Haidong Yuan
In this article I study the dynamics of open quantum system in Markovian environment. I give necessary and sufficient conditions for such dynamics to be majorization monotone, which are those dynamics always mixing the states.
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Williamson majorization theory of fermionic non-Gaussianity
本文建立费米子非高斯性的威廉姆森 majorization 定律，将相关量化指标转化为强单调量，推导态转换条件，且理论可在现有量子设备上验证。
Monotones and invariants for multi-particle quantum states
我们引入了新的纠缠单调，推广到多方的情况下，那些产生的基于优序的二体态纠缠的偏序。我们给出了一些限制的例子，他们施加的确定性和概率之间的转换多体状态通过本地行动和经典的通信。这些限制包括并非出于任何双边考虑的限制。我们推导出超乘法关系，每个国家的单调性和集体处理时，各方共享几个国家的单调性。我们还调查了多项式不变量下的局部酉变换，并表明，其中一大类是不变的集体酉处理和乘法，把限制，例如，一个国家的多个副本的精确转换到另一个多个副本。
Catalytic quantum thermodynamics beyond additivity and reduced-state monotones
本文提出基于非加性分歧的框架，揭示催化贡献并提供非平凡约束，证明减少态数据不足以描述热力学可及性，需联合态敏感描述。
Sequences of resource monotones from modular Hamiltonian polynomials
本文构造了两类源于模哈密顿量多项式期望值的无限纠缠与资源单调量，用于推导信息擦除功成本、熵产生及 Clausius 不等式的更严格界限，并考察临界离散理论中的优超行为。
Majorization theory for quasiprobabilities
本文针对现有优化框架无法处理取负值且定义在无限空间上的函数的问题，提出适用于拟概率分布的优化概念，推广了经典优化定理并将其应用于量子资源理论，为评估无限测度空间可积函数的无序性提供了全面框架。
Motivated by reachability questions in coherently controlled open quantum systems coupled to a thermal bath, as well as recent progress in the field of thermo-/vector-majorization we generalize classical majorization from unital quantum channels to channels with an arbitrary fixed point $D$ of full rank. Such channels preserve some Gibbs-state and thus play an important role in the resource theory of quantum thermodynamics, in particular in thermo-majorization. Based on this we investigate $D$-majorization on matrices in terms of its topological and order properties, such as existence of uniqu…
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…
We test the principle of majorization [J. I. Latorre and M. A. Martin-Delgado, Phys. Rev. A 66, 022305 (2002)] in random circuits. Three classes of circuits were considered: (i) universal, (ii) classically simulatable, and (iii) neither universal nor classically simulatable. The studied families are: {CNOT, H, T}, {CNOT, H, NOT}, {CNOT, H, S} (Clifford), matchgates, and IQP (instantaneous quantum polynomial-time). We verified that all the families of circuits satisfy on average the principle of decreasing majorization. In most cases the asymptotic state (number of gates going to infinity) beha…
The Majorization Principle is a fundamental statement governing the dynamics of information processing in optimal and efficient quantum algorithms. While quantum computation can be modeled to be reversible, due to the unitary evolution undergone by the system, these quantum algorithms are conjectured to obey a quantum arrow of time dictated by the Majorization Principle: the probability distribution associated to the outcomes gets ordered step-by-step until achieving the result of the computation. Here we report on the experimental observation of the effects of the Majorization Principle for t…
Although entropy is a necessary and sufficient quantity to characterize the order of work content for equal energetic (EE) states in the asymptotic limit, for the finite quantum systems, the relation is not so linear and requires detail investigation. Toward this, we have considered a resource theoretic framework taking the energy preserving operations (EPO) as free, to compare the amount of extractable work from two different quantum states. Under EPO, majorization becomes a necessary criterion for state transformation. It is also shown that the passive state energy is a concave function and …
For both unitary and open qubit dynamics, we compare asymmetry monotone-based bounds on the minimal time required for an initial qubit state to evolve to a final qubit state from which it is probabilistically distinguishable with fixed minimal error probability (i.e., the minimal error distinguishability time). For the case of unitary dynamics generated by a time-independent Hamiltonian, we derive a necessary and sufficient condition on two asymmetry monotones that guarantees that an arbitrary state of a two-level quantum system or a separable state of $N$ two-level quantum systems will unitar…
An analytical approach is developed to the problem of computation of monotone Riemannian metrics (e.g. Bogoliubov-Kubo-Mori, Bures, Chernoff, etc.) on the set of quantum states. The obtained expressions originate from the Morozova, Chencov and Petz correspondence of monotone metrics to operator monotone functions. The used mathematical technique provides analytical expansions in terms of the thermodynamic mean values of iterated (nested) commutators of a model Hamiltonian T with the operator S involved through the control parameter $h$. Due to the sum rules for the frequency moments of the dyn…
What can one infer about the dynamical evolution of quantum systems just by symmetry considerations? For Markovian dynamics in finite dimensions, we present a simple construction that assigns to each symmetry of the generator a family of scalar functions over quantum states that are monotonic under the time evolution. The aforementioned monotones can be utilized to identify states that are non-reachable from an initial state by the time evolution and include all constraints imposed by conserved quantities, providing a generalization of Noether's theorem for this class of dynamics. As a special…
We give sufficient conditions ensuring the strong ergodic property of unique mixing for $C^*$-dynamical systems arising from Yang-Baxter-Hecke quantisation. We discuss whether they can be applied to some important cases including monotone, Boson, Fermion and Boolean $C^*$-algebras in a unified version. The monotone and the Boolean cases are treated in full generality, the Bose/Fermi cases being already widely investigated. In fact, on one hand we show that the set of stationary stochastic processes are isomorphic to a segment in both the situations, on the other hand the Boolean processes enjo…
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