We investigate the decoherence dynamics of a hydrogen atom interacting with a thermal environment through momentum–momentum coupling within the quantum Brownian motion (QBM) framework. Unlike the conventional position coupling paradigm, we consider a bilinear interaction Hamiltonian in which the radial momentum of the hydrogen atom couples to the momenta of environmental oscillators. Using the Born–Markov approximation, we derive a master equation for the reduced density operator of the hydrogen atom. The radial dynamics are treated algebraically using ladder operators, allowing us to obtain a closed-form expression for the time evolution of the momentum operator in the interaction picture. We compute the environment induced decoherence coefficient in terms of the environmental spectral density and a characteristic hydrogenic frequency. For a Lorentz–Drude spectral density, we analyze how decoherence rate varies with the hydrogen atom principal and angular momentum quantum numbers. Our results show that decoherence is strongest for low-[Formula: see text], low-[Formula: see text] states, while it is significantly reduced for Rydberg and high angular momentum states due to their narrow radial momentum distributions. This reduction reflects a relative robustness of highly excited hydrogenic states against environmental noise, which is relevant for applications relying on long atomic coherence times.
In classical information theory, the most important theorems are the cod-ing theorems, which were discussed by calculating the mean entropy and the mean mu-tual entropy defined by the classical dynamical entropy (Kolmogorov-Sinai). The quan-tum dynamical entropy was first studied by Emch [13] and Connes-Stormer [11]. Afterthat, several approaches for introducing the quantum dynamical entropy were proposed[10, 3, 8, 39, 15, 44, 9, 27, 28, 2, 19, 45]. The efficiency of information transmission for thequantum processes is investigated by using the von Neumann entropy [22] and the Ohyamutual entropy [24]. These entropies were extended to S-mixing entropy by Ohya [26, 27] ingeneral quantum systems. The mean entropy and the mean mutual entropy for the quantumdynamical systems were introduced based on the S-mixing entropy. In this paper, basedon research into the dynamical entropy and mean mutual entropy of quantum systems,this study investigates the characteristics of quantum channels that exhibit entanglement,a property unique to quantum systems, and investigates the behaviour of quantum entropyfor compound quantum channels by changing the perspective from information transmis-sion between input and output to a new perspective of information transmission from theinitial state to the final state.
The requirement of complete positivity is very often regarded as a fundamental consistency condition for the description of open quantum dynamics. We critically examine this requirement and discuss both its physical motivations and its limitations. We analyse proposals based on restricting the domain of non-completely positive maps to subsets of compatible initial states. Using isotropic states as a concrete example, we show that such domain restrictions become increasingly severe with growing system dimension, revealing an intrinsic weakness of the compatibility-based approach.
Quantum indistinguishability of non-orthogonal quantum states is a valuable resource in quantum information applications such as cryptography and randomness generation. In this article, we present a sequential state-discrimination scheme that enables multiple parties to share quantum uncertainty, in terms of the max relative entropy, generated by a single party. Our scheme is based upon maximum-confidence measurements and takes advantages of weak measurements to allow a number of parties to perform state discrimination on a single quantum system. We review known sequential state discrimination and show how our scheme would work through a number of examples where ensembles may or may not contain symmetries. Our results will have a role to play in understanding the ultimate limits of sequential information extraction and guide the development of quantum resource sharing in sequential settings.
Self-testing constitutes one of the most powerful forms of device certification, enabling a complete and device-independent characterization of a quantum apparatus solely from the observed correlations. In a recent work by the authors [23], a general framework was introduced for constructing Bell inequalities that self-test entire families of Clifford generators. In this manuscript, we develop an alternative and complementary self-testing criterion based on symmetric spanning sets. This formulation provides an explicit and constructive route to designing self-testing Bell inequalities in arbitrary dimensions.
The partial transpose map is a linear map widely used quantum information theory. We study the equality condition for a matrix inequality generated by partial transpose, namely (∑^K_j=1 A_j^T ⊗ B_j)≤ K ·(∑^K_j=1 A_j ⊗ B_j), where A_j's and B_j's are respectively the matrices of the same size, and K is the Schmidt rank. We explicitly construct the condition when A_i's are column or row vectors, or 2× 2 matrices. For the case where the Schmidt rank equals the dimension of A_j, we extend the results from 2× 2 matrices to square matrices, and further to rectangular matrices. In detail, we show that ∑^K_j=1 A_j ⊗ B_j is locally equivalent to an elegant block-diagonal form consisting solely of identity and zero matrices. We also study the general case for K=2, and it turns out that the key is to characterize the expression of matrices A_j's and B_j's.
Stochastic unravelings are a widely used tool to solve open quantum system dynamics, in which the exact solution is obtained via an average over a stochastic process on the set of pure quantum states. Recently, the generalized rate operator unraveling formalism was derived, allowing not only for an engineering of the stochastic realizations, but also to unravel without reverse jumps even for some dynamics in which P-divisibility is violated, thus hugely improving the simulation efficiency. This is possible because the unraveling depend on an arbitrary non-linear transformation which can incorporate the memory effects. In this work, a stochastic Schrödinger equation for this formalism is derived, both for cases with and without reverse jumps. It is also shown that a failure of this method can be used to witness master equations leading unphysical time evolutions, independently on the particular non-linear transformation considered.
This paper introduces a symmetric group dynamics on quantum Markov chains on Cayley trees (QMCCT). By applying symmetric group actions, we establish a novel algebraic perspective that enables the systematic study of local correlation functions in QMCCT. This approach provides a powerful tool for investigating phase transitions and characterizing ergodic properties in these systems. We further extend this framework to explore QMCCT associated with Open Quantum Random Walks (OQRWs). The integration of symmetric group dynamics allows for a detailed analysis of the interplay between group-theoretic symmetries and the stochastic processes underlying QMCCT, particularly in the context of OQRWs. Our results demonstrate the potential of this approach to uncover new insights into the structure and behaviour of quantum Markov chains.
In this paper we investigate quantum Hellinger type divergences which were studied by Bhatia-Gaubert-Jain (2019), Pitrik-Virosztek (2020), and Dinh-Lie-Osaka-Phan (2025). In particular, when g : [0,infinity) -> [0,infinity) is a convex function defined by the form g(t) = alpha t(s) (alpha > 0,s is an element of [1, 2]) and f : [0,infinity) -> [0,infinity) is an operator monotone function with f '(1) = lambda is an element of [0, 1], we introduce the quantum quantitative measure Phi(g,sigma)(A,B) = Tr(g(A del B-lambda - A sigma B-f)) for positive definite matrices A and B, and show that Phi(g,sigma )is a quantum divergence in the sense of Bhatia-Gaubert-Jain and also show that it is jointly convex and satisfies the data processing property by a trace preserving positive unital map Phi, that is, Psi g,sigma(A,B) >= Psi(g,sigma)(Phi(A), Phi(B)).
For two square matrices A,B, the matrix A is said to be second-order commutative with respect to B if they are not commutative but A, A,B = O. In this paper, the general explicit parametrisation of second-order commutative 3 x 3 and 4 x 4 pairs will be given. We also consider its applications in solving certain differential equations arising in an NMR model and to the parametrisations of ladder operators in quantum physics.
We study the asymptotic dynamics of open quantum systems in the Heisenberg picture. We find an explicit expression for the attractor subspace and the dynamics that takes place in it. We present the relationship between the attractor subspaces in the Schrödinger and Heisenberg pictures and, in particular, the connection between their algebraic structures. An unfolding theorem of the asymptotics, as well as the fine structure of the recently introduced Choi-Effros decoherence-free algebra, are also discussed. Finally, we show how to extend all the results to the class of Schwarz maps.
Given the interaction graph of a Markov generator of weak coupling limit type, we propose its partition by means of a discrete metric, inspired by the metric circle. This gives us simplest but richer description of its invariant states. By restricting the notions of detailed balance and non-detailed balance, we show that the complete description of the invariant state depends only on the dynamics of a complete and connected subgraph of the interaction graph.
The quantum exclusion semigroup constructed from quantum Bernoulli noise can be decomposed into actions on the diagonal and off-diagonal operator spaces. Its action on the diagonal subspace describes a classical Markov process. This paper analyzes the convergence properties of this semigroup. A key result shows that the exponential convergence rate of the quantum semigroup (quantified via the spectral gap) matches precisely the convergence rate of its classical diagonal counterpart towards the unique invariant measure. Furthermore, we provide explicit computations or estimates of the exponential convergence rate in specific examples.
Delayed-choice experiments challenge classical intuitions by allowing the configuration of an interferometer to be chosen after a quantum system has already entered it. While these experiments support Bohr's complementarity principle, the introduction of quantum control reveals that the manifestation of complementarity depends critically on the full physical context - including quantum correlations and the causal order of operations. In this work, we propose and analyze a modified entanglement-assisted delayed-choice experiment that maintains the same final visibility as the standard setup but reverses its causal structure. Here, we go beyond output statistics to examine how wave-particle realism evolves throughout the interferometer. Using a contextual realism quantifier, we show that wave and particle realism can be meaningfully assigned at intermediate stages with a clear connection with the final interferometric visibility. Specifically, our results show that modifying the causal order of operations and information structure, whether through entanglement tuning or post-selection, leads to significant variations in the wave-particle complementarity relation.
The weak values and weak measurement formalism were initially limited to pure states which was later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be abstract properties of systems describing a complete picture between successive measurements in the two-state vector formalism (TSVF). The remarkable achievements of the weak value formalism in experimental quantum mechanics have persuaded most of quantum physicists that it is impeccable. However, we explore a scenario where the formalism of weak values for mixed states is employed in a quantum communication protocol but discover that it generates inaccurate outcomes. This reinforces our previous conclusion that the weak values may not be elements of the reality of weak measurements, contrary to what the pioneers of weak values proposed.
Quantum entanglement is an important phenomenon in quantum information theory. To detect entanglement theoretically, positive but not completely positive maps are used. The Kadison-Schwarz (KS) inequality interpolates between positivity and complete positivity. KS maps may be key to understanding and detecting entanglement. We provide a description of a subset of KS maps on M2(& Copf;) that are unital. This allows for the classification of a wider class of positive maps than the well known bistochastic maps. We derive the conditions for a unital map to be a KS map, and provide nontrivial examples of such a map.
We study k-positive linear maps on matrix algebras and address two problems, (i) characterizations of k-positivity and (ii) generation of non-decomposable k-positive maps. On the characterization side, we derive optimization-based conditions equivalent to k-positivity that (a) reduce to a simple check when k=d, (b) reveal a direct link to the spectral norm of certain order-3 tensors (aligning with known NP-hardness barriers for k<d), and (c) recast k-positivity as a novel optimization problem over separable states, thereby connecting it explicitly to separability testing. On the generation side, we introduce a Lie-semigroup-based method that, starting from a single k-positive map, produces one-parameter families that remain k-positive and non-decomposable for small enough times. We illustrate this by generating such families for d=3 and d=4. We also formulate a semi-definite program (SDP) to test an equivalent form of the positive partial transpose (PPT) square conjecture (and do not find any violation of the latter). Our results provide practical computational tools for certifying k-positivity and a systematic way to sample k-positive non-decomposable maps.
Starting from the three Pauli matrices, it is possible to construct a synthesis procedure for an arbitrary quantum circuit. A prominent role is played by X-circuits and Y-circuits. They constitute the [Formula: see text]-dimensional subgroups XU([Formula: see text]) and YU([Formula: see text]) of the [Formula: see text]-dimensional group U([Formula: see text]). The former are described by unitary matrices with all line sums equal to 1. The latter are described by unitary matrices with all weighted line sums equal to 1. Whereas the group XU([Formula: see text]) has been studied before, investigation of the group YU([Formula: see text]) is new.
Nowadays, it is widely acknowledged that information can serve as a thermodynamic fuel capable of powering the extraction of useful work through measurements and feedback control. Moreover, it has been demonstrated that the work extractable from a correlated bipartite state can effectively distinguish entangled states from separable ones. In this context, we introduce an operational criterion denoted as [Formula: see text] to witness the presence of entanglement in a two-mode Gaussian state [Formula: see text], based on the amount of work that can be extracted from a thermal bath using a Szilard-like engine. In this setup, the state [Formula: see text] acts as the working medium of the engine, where modes [Formula: see text] and [Formula: see text] are generated during the first and second transitions of a nondegenerate three-level laser, and are coupled to a shared two-mode thermal bath. Our results reveal that the proposed criterion [Formula: see text] vanishes when [Formula: see text] is a product state. Furthermore, [Formula: see text] reaches its maximum value when [Formula: see text] is coupled to a vacuum bath, but it diminishes under the influence of thermal noise. Notably, the degree of entanglement detected by [Formula: see text] can be tuned via the atomic coherence of the laser. Finally, a comparison of [Formula: see text] with a reliable measure of entanglement such as logarithmic negativity, demonstrates perfect agreement in identifying the presence of entanglement in [Formula: see text].
We introduce a notion of quasi-stationary state (QSS) in the context of quantum Markov semigroups that generalizes the one of quasi-stationary distribution in the case of classical Markov chains. We provide an operational interpretation of QSSs using the theory of direct and indirect quantum measurements. Moreover, we prove that there is a connection between QSSs and spectral properties of the quantum Markov semigroup. Finally, we discuss some examples which, despite their simplicity, already show interesting features.
