Related papers: Generalization of Quantum Error Correction via the…
Recent advances in our understanding of foundations of quantum mechanics have shown that information can be made objective through quantum states. Such objectification processes, predicted e.g. in a variety of quantum open systems, must…
Encoding in a high-dimensional Hilbert space improves noise resilience in quantum information processing. This approach, however, may result in cross-mode coupling and detection complexities, thereby reducing quantum cryptography…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
A typical quantum experiment has a bunch of apparatuses placed so that quantum systems can pass between them. We regard each use of an apparatus, along with some given outcome on the apparatus (a certain detector click or a certain meter…
Let ${\cal S}(\mathcal{H})$ denote the set of all self-adjoint operators (not necessarily bounded) on a Hilbert space $\mathcal{H}$, which is the set of all physical quantities on a quantum system $\mathcal{H}$. We introduce a binary…
Quantum metrology is a general term for methods to precisely estimate the value of an unknown parameter by actively using quantum resources. In particular, some classes of entangled states can be used to significantly suppress the…
A group theoretic framework is introduced that simplifies the description of known quantum error-correcting codes and greatly facilitates the construction of new examples. Codes are given which map 3 qubits to 8 qubits correcting 1 error, 4…
Noise and errors are inevitable parts of any practical implementation of a quantum computer. As a result, large-scale quantum computation will require ways to detect and correct errors on quantum information. Here, we present such a quantum…
Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…
Quantum annealing is a promising method for solving combinational optimization problems and performing quantum chemical calculations. The main sources of errors in quantum annealing are the effects of decoherence and non-adiabatic…
We present a general framework of quantum error-correcting codes (QECCs) as a subspace of a complex Hilbert space and the corresponding error models. Then we illustrate how QECCs can be constructed using techniques from algebraic coding…
We consider quantum metrology in noisy environments, where the effect of noise and decoherence limits the achievable gain in precision by quantum entanglement. We show that by using tools from quantum error-correction this limitation can be…
In this paper, we will propose the most general form of the deformation of Heisenberg algebra motivated by the generalized uncertainty principle. This deformation of the Heisenberg algebra will deform all quantum mechanical systems. The…
The mechanism of describing quantum states by standard probability (tomographic one) instead of wave function or density matrix is elucidated. Quantum tomography is formulated in an abstract Hilbert space framework, by means of the identity…
Classical machine learning theory and theory of quantum computations are among of the most rapidly developing scientific areas in our days. In recent years, researchers investigated if quantum computing can help to improve classical machine…
These lecture notes aim to provide a clear and comprehensive introduction to using open quantum system theory for quantum algorithms. The main arguments are Variational Quantum Algorithms, Quantum Error Correction, Dynamical Decoupling and…
Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…
We show that quantum subdynamics of an open quantum system can always be described by a Hermitian map, irrespective of the form of the initial total system state. Since the theory of quantum error correction was developed based on the…
An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…
We apply the generalized Abel-Plana formula for the investigation of one-loop quantum effects on manifolds with boundaries. This allows to extract from the vacuum expectation values of local physical observables the parts corresponding to…