Related papers: Petz recovery maps for qudit quantum channels
Numerous quantum many-body systems are characterized by either fundamental or emergent constraints---such as gauge symmetries or parity superselection for fermions---which effectively limit the accessible observables and realizable…
Quantitative Susceptibility Mapping (QSM) is a new phase-based technique for quantifying magnetic susceptibility. The existing QSM reconstruction methods generally require complicated pre-processing on high-quality phase data. In this work,…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
The quantum data processing inequality asserts that two quantum states become harder to distinguish when a noisy channel is applied. On the other hand, a reverse quantum data processing inequality characterizes whether distinguishability is…
Constructing reduced representations of high-dimensional systems is a fundamental problem in physical chemistry. Many unsupervised machine learning methods can automatically find such low-dimensional representations. However, an often…
We investigate the possibility of dividing quantum channels into concatenations of other channels, thereby studying the semigroup structure of the set of completely-positive trace-preserving maps. We show the existence of 'indivisible'…
We present two projects concerning the main part of my PhD work. In the first one we study quantum channels, which are the most general operations mapping quantum states into quantum states, from the point of view of their divisibility…
The recovery of fragile quantum states from decoherence is the basis of building a quantum memory, with applications ranging from quantum communications to quantum computing. Many recovery techniques, such as quantum error correction, rely…
Anatomically guided PET reconstruction using MRI information has been shown to have the potential to improve PET image quality. However, these improvements are limited to PET scans with paired MRI information. In this work we employed a…
In this work, we introduce a general, gradient-based method that optimises codewords for a given noise channel and fixed recovery. We do so by differentiating fidelity and descending on the complex coefficients using finite-difference…
Quantization-aware training (QAT) is an effective method to drastically reduce the memory footprint of LLMs while keeping performance degradation at an acceptable level. However, the optimal choice of quantization format and bit-width…
Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no…
Separability of quantum states is analyzed with the use of the Choi-Jamiolkowski isomorphism. Spectral separability criteria are derived. The presented approach is illustrated with various examples, among which a separable decomposition of…
We determine the minimal experimental resources that ensure a unique solution in the estimation of trace-preserving quantum channels with both direct and convex optimization methods. A convenient parametrization of the constrained set is…
Completely positive maps are useful in modeling the discrete evolution of quantum systems. Spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to…
To store quantum information, quantum memory plays a central intermediate ingredient in a network. The minimal criterion for a reliable quantum memory is the maintenance of the entangled state, which can be described by the…
Efficient methods for the simulation of quantum circuits on classic computers are crucial for their analysis due to the exponential growth of the problem size with the number of qubits. Here we study lumping methods based on bisimulation,…
Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit…
A convex optimization based method is proposed for quantum process tomography, in the case of known channel model structure, but unknown channel parameters. The main idea is to select an affine parametrization of the Choi matrix as a set of…
We calculate the quantum capacity of an amplitude-damping channel with time correlated Markov noise, for two channel uses. Our results show that memory of the channel increases it's ability to transmit quantum information significantly. We…