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Thermodynamic Formalism for Continuous-Time Quantum Markov Semigroups: the Detailed Balance Condition, Entropy, Pressure and Equilibrium Quantum Processes Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2024-01-23 Jader E. Brasil, Josué Knorst, Artur O. Lopes
Let Mn(ℂ) denote the set of n by n complex matrices. Consider continuous time quantum semigroups 𝒫t=etℒ, t≥0, where ℒ:Mn(ℂ)→Mn(ℂ) is the infinitesimal generator. If we assume that ℒ(I)=0, we will call etℒ, t≥0 a quantum Markov semigroup. Given a stationary density matrix ρ=ρℒ, for the quantum Markov semigroup 𝒫t, t≥0, we can define a continuous time stationary quantum Markov process, denoted by Xt
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Hypergroup Structures of Open Quantum Random Walks on Distance Sets Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2024-01-23 Yusuke Sawada
Wildberger introduced the method of constructing a Hermitian discrete hypergroup from a random walk on a graph. In this study, we will apply his method to an open quantum random walk (OQRW) on a distance set and show that any discrete hypergroup that is not necessarily Hermitian can be realized using the OQRW on a distance set. We also investigate the distributions of OQRWs on distance sets in the
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Geometric versus Entropic Gaussian Correlations in an Open Quantum System of Two Bosonic Modes Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2024-01-23 Alina Stoica, Aurelian Isar
Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification
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2-Point Markov Evolutions Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2024-01-23 Luigi Accardi, Ameur Dhahri
We study the Markov evolutions associated to the expected Markov processes.
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Deviation from Equilibrium of QMS of Weak Coupling Limit Type with Respect to Uniform and Completely Nonequilibrium Invariant States Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2024-01-23 M. A. Cruz de la Rosa, J. C. García, F. Guererro-Poblete, A. Hernández
We study the deviation from equilibrium with respect to a special class of states, the so called uniform and completely nonequilibrium, which were introduced and characterized in [11]. We compute explicitly such a deviation, we obtain an equivalent expression in terms of circulant matrices and give a bound for it. Finally, as an example, we make explicit computations in the three level case.
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Göran Lindblad in Memoriam Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Ingemar Bengtsson
This is a brief account of the life and work of Göran Lindblad.
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A Neo-Copenhagen Quantum Mechanics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Göran Lindblad
An analysis of the quantum measurement problem is presented which is a modest modification of the standard one often called the Copenhagen interpretation. The starting assumption is that QM is universal, and that all evolutions are unitary. We must also assume that the set of evolutions is restricted to allow the existence of stable structures for the equipment in our laboratory, including the measurement
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Random Lindblad Operators Obeying Detailed Balance Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Wojciech Tarnowski, Dariusz Chruściński, Sergey Denisov, Karol Życzkowski
We introduce different ensembles of random Lindblad operators ℒ, which satisfy quantum detailed balance condition with respect to given stationary state σ of size N, and investigate their spectral properties. Such operators are known as ‘Davies generators’ and their eigenvalues are real; however, their spectral densities depend on σ. We propose different structured ensembles of random matrices, which
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Exceptional Points and Exponential Sensitivity for Periodically Driven Lindblad Equations Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Jonas Larson, Sofia Qvarfort
In this contribution to the memorial issue of Göran Lindblad, we investigate the periodically driven Lindblad equation for a two-level system. We analyze the system using both adiabatic diagonalization and numerical simulations of the time-evolution, as well as Floquet theory. Adiabatic diagonalization reveals the presence of exceptional points in the system, which depend on the system parameters.
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Long-Time Relaxation of a Finite Spin Bath Linearly Coupled to a Qubit Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Jukka P. Pekola, Bayan Karimi, Marco Cattaneo, Sabrina Maniscalco
We discuss the long-time relaxation of a qubit linearly coupled to a finite bath of N spins (two-level systems, TLSs), with the interaction Hamiltonian in rotating wave approximation. We focus on the regime N≫1, assuming that the qubit–bath coupling is weak, that the range of spin frequencies is sufficiently broad, and that all the spins are initialized in the ground state. Despite the model being
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Wave Matrix Lindbladization I: Quantum Programs for Simulating Markovian Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Dhrumil Patel, Mark M. Wilde
Density Matrix Exponentiation is a technique for simulating Hamiltonian dynamics when the Hamiltonian to be simulated is available as a quantum state. In this paper, we present a natural analogue to this technique, for simulating Markovian dynamics governed by the well known Lindblad master equation. For this purpose, we first propose an input model in which a Lindblad operator L is encoded into a
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A Perspective on Lindblad’s Non-Equilibrium Entropy Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-07-20 Erik Aurell, Ryoichi Kawai
In 1983 Göran Lindblad published a monograph on nonequilibrium thermodynamics. We here summarize the contents of this book, and provide a perspective on its relation to later developments in statistical physics and quantum physics. We high-light two aspects. The first is the idea that while all unitaries can be allowed in principle, different theories result from limiting which unitary evolutions are
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On the Generators of Quantum Dynamical Semigroups with Invariant Subalgebras Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-03-31 Markus Hasenöhrl, Matthias C. Caro
The problem of characterizing GKLS-generators and CP-maps with an invariant von Neumann algebra 𝒜 appeared in different guises in the literature. We prove two unifying results, which hold even for weakly closed *-algebras: first, we show how to construct a normal form for 𝒜-invariant GKLS-generators, if a normal form for 𝒜-invariant CP-maps is known — rendering the two problems essentially equivalent
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G-Circulant Quantum Markov Semigroups Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-03-31 Jorge R. Bolaños-Servín, Roberto Quezada, Josué Vázquez-Becerra
We broaden the study of circulant Quantum Markov Semigroups (QMS). First, we introduce the notions of G-circulant GKSL generator and G-circulant QMS from the circulant case, corresponding to ℤn, to an arbitrary finite group G. Second, we show that each G-circulant GKSL generator has a block-diagonal representation Q⊗𝟙G, where Q is a G-circulant matrix determined by some α∈ℓ2(G). Denoting by H the
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Quantum-Dynamical Semigroups and the Church of the Larger Hilbert Space Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-03-31 Frederik vom Ende
In this work we investigate Stinespring dilations of quantum-dynamical semigroups, which are known to exist by means of a constructive proof given by Davies in the early 70s. We show that if the semigroup describes an open system, that is, if it does not consist of only unitary channels, then the evolution of the dilated closed system has to be generated by an unbounded Hamiltonian; subsequently the
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Hopf Structure for the q-Lévy-Meixner Oscillator Algebra Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-03-31 Anis Riahi, Habib Rebei, Amine Ettaieb, Ziyad Ali Alhussain, Hedi Ben Elmonser
The main purpose of this paper is to investigate a generalized oscillator algebra, naturally associated with the q-Lévy-Meixner polynomials. We solve the problem of the Hopf algebraic structure for the q-deformed Lévy-Meixner oscillator algebra based on the one-parameter deformation of canonical commutation relations.
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Exploring the Limits of Controlled Markovian Quantum Dynamics with Thermal Resources Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-03-31 Frederik vom Ende, Emanuel Malvetti, Gunther Dirr, Thomas Schulte-Herbrüggen
Our aim is twofold: First, we rigorously analyse the generators of quantum-dynamical semigroups of thermodynamic processes. We characterise a wide class of gksl-generators for quantum maps within thermal operations and argue that every infinitesimal generator of (a one-parameter semigroup of) Markovian thermal operations belongs to this class. We completely classify and visualise them and their non-Markovian
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“What Is Life?”: Open Quantum Systems Approach Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-02-01 Irina Basieva, Andrei Khrennikov
Recently, the quantum formalism and methodology have been used in application to the modelling of information processing in biosystems, mainly to the process of decision making and psychological behaviour (but some applications in microbiology and genetics are considered as well). Since a living system is fundamentally open (an isolated biosystem is dead), the theory of open quantum systems is the
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The Quantum Mechanics Canonically Associated to Free Probability I: Free Momentum and Associated Kinetic Energy Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-02-01 Luigi Accardi, Tarek Hamdi, Yun Gang Lu
After a short review of the quantum mechanics canonically associated with a classical real valued random variable with all moments, we begin to study the quantum mechanics canonically associated to the standard semi-circle random variableX, characterized by the fact that its probability distribution is the semi-circle law μ on [−2,2]. We prove that, in the identification of L2([−2,2],μ) with the 1-mode
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The Quantum Mechanics Canonically Associated to Free Probability II: The Normal and Inverse Normal Order Problem Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-02-01 Luigi Accardi, Tarek Hamdi, Yun Gang Lu
In the first part of the present paper, we have proved that, in order to find an explicit expression for the action, on the μ-orthogonal polynomials, of the 1-parameter unitary groups eitP and eitP2/2, the solution of the inverse normal order problem on the quantum algebra canonically associated to the classical semi-circle random variable is required. In this paper we solve this problem. The solution
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Non-Perturbative Treatment of Open-System Multi-Time Expectation Values in Gaussian Bosonic Environments Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2023-02-01 Andrea Smirne, Dario Tamascelli, James Lim, Martin B. Plenio, Susana F. Huelga
We determine the conditions for the equivalence between the multi-time expectation values of a general finite-dimensional open quantum system when interacting with, respectively, an environment undergoing a free unitary evolution or a discrete environment under a free evolution fixed by a proper Gorini-Kossakowski-Lindblad-Sudarshan generator. We prove that the equivalence holds if both environments
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Linear Maps as Sufficient Criteria for Entanglement Depth and Compatibility in Many-Body Systems Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-12-27 Maciej Lewenstein, Guillem Müller-Rigat, Jordi Tura, Anna Sanpera
Physical transformations are described by linear maps that are completely positive and trace preserving (CPTP). However, maps that are positive (P) but not completely positive (CP) are instrumental to derive separability/entanglement criteria. Moreover, the properties of such maps can be linked to entanglement properties of the states they detect. Here, we extend the results presented in [34], where
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Unidirectional Information Flow and Positive Divisibility are Nonequivalent Notions of Quantum Markovianity for Noninvertible Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-12-27 Ángel Rivas
We construct a dynamical map which is not positive divisible and does not present information backflow either (as measured by trace norm quantifiers). It is formulated for a qutrit system undergoing noninvertible dynamics. This provides an evidence that the two definitions of quantum Markovianity based on the absence of information backflow and positive divisibility are nonequivalent for general noninvertible
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Random Walk on Quantum Blobs Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-12-27 Arkadiusz Jadczyk
We describe the action of the symplectic group on the homogeneous space of squeezed states (quantum blobs) and extend this action to the semigroup. We then extend the metaplectic representation to the metaplectic (or oscillator) semigroup and study the properties of such an extension using Bargmann-Fock space. The shape geometry of squeezing is analyzed and noncommuting elements from the symplectic
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On Quasi-Inversion of Quantum Channels in 2 and in Higher Dimensions Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-12-27 Vahid Karimipour
We review the concept of the quasi-inverse of qubit channels and of higher dimensional channels. Quasi-inverse is a channel which when concatenaded to the original channel, increases its average fidelity in an optimal way. For qubit channels, we fully characterize the quasi-inverse, while for higher dimensional channels, we prove general theorems and provide bounds for the increased average fidelity
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A Brief Journey through Collision Models for Multipartite Open Quantum Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-12-27 Marco Cattaneo, Gian Luca Giorgi, Roberta Zambrini, Sabrina Maniscalco
The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed “ancillas”. In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested
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The Kossakowski Matrix and Strict Positivity of Markovian Quantum Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Julián Agredo, Franco Fagnola, Damiano Poletti
We investigate the relationship between strict positivity of the Kossakowski matrix, irreducibility and positivity improvement properties of Markovian quantum dynamics. We show that for a Gaussian quantum dynamical semigroup strict positivity of the Kossakowski matrix implies irreducibility and, with an additional technical assumption, that the support of any initial state is the whole space for any
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Stochastic versus Periodic Quantum Collision Models Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Francesco Ciccarello
Most literature on quantum collision models (CMs) usually considers periodic weak collisions featuring a fixed waiting time between two next collisions. Some works have yet addressed CMs with random waiting time and strong collisions (stochastic CMs). This short paper discusses how the open dynamics arising from these two types of models can be formally mapped with one another. This can be achieved
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Quantifying non-Markovian Memory in a Superconducting Quantum Computer Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Joshua Morris, Felix A. Pollock, Kavan Modi
We analyze the temporal correlations in a sequence of gates by characterizing the performance of a gate conditioned on the gate that preceded it. With this method, we estimate (i) the size of fluctuations in the performance of a gate, i.e., errors due to non-Markovianity; (ii) the length of the memory; and (iii) the total size of the memory. Our results strongly indicate the presence of nontrivial
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On the Use of Total State Decompositions for the Study of Reduced Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Andrea Smirne, Nina Megier, Bassano Vacchini
The description of the dynamics of an open quantum system in the presence of initial correlations with the environment needs different mathematical tools than the standard approach to reduced dynamics, which is based on the use of a time-dependent completely positive trace preserving (CPTP) map. Here, we take into account an approach that is based on a decomposition of any possibly correlated bipartite
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Correlations in Noisy Measurements Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Seungchan Seo, Jiheon Seong, Joonwoo Bae
Although a measurement on the computational basis is devised in quantum computing, e.g., cloud-based quantum computing services, a quantum measurement in a realistic scenario is noisy. In particular, a measurement readout error in the era of noisy-intermediate-scale-quantum technologies is significant. In this work, we consider measurements on multiple qubits in a realistic scenario and present a method
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Nature and Origin of Operators Entering the Master Equation of an Open Quantum System Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-11-02 Giovanni Spaventa, Paola Verrucchi
By exploiting the peculiarities of a recently introduced formalism for describing open quantum systems (the parametric representation with environmental coherent states) we derive an equation of motion for the reduced density operator of an open quantum system that has the same structure of the celebrated Gorini–Kossakowski–Sudarshan–Lindblad equation, but holds regardless of Markovianity being assumed
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Local Generation of Entanglement with Redfield Dynamics Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-08-31 F. Benatti, D. Chruściński, R. Floreanini
In phenomenological applications, time evolutions of Bloch-Redfield type are widely adopted for modelling open system dynamics, despite their nonpositive preserving character: this physical inconsistency, that in general shows up at small times, is usually cured by suitably restricting the space of allowed initial states. Nevertheless, additional problems may arise in relation to entanglement: specifically
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Accessible Maps in a Group of Classical or Quantum Channels Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-08-31 Koorosh Sadri, Fereshte Shahbeigi, Zbigniew Puchała, Karol Życzkowski
We study the problem of accessibility in a set of classical and quantum channels admitting a group structure. Group properties of the set of channels, and the structure of the closure of the analyzed group G plays a pivotal role in this regard. The set of all convex combinations of the group elements contains a subset of channels that are accessible by a dynamical semigroup. We demonstrate that accessible
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Open Quantum Random Walks and Quantum Markov chains on Trees I: Phase transitions Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-08-31 Farrukh Mukhamedov, Abdessatar Souissi, Tarek Hamdi
In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution ℙρ of OQRW. However, we are going to look at the probability distribution as a Markov field over the Cayley tree. Such kind of consideration
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Non-Hermitian Physics and Master Equations Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-08-31 Federico Roccati, G. Massimo Palma, Francesco Ciccarello, Fabio Bagarello
A longstanding tool to characterize the evolution of open Markovian quantum systems is the GKSL (Gorini-Kossakowski-Sudarshan-Lindblad) master equation. However, in some cases, open quantum systems can be effectively described with non-Hermitian Hamiltonians, which have attracted great interest in the last twenty years due to a number of unconventional properties, such as the appearance of exceptional
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The Legacy of Andrzej Kossakowski Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Dariusz Chruściński
I review here a small part of Andrzej Kossakowski scientific activity focusing on his pioneering contribution to the evolution of open quantum systems (celebrated Gorini-Kossakowski-Lindblad-Sudarshan (GKLS) master equation) and positive maps in operator algebras. These particular topics turned out to be of primary importance for fundamentals of quantum physics and the rapid development of modern quantum
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Remembering Andrzej Kossakowski Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Saverio Pascazio
When someone disappears, where do their ideas go?
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Three Favourite Dimensions of Andrzej: Along His Path to a Scientific Discovery Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Karol Życzkowski
Some achievements of the late Andrzej Kossakowski in the field of statistical physics and quantum theory are presented. We recall also his attempt to find an analytical solution of the 3-dimensional Ising model.
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A Markov–Dobrushin Inequality for Quantum Channels Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Luigi Accardi, Yun Gang Lu, Abdessatar Souissi
We propose a quantum extension of the Markov-Dobrushin inequality. As an application, we estimate the Markov-Dobrushin constant for some classes of quantum Markov channels, in particular for the Pauli channel, widely studied in quantum information theory.
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Dynamical Maps and Symmetroids Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo
Starting from the canonical symmetroid 𝒮(G) associated with a groupoid G, the issue of describing dynamical maps in the groupoidal approach to quantum mechanics is addressed. After inducing a Haar measure on the canonical symmetroid 𝒮(G), the associated von Neumann groupoid algebra is constructed. It is shown that the left-regular representation allows to define linear maps on the groupoid-algebra
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Indistinguishability-Enhanced Entanglement Recovery by Spatially Localized Operations and Classical Communication Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-07-01 Matteo Piccolini, Farzam Nosrati, Roberto Morandotti, Rosario Lo Franco
We extend a procedure exploiting spatial indistinguishability of identical particles to recover the spoiled entanglement between two qubits interacting with Markovian noisy environments. Here, the spatially localized operations and classical communication (sLOCC) operational framework is used to activate the entanglement restoration from the indistinguishable constituents. We consider the realistic
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Reduced Dynamics in Open Bosonic and Fermionic Systems Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-05-10 Ioannis Lyris, Panagiotis Lykourgias, Alexandros I. Karanikas
In this work we study the reduced dynamics of a system embedded in a quantum environment, with the use of correlation functions produced through appropriately defined reduced generating functionals. Our construction is based on expressing these functionals in terms of consistently defined coherent-state path integrals in the framework of the Keldysh-Schwinger out-of-equilibrium formalism.
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A Rigidity Property of Complete Systems of Mutually Unbiased Bases Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-05-10 Máté Matolcsi, Mihály Weiner
Suppose that for some unit vectors b1,…bn in ℂd we have that for any j≠k bj is either orthogonal to bk or |〈bj,bk〉|2 = 1/d (i.e., bj and bk are unbiased). We prove that if n = d(d + 1), then these vectors necessarily form a complete system of mutually unbiased bases, that is, they can be arranged into d + 1 orthonormal bases, all being mutually unbiased with respect to each other.
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Nonlinear Optimal Feedback Control of the Two-Level Open Non-Markovian Stochastic Quantum System Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-05-10 Shahid Qamar, Shuang Cong, Kezhi Li, Zhixiang Dong, Feng Shuang
In this paper, a nonlinear optimal feedback control based on the nonlinear state estimator for a two-level open non-Markovian stochastic quantum system is proposed. The proposed nonlinear state estimator is designed by using the state-dependent differential Riccati equation and constructed to optimally estimate the state. The estimated state is updated by the output data of continuous weak measurement
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A Note on Improved Treatment of Gaussian Communication Process Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2022-05-10 Taihei Takahash, Noboru Watanabe
In order to discuss the efficiency of information transmission of the Gaussian communication processes consistently, we introduced an entropy type functional and a mutual entropy type functional in reference [16]. In that study, we used the set of Gaussian input measures with covariance operators of trace one. In this paper, we refine the formulation and modify the entropy type complexity and the mutual
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Uniform and Completely Nonequilibrium Invariant States for Weak Coupling Limit Type Quantum Markov Semigroups Associated with Eulerian Cycles Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 M. A. Cruz de la Rosa, J. C. García-Corte, F. Guerrero-Poblet
We define the uniform and completely nonequilibrium invariant states, which are associated with Eulerian cycles; once we did this, we use the Hierholzer’s algorithm to obtain a canonical Euler-Hierholzer cycle, and for it, characterize the invariant state. For the simplest case of nonequilibrium, we give sufficient conditions for these states to be invariant and write its eigenvalues explicitly.
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Complete Positivity of Two Class of Maps Involving Depolarizing and Transpose-Depolarizing Channels Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 Xiuhong Sun, Yuan Li
In this note, we mainly study the necessary and sufficient conditions for the complete positivity of generalizations of depolarizing and transpose-depolarizing channels. Specifically, we define ΨA,±(X) := tr(AX)I ± X and ΦA,±(X) := tr(AX)I ± Xt, where A ∈ℬ(ℋ) (the set of all bounded linear operators on the finite-dimensional Hilbert space ℋ) is given and Xt is the transpose of X ∈ℬ(ℋ) in a fixed orthonormal
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On the Speed Limit for Imaginary-Time Schrödinger Equation with Application to Quantum Searches Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 Jie Sun, Songfeng Lu
Recently, Okuyama and Ohzek [1] derived a speed limit for the imaginary-time Schrödinger equation, which is inspired by the prior work of Kieu, who had shown a new class of time–energy uncertainty relations suitable for actually evaluating the speed limit of quantum dynamics. In this paper, we apply the result of Okuyama and Ohzek to obtain a generalized speed limit for Grover’s search in imaginary-time
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On Extremal Positive Maps of Three-Dimensional Matrix Algebra Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 Piotr Ługiewicz, Robert Olkiewicz
A class of bistochastic maps of three-dimensional matrix algebra which preserves a one-dimensional projector is studied.
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On a New Family of Extremal Positive Maps of Three-Dimensional Matrix Algebra Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 Piotr Ługiewicz, Robert Olkiewicz
We present a new one-parameter family of extremal positive maps on the three-dimensional matrix algebra. The new elements are characterized as mappings that preserve a one-dimensional orthogonal projector.
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Detection Power of Separability Criteria Based on a Correlation Tensor: A Case Study Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-12-21 Gniewomir Sarbicki, Giovanni Scala, Dariusz Chruściński
Detection power of separability criteria based on a correlation tensor is tested within a family of generalized isotropic states in d1 ⊗ d2. For d1 ≤ d2 all these criteria are weaker than the positive partial transposition (PPT) criterion. Interestingly, our analysis supports the recent conjecture that a criterion based on symmetrically informationally complete positive operator-valued measure (SIC-POVMs)
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Gaussian Quantum Markov Semigroups on a One-Mode Fock Space: Irreducibility and Normal Invariant States Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-08-30 J. Agredo, F. Fagnola, D. Poletti
We consider the most general Gaussian quantum Markov semigroup on a one-mode Fock space, discuss its construction from the generalized GKSL representation of the generator. We prove the known explicit formula on Weyl operators, characterize irreducibility and its equivalence to a Hörmander type condition on commutators and establish necessary and sufficient conditions for existence and uniqueness of
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Preparing Decoherence-Recoherence Times of a Qubit with Special Nonselective Measurement Schemes Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-08-30 Filippo Giraldi
The appearance of decoherence-recoherence events is analyzed in a dephasing model of a qubit which interacts with a bosonic environment. The initial condition is prepared from the thermal state of the whole system by performing a nonselective measurement on the qubit. Decoherence-recoherence events appear in the reduced dynamics of the qubit uniquely if special nonselective preparation measurements
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Infinite-Volume Limit of Stochastic s-d System with Single-Component Impurity and s-Electron Spins Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-08-30 Jan Maćkowiak
A Hamiltonian H, with locally smeared Ising-type s-d exchange between s-electrons and magnetic impurities, in a dilute magnetic alloy, is investigated. The Feynman-Kac theorem, Laplace expansion and Bogolyubov inequality are applied to obtain a lower and upper bound (lb and ub) on the system’s free energy per conducting electron f(H,β). The two bounds differ, in the infinite-volume limit by a term
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A Class of Quantum Markov Fields on Tree-like Graphs: Ising-type Model on a Husimi Tree Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-08-30 Abdessatar Souissi
A new class of forward quantum Markov fields (FQMFs) is introduced. The structure of these quantum Markov fields is investigated in the finer structure of a quasi-local algebra of observable over a tree-like graph. We provide an effective construction of a class of FQMCs. Moreover, we show the existence of three FMRFs associated with an Ising type model on a Husimi tree.
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Explicit Construction of Optimal Witnesses for Input-Output Correlations Attainable by Quantum Channels Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-04-29 Michele Dall’Arno, Sarah Brandsen, Francesco Buscemi
Given a quantum channel — that is, a completely positive trace-preserving linear map — as the only communication resource available between two parties, we consider the problem of characterizing the set of classical noisy channels that can be obtained from it by means of suitable classical-quantum encodings and quantum-classical decodings, respectively, on the sender’s and the receiver’s side. We consider
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Breaking of the Similarity Principle in Markov Generators of Low Density Limit Type and the Role of Degeneracies in the Landscape of Invariant States Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-04-29 L. Accardi, J. C. García-Corte, F. Guerrero-Poblete, R. Quezada
The similarity principle is an extension of the principle of thermal relaxation that naturally arises in the stochastic limit of quantum theory. We construct examples of Low Density Limit (LDL) generators, associated to an environment state in equilibrium at inverse temperature β, which admit non-(β, HS)-equilibrium states. We prove that in some cases, the attraction domain of the (β, HS)-equilibrium
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A Class of Quasi-Eternal Non-Markovian Pauli Channels and Their Measure Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-04-29 Shrikant Utagi, Vinod N. Rao, R. Srikanth, Subhashish Banerjee
We study a class of qubit non-Markovian general Pauli dynamical maps with multiple singularities in the generator. We discuss a few easy examples involving trigonometric or other nonmonotonic time dependence of the map, and discuss in detail the structure of channels which don’t have any trigonometric functional dependence. We demystify the concept of a singularity here, showing that it corresponds
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Andrzej Kossakowski, 1938–2021 — In Memory of Professor A. Kossakowski, Editor of OSID in 1992–2021 Open Syst. Inf. Dyn. (IF 0.8) Pub Date : 2021-03-01 Dariusz Chruściński,Andrzej Jamiołkowski,Miłosz Michalski,Ryszard Mrugała