both conjectures by constructing explicit diagonal qutrit counterexamples. Building on his analysis, we prove a uniform no-go theorem for standard couplings. In every dimension $d\geq3$, no fixed cost operator makes either the optimal cost or its square root a metric, with violations occurring already among commuting states. The obstruction persists under stabilization of the SWAP cost. For channel-induced couplings, global nonnegativity and vanishing self-cost force the cost operator to be zero, precluding point separation when $d\geq2$. Taken together, these no-go results show that fixed-cost coupling formulations do not lead to metrics on the full quantum state space.

quant-ph↗

arXiv2026

Reasoning about Continuous-Variable Quantum Systems

Continuous-variable quantum computing (CVQC) is a computing paradigm in which measurements yield values over a continuous domain. CVQC is both a convenient omputational framework for modeling physical quantum systems, and a good abstraction for hardware platforms based on quantum optics. Yet, the semantic foundations of CVQC remain underdeveloped. To address this gap, we develop a formal semantics for a core CV quantum programming language, and sound verification methods for program correctness. A main contribution of this work is to isolate a well-behaved quantitative predicate domain that achieves sufficient expressiveness to accommodate unbounded values as they arise in the infinite-dimensional, continuous setting. Specifically, we choose closed positive quadratic forms as semantic predicates, representing finite expectations, domains of finiteness, and infinite penalties in one ordered object. We validate our choice by establishing that our semantic predicates satisfy desirable closure properties including the definition of weakest preconditions. We validate our design with two case studies, including an example based on the celebrated GKP error-correcting code, for which we establish a second moment bound.

cs.LO↗

arXiv2025

Complete Relational Logic for Infinite-Dimensional Quantum Programs with Unbounded Assertions

We present sound and complete relational program logics for infinite-dimensional quantum and classical-quantum programs. The logics model assertions as self-adjoint unbounded linear relations, which simultaneously support quantitative and qualitative reasoning. Our main theoretical results include new convergence theorems and infinite-dimensional duality theorems for infinite-dimensional quantum states, which we use to establish completeness.

quant-ph↗

arXiv2025

Assessing the Ship Motion Prediction Capabilities of the Open-Source Model NEMOH Against Field Observations

Accurate ship motion prediction is critical for safe and efficient maritime operations, particularly in open ocean environments. This study evaluates the capability of NEMOH, an open-source potential flow boundary element solver, as an example of a ship motion prediction tool for real-world open ocean conditions. A linear model, known as the Response Amplitude Operator (RAO), is obtained using NEMOH, and is combined with the wave directional spectrum derived from the WaMoS-II marine radar on the research vessel Akademik Tryoshnikov during the Antarctic Circumnavigation Expedition (ACE) to predict ship motion responses in the frequency domain. Predictions of heave, pitch and roll are benchmarked against concurrent ship motion observations recorded by an onboard inertial measurement unit (IMU). The comparisons, based on the zeroth order moment of the ship motion spectrum, demonstrate a reliable heave prediction (Pearson correlation coefficient r=0.89, scatter index SI=0.41), a reasonable pitch prediction (r=0.80, SI=0.47), and an acceptable roll prediction (r=0.63, SI=0.84). More significant discrepancies for pitch and roll are identified under specific extreme sea conditions. The results demonstrate the capability of NEMOH, offering insights into its applicability for real-world maritime operations.

physics.flu-dyn↗

arXiv2025

A Noncommutative Nullstellensatz for Perfect Two-Answer Quantum Nonlocal Games

This paper introduces a noncommutative version of the Nullstellensatz, motivated by the study of quantum nonlocal games. It has been proved that a two-answer nonlocal game with a perfect quantum strategy also admits a perfect classical strategy. We generalize this result to the infinite-dimensional case, showing that a two-answer game with a perfect commuting operator strategy also admits a perfect classical strategy. This result induces a special case of noncommutative Nullstellensatz.

quant-ph↗

arXiv2024

Perfect Quantum Approximate Strategies for Imitation Games

We prove that an imitation game has a perfect quantum approximate strategy if and only if there exists a bi-tracial state on the minimal tensor product of two universal C${^*}$-algebras, which induces the perfect correlation. Moreover, we are trying to relate imitation games to the minimal tensor product of two universal C${^*}$-algebras and demonstrate that an imitation game has a perfect quantum approximate strategy if and only if there exist a von Neumann algebra and an amenable tracial state on it, such that the perfect correlation can be induced by the tracial state. However, We encountered some difficulties regarding continuity in the proof process. In section 2 we get some results for special cases, and in section 3 we list our problems.

math.OA↗

arXiv2023

Data-Driven Goal Recognition in Transhumeral Prostheses Using Process Mining Techniques

A transhumeral prosthesis restores missing anatomical segments below the shoulder, including the hand. Active prostheses utilize real-valued, continuous sensor data to recognize patient target poses, or goals, and proactively move the artificial limb. Previous studies have examined how well the data collected in stationary poses, without considering the time steps, can help discriminate the goals. In this case study paper, we focus on using time series data from surface electromyography electrodes and kinematic sensors to sequentially recognize patients' goals. Our approach involves transforming the data into discrete events and training an existing process mining-based goal recognition system. Results from data collected in a virtual reality setting with ten subjects demonstrate the effectiveness of our proposed goal recognition approach, which achieves significantly better precision and recall than the state-of-the-art machine learning techniques and is less confident when wrong, which is beneficial when approximating smoother movements of prostheses.

cs.RO↗

arXiv2023

A Characterization of Perfect Strategies for Mirror Games

We associate mirror games with the universal game algebra and use the *-representation to describe quantum commuting operator strategies. We provide an algebraic characterization of whether or not a mirror game has perfect commuting operator strategies. This new characterization uses a smaller algebra introduced by Paulsen and others for synchronous games and the noncommutative Nullstellensatz developed by Cimpric, Helton and collaborators. An algorithm based on noncommutative Gr\"obner basis computation and semidefinite programming is given for certifying that a given mirror game has no perfect commuting operator strategies.

math.OA↗

arXiv2020

The Use of Implicit Human Motor Behaviour in the Online Personalisation of Prosthetic Interfaces

In previous work, the authors proposed a data-driven optimisation algorithm for the personalisation of human-prosthetic interfaces, demonstrating the possibility of adapting prosthesis behaviour to its user while the user performs tasks with it. This method requires that the human and the prosthesis personalisation algorithm have same pre-defined objective function. This was previously ensured by providing the human with explicit feedback on what the objective function is. However, constantly displaying this information to the prosthesis user is impractical. Moreover, the method utilised task information in the objective function which may not be available from the wearable sensors typically used in prosthetic applications. In this work, the previous approach is extended to use a prosthesis objective function based on implicit human motor behaviour, which represents able-bodied human motor control and is measureable using wearable sensors. The approach is tested in a hardware implementation of the personalisation algorithm on a prosthetic elbow, where the prosthetic objective function is a function of upper-body compensation, and is measured using wearable IMUs. Experimental results on able-bodied subjects using a supernumerary prosthetic elbow mounted on an elbow orthosis suggest that it is possible to use a prosthesis objective function which is implicit in human behaviour to achieve collaboration without providing explicit feedback to the human, motivating further studies.

cs.RO↗