Related papers: A polar decomposition for quantum channels (with a…
We study the problem of approximating a quantum channel by one with as few Kraus operators as possible (in the sense that, for any input state, the output states of the two channels should be close to one another). Our main result is that…
Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum…
We analyze quantum communication properties of phase-covariant channels depending on their degree of non-unitality. In particular, we derive analytical formulas for minimal and maximal channel fidelity on pure states and maximal output…
A major challenge in quantum communication is addressing the negative effects of noise on channel capacity, especially for completely depolarizing channels, where information transmission is inherently impossible. The concept of indefinite…
It is widely accepted that noisy quantum devices are limited to logarithmic depth circuits unless mid-circuit measurements and error correction are employed. However, this conclusion holds only for unital error channels, such as…
The development of quantum walks in the context of quantum computation, as generalisations of random walk techniques, led rapidly to several new quantum algorithms. These all follow unitary quantum evolution, apart from the final…
Fault-tolerant quantum computing requires classical hardware to perform the decoding necessary for error correction. The Union-Find decoder is one of the best candidates for this. It has remarkably organic characteristics, involving the…
Channel polarization is a phenomenon in which a particular recursive encoding induces a set of synthesized channels from many instances of a memoryless channel, such that a fraction of the synthesized channels becomes near perfect for data…
Polar coding is a method for communication over noisy classical channels which is provably capacity-achieving and has an efficient encoding and decoding. Recently, this method has been generalized to the realm of quantum information…
In this work we aim at quantifying quantum channel output similarity. In order to achieve this, we introduce the notion of quantum channel superfidelity, which gives us an upper bound on the quantum channel fidelity. This quantity is…
Decoherence is a fundamental obstacle to the implementation of large-scale and low-noise quantum information processing devices. In this work, we suggest an approach for suppressing errors by employing pre-processing and post-processing…
With the rapid developments in quantum hardware comes a push towards the first practical applications on these devices. While fully fault-tolerant quantum computers may still be years away, one may ask if there exist intermediate forms of…
Quantum channels, a subset of quantum maps, describe the unitary and non-unitary evolution of quantum systems. We study a generalization of the concept of Pauli maps to the case of multipartite high dimensional quantum systems through the…
Conventional decoding algorithms for polar codes strive to balance achievable performance and computational complexity in classical computing. While maximum likelihood (ML) decoding guarantees optimal performance, its NP-hard nature makes…
The ability to transfer coherent quantum information between systems is a fundamental component of quantum technologies and leads to coherent correlations within the global quantum process. However correlation structures in quantum channels…
It is known that polar codes can be efficiently constructed for binary-input channels. At the same time, existing algorithms for general input alphabets are less practical because of high complexity. We address the construction problem for…
In crystalline solids, the electronic polarization follows the \emph{generalized Neumann's principle}, under which all crystallographic point groups can, in principle, support ferroelectric polarization. However, in high-symmetry…
Entanglement fidelity quantifies how well a quantum channel preserves the correlations between a transmitted system and an inaccessible reference system. We derive closed-form expressions for the entanglement fidelity associated with…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Quantum Computing in the Noisy Intermediate-Scale Quantum (NISQ) era has shown promising applications in machine learning, optimization, and cryptography. Despite the progress, challenges persist due to system noise, errors, and decoherence…