Related papers: Renormalized quantum tomography
Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure…
Quantum state tomography is an elementary tool to fully characterize an unknown quantum state. As the quantum hardware scales up in size, the standard quantum state tomography becomes increasingly challenging due to its exponentially…
We develop an algebraic frame for the simultaneous treatment of actual and possible properties of quantum systems. We show that, in spite of the fact that the language is enriched with the addition of a modal operator to the orthomodular…
We explore the conceptual usefulness of Riemannian geometric tools induced by the statistical concept of distinguishability in quantifying the effect of a depolarizing channel on quantum states. Specifically, we compare the geometries of…
The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing…
Quantum process tomography (QPT) plays a central role in characterizing quantum gates and circuits, diagnosing quantum devices, calibrating hardware, and supporting quantum error correction. However, conventional QPT methods face challenges…
In these lectures we develop the projection operator method for quantum groups. Here the term "quantum groups" means q-deformed universal enveloping algebras of contragredient Lie (super)algebras of finite growth. Contains of the lectures…
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and circuits are naturally interpretable in such structures. We consider…
Continuous-variable quantum systems are foundational to quantum computation, communication, and sensing. While traditional representations using wave functions or density matrices are often impractical, the tomographic picture of quantum…
We review the basic properties of effective actions of families of theories (i.e., the actions depending on additional non-perturbative moduli along with perturbative couplings), and their description in terms of operators (called…
The no-programming theorem prohibits the existence of a Universal Programmable Quantum Processor. This statement has several implications in relation to quantum computation, but also to other tasks of quantum information processing, making…
Boundary theories of static bulk topological phases of matter are obstructed in the sense that they cannot be realized on their own as isolated systems. The obstruction can be quantified/characterized by quantum anomalies, in particular…
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is…
We propose and evaluate experimentally an approach to quantum process tomography that completely removes the scaling problem plaguing the standard approach. The key to this simplification is the incorporation of prior knowledge of the class…
For an unbounded operator $S$ on a Banach space the existence of invariant subspaces corresponding to its spectrum in the left and right half-plane is proved. The general assumption on $S$ is the uniform boundedness of the resolvent along…
Higher-order quantum theory is an extension of quantum theory where one introduces transformations whose input and output are transformations, thus generalizing the notion of channels and quantum operations. The generalization then goes…
Of crucial importance to the development of quantum computing and information has been the construction of a quantum operations formalism that admits a description of quantum noise while simultaneously revealing the behavior of an open…
We develop the first steps towards an analysis of geometry on the quantum spacetime proposed in [1]. The homogeneous elements of the universal differential algebra are naturally identified with operators living in tensor powers of Quantum…
Quantum process tomography is a necessary tool for verifying quantum gates and diagnosing faults in architectures and gate design. We show that the standard approach of process tomography is grossly inaccurate in the case where the states…