The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic regime. We show that this is no longer the case when one allows stochastic protocols that may only succeed with some probability, in which case the quantum relative entropy is insufficient to characterize the rates of asymptotic state transformations, and a new entropic quantity based on a regularization of the Hilbert projective metric comes into play. Such a scenario is motivated by a setting where the cost associated with transformations of quantum states, typically taken to be the number of copies of a given state, is instead identified with the size of the quantum memory needed to realize the protocol. Our approach allows for constructing transformation protocols that achieve strictly higher rates than those imposed by the relative entropy. Focusing on the task of resource distillation, we give broadly applicable strong converse bounds on the asymptotic rates of probabilistic distillation protocols, and show them to be tight in relevant settings such as entanglement distillation with non-entangling operations. This generalizes and extends previously known limitations that only applied to deterministic protocols. Our methods are based on recent results for probabilistic one-shot transformations as well as a new asymptotic equipartition property for the projective relative entropy.
Entropic uncertainty relations play an important role in both fundamentals and applications of quantum theory. Although they have been well-investigated in quantum theory, little is known about entropic uncertainty in generalized probabilistic theories (GPTs). The current study explores two types of entropic uncertainty relations, preparation and measurement uncertainty relations, in a class of GPTs which can be considered generalizations of quantum theory. Not only a method for obtaining entropic preparation uncertainty relations but also an entropic measurement uncertainty relation similar t…
The celebrated Bell-Kochen-Specker no-go theorem asserts that quantum mechanics does not present the property of realism, the essence of the theorem is the lack of a joint probability distributions for some experiment settings. In this work, we exploit the information theoretic form of the theorem using information measure instead of probabilistic measure and indicate that quantum mechanics does not present such entropic realism neither. The entropic form of Gleason's no-disturbance principle is developed and it turns out to be characterized by the intersection of several entropic cones. Entro…
Overcoming the Matrix-Product-State Encoding Barrier via DMRG-Guided Probabilistic Imaginary-Time Evolution
Quemix Inc.（Quemix公司）；Department of Physics, The University of Tokyo（东京大学物理系）；Quantum Materials and Applications Research Center, National Institutes for Quantum Science and Technology（量子科学技术研究院量子材料与应用程序研究中心）
We introduce a modular-value two-qubit gate and explore its advantages in experimentally-limited situations. The gate is defined such that the final state of a target qubit is fully controlled by a pre- and post-selection procedure in a control qubit given an (imperfect or technically limited) intermediate conditional qubit-qubit interaction. As an example of the gate and its benefit, we make the connection to a postselected cross phase modulation scenario when a undesired absorption is present. Probabilistic amplification of a small cross phase while mitigating relative absorption is possible…
In realistic stabiliser-based quantum error correction there are many ways in which real physical systems deviate from simple toy models of error. Stabiliser measurements may not always be deterministic or may suffer from erasure errors, such that they do not supply syndrome outcomes required for error correction. In this paper, we study the performance of the toric code under a model of probabilistic stabiliser measurement. We find that, even under a completely continuous model of syndrome extraction, the threshold can be maintained at reasonably high values of $1.69\%$ by suitably modifying …
Analysing causal structures in generalised probabilistic theories
Institute for Quantum Optics and Quantum Information (IQOQI) Vienna, Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所维也纳）；Department of Mathematics, University of York（约克大学数学系）
Overcoming Dimensional Factorization Limits in Discrete Diffusion Models through Quantum Joint Distribution Learning
Faculty of Innovation Engineering, Macau University of Science and Technology（澳门科学技术大学创新工程学院）；Department of Electrical and Computer Engineering, New Jersey Institute of Technology（新泽西理工学院电气与计算机工程系）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）；School of Electronic and Information Engineering, Foshan University（佛山大学电子与信息工程学院）；College of Mathematics and Informatics, South China Agricultural University（华南农业大学数学与信息学院）
Probabilistic generation of two-mode binomial cat states using cross-Kerr interactions
Institute for Quantum Materials and Technology, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院量子材料与技术研究所）；Institute for Theory of Condensed Matter, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院凝聚态理论研究所）；Institut de Science et d’Ingénierie Supramoléculaires (ISIS, UMR7006), University of Strasbourg and CNRS（斯特拉斯堡大学与法国国家科学研究中心超分子科学与工程学院）；Nordita, KTH Royal Institute of Technology and Stockholm University（斯德哥尔摩皇家理工学院与斯德哥尔摩大学诺迪塔中心）；Department of Physics, Stockholm University（斯德哥尔摩大学物理系）
Motivated by quantum resource theories, we introduce a notion of incompatibility for quantum measurements relative to a reference basis. The notion arises by considering states diagonal in that basis and investigating whether probability distributions associated with different quantum measurements can be converted into one another by probabilistic post-processing. The induced preorder over quantum measurements is directly related to multivariate majorization and gives rise to families of monotones, i.e., scalar quantifiers that preserve the ordering. For the case of orthogonal measurement we e…
