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In the study of open quantum systems, one commonly describes the evolution of a system of interest through reduced dynamics, obtained by treating the environment indirectly rather than as a part of the full model. This thesis presents an…
Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two…
We show that a sequence $\{\Phi_n\}$ of quantum channels strongly converges to a quantum channel $\Phi_0$ if and only if there exist a common environment for all the channels and a corresponding sequence $\{V_n\}$ of Stinespring isometries…
World-wide efforts aim at the realization of advanced quantum simulators and processors. However, despite the development of intricate hardware and pulse control systems, it may still not be generally known which effective quantum dynamics,…
The recently introduced random purification channel, which converts $n$ copies of an arbitrary mixed quantum state into $n$ copies of the same uniformly random purification, has emerged as a powerful tool in quantum information theory.…
The study of quantum channels is the most fundamental theoretical problem in quantum information and quantum communication theory. The link product theory of quantum channels is an important tool for studying quantum networks. In this…
A variety of tasks in quantum control, ranging from purification and cooling, to quantum stabilization and open-system simulation, rely on the ability to implement a target quantum channel over a specified time interval within prescribed…
For a unital completely positive map $\Phi$ ("quantum channel") governing the time propagation of a quantum system, the Stinespring representation gives an enlarged system evolving unitarily. We argue that the Stinespring representations of…
Since precisely controlling dissipation in realistic environments is challenging, digital simulation of the Lindblad master equation (LME) is of great significance for understanding nonequilibrium dynamics in open quantum systems. However,…
Simulating the dynamics of open quantum systems is a crucial task in quantum computing, offering wide-ranging applications but remaining computationally challenging. In this paper, we propose two quantum algorithms for simulating the…
We introduce a quantum channel to model the dissipative dynamics resulting from the coupling between spin and motional degrees of freedom in chains of neutral atoms with Rydberg interactions. The quantum channel acts on the reduced spin…
Inferring the dynamical generator of a many-body quantum system from measurement data is essential for the verification, calibration, and control of quantum processors. When the system is open, this task becomes considerably harder than in…
Designing quantum algorithms for simulating quantum systems has seen enormous progress, yet few studies have been done to develop quantum algorithms for open quantum dynamics despite its importance in modeling the system-environment…
We study the task of lifting arbitrary quantum states and channels to purifications and Stinespring dilations, respectively, in both the probabilistic exact and deterministic approximate settings. We formalize this task through a general…
We examine the time discretization of Lindblad master equations in infinite-dimensional Hilbert spaces. Our study is motivated by the fact that, with unbounded Lindbladian, projecting the evolution onto a finite-dimensional subspace using a…
We explore the symmetry properties of Stinespring dilations of single-qubit Pauli channels, addressing both the generic case and the specific examples of phase damping and depolarizing channels. For each scenario, we derive the…
Understanding dissipation in open quantum systems is crucial for the development of robust quantum technologies. In this work, we introduce a Transformer-based machine learning framework to infer time-dependent dissipation rates in quantum…
In this paper we return to the problem of reduced-state dynamics in the presence of an interacting environment. The question we investigate is how to appropriately model a particular system evolution given some knowledge of the…
Tensor networks offer a valuable framework for implementing Lindbladian dynamics in many-body open quantum systems with nearest-neighbor couplings. In particular, a tensor network ansatz known as the Locally Purified Density Operator…
We introduce a hybrid quantum-classical framework for efficiently implementing approximate unitary dilations of non-unitary operators with enhanced noise resilience. The method embeds a target non-unitary operator into a subblock of a…