arXiv subjects

Jaroslav Kysela

Publications and source records attributed to Jaroslav Kysela.

11 recordsLinked to original sources

arXiv2026

YZ-plane measurement-based quantum computation: Universality and Parity Architecture implementation

We define the class of register-logic graphs and prove that any uniformly deterministic measurement-based quantum computation (MBQC) where the inputs coincide with the outputs must be driven on such graphs by measurements in the $YZ$ plane of the Bloch sphere. This observation is revisited in the context that goes beyond uniform determinism, where we present a universal $YZ$-plane-only measurement pattern and establish a connection between $YZ$-plane-only and $XZ$-plane-only patterns. These results conclude the line of research on universal patterns with measurements restricted to one of the principal planes of the Bloch sphere. We further demonstrate, within the framework of the Parity Architecture, that $YZ$-plane patterns with the register-logic graph can be embedded into another graph with purely local interactions, and we extend this case to the scenario of universal quantum computation.

quant-ph↗

arXiv2025

Subjective nature of path information in quantum mechanics

Common sense suggests that a particle must have a definite origin if its full path information is available. In quantum mechanics, the knowledge of path information is captured through the well-established duality relation between path distinguishability and interference visibility. If visibility is zero, high path distinguishability can be achieved, which enables one to determine with high predictive power where the particle originates. We investigate the complementarity between path information and interference visibility through an experiment involving three sources emitting into identical modes. Our findings challenge the classical intuition that a particle can be traced back to its origin through its trajectory when full path information is available. By grouping the crystals in different ways, we demonstrate that it is impossible to ascribe a definite physical origin to the photon pair, even if the emission probability of one individual source is zero and full path information is available. Our results shed new light on the physical interpretation of probability assignment and path information beyond its mathematical meaning and show that the interpretation of path information in quantum mechanics is subjective.

quant-ph↗

arXiv2024

Visibility Stokes parameters as a foundation for quantum information science with undetected photons

The framework of measurement operators plays a fundamental role in extracting information about quantum systems. Recently, techniques based on induced coherence have been developed to access the same information for undetected photons. However, there has been a lack of consistent reformulation of quantum operators for these techniques. In this work, we introduce a set of parameters that quantify the polarization of undetected photons based on measured visibilities. Given their similarity to classical counterparts, we refer to them as visibility Stokes parameters. We apply these parameters and the corresponding quantum operators to the problem of quantum state tomography, thoroughly analyzing the environment of undetected photons and its role in the reconstruction process. Because these parameters provide a more intuitive and consistent understanding of the measurement process, we believe that some established quantum information protocols could be adapted for undetected photons.

quant-ph↗

arXiv2023

State independent QKD

We present an adaptive procedure for aligning quantum non-locality experiments without any knowledge of the two-qudit state shared by the participating parties. The quantum state produced by the source, its unitary evolution as well as the actual measurement bases remain unknown to both parties at all times. The entanglement of the quantum state helps establish desired correlations between individual measurement bases of the two distant parties. We implement the procedure in a fiber-based quantum key distribution (QKD) setup with polarization-entangled photons, where we do not rely on any additional alignment tools such as lasers or polarizers. In a QKD scenario the procedure can be done without any additional measurements as those that are performed regardless.

quant-ph↗

arXiv2023

Quantum state tomography of undetected photons

The measurement of quantum states is one of the most important problems in quantum mechanics. We introduce a quantum state tomography technique in which the state of a qubit is reconstructed, while the qubit remains undetected. The key ingredients are: (i) employing an additional qubit, (ii) aligning the undetected qubit with a known reference state by using path identity, and (iii) measuring the additional qubit to reconstruct the undetected qubit state. We theoretically establish and experimentally demonstrate the method with photonic polarization states. The principle underlying our method could also be applied to quantum entities other than photons.

quant-ph↗

arXiv2022

Arbitrary unitaries in orbital angular momentum of single photons

A simple argument is presented that explicitly shows how to construct an arbitrary quantum gate acting on orbital angular momentum (OAM) of single photons. The scheme can be applied to implement subspace multiplexing, where a single high-dimensional OAM qudit represents effectively a stack of multiple independent lower-dimensional qudits. A special subclass of unitaries composed of single-photon controlled gates is studied in detail and notable examples of the general approach are discussed. The generalization of the simple argument leads to the parallelization scheme, which results in the savings of resources. The presented schemes utilize only conventional optical elements and apply not only to single photons but also to classical light.

quant-ph↗

arXiv2021

High-dimensional quantum Fourier transform of twisted light

The Fourier transform proves indispensable in the processing of classical information as well as in the quantum domain, where it finds many applications ranging from state reconstruction to prime factoring. An implementation scheme of the $d$-dimensional Fourier transform acting on single photons is known that uses the path encoding and requires $O(d \log d)$ optical elements. In this paper we present an alternative design that uses the orbital angular momentum as a carrier of information and needs only $O(\sqrt{d}\log d)$ elements, rendering the path-encoded design inefficient. The advantageous scaling and the fact that our approach uses only conventional optical elements allows for the implementation of a 256-dimensional Fourier transform with the existing technology. Improvements to our design, as well as explicit setups for low dimensions, are also presented.

quant-ph↗

arXiv2020

Fourier Transform of the Orbital Angular Momentum of a Single Photon

Optical networks implementing single-qudit quantum computation gates may exhibit superior properties to those for qubits as each of the optical elements in the network can work in parallel on many optical modes simultaneously. We present an important class of such networks, that implements in a deterministic and efficient way the quantum Fourier transform (QFT) in an arbitrarily large dimension. These networks redistribute the initial quantum state into the path and orbital angular momentum (OAM) degrees of freedom and exhibit two modes of operation. Either the OAM-only QFT can be implemented, which uses the path as an internal auxiliary degree of freedom, or the path-only QFT is implemented, which uses the OAM as the auxiliary degree of freedom. The resources for both schemes scale linearly $O(d)$ with the dimension $d$ of the system, beating the best known bounds for the path-encoded QFT. While the QFT of the orbital angular momentum states of single photons has been applied in a multitude of experiments, these schemes require specially designed elements with non-trivial phase profiles. In contrast, we present a different approach that utilizes only conventional optical elements.

quant-ph↗

arXiv2019

Deterministic Twirling with Low Resources

Twirling operations, which average a quantum state with respect to a unitary subgroup, have become a frequently-employed tool in quantum information processing. We investigate the efficient implementation of twirling operations with minimal resources, without necessitating the ability to perform all possible unitary operations on the quantum system of interest. We present a general algebraic method allowing us to choose a set of - typically very few - unitary operators which, when applied randomly and repeatedly, produce the given twirling operation exponentially quickly. The method is applied to twirling operations for bipartite quantum systems with respect to the unitary group $U(d)\otimes U(d)$, an essential ingredient in entanglement distillation protocols. In particular, we provide a complete classification of sets of unitary operators capable of performing twirling on two qubits. Moreover, we construct a generic set containing at most three unitary operators achieving the twirling operation for a general two-qudit system.

quant-ph↗

arXiv2019

Experimental High-Dimensional Entanglement by Path Identity

Versatile and high-brightness sources of high-dimensional entangled photon pairs are important for emerging quantum technologies such as secure quantum communication. Here, we experimentally demonstrate a new scalable method to create photon pairs carrying orbital angular momentum that are entangled in arbitrarily high dimensions. Our method relies on indistinguishable photon pairs created coherently in different sources. We demonstrate the creation of three-dimensionally entangled states and show how to incrementally increase the dimensionality of entanglement. The generated states retain their quality even in higher dimensions. In addition, the modular structure of our approach allows for generalization to various degrees of freedom and even implementation in integrated compact devices. We therefore expect that future quantum technologies and fundamental tests of nature in higher dimensions will benefit from this novel approach.

quant-ph↗

arXiv2018

Arbitrary d-dimensional Pauli X-Gates of a flying Qudit

High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform lossless arbitrary high-dimensional Pauli-X gates for single photon. The X-gate consists of a cyclic permutation of qudit basis vectors, and, together with the Z gate, forms the basis for performing arbitrary transformations. We propose an implementation of such gates on the orbital angular momentum of photons. The proposed experimental setups only use two basic optical elements such as mode-sorters and mode-shifters -- thus could be implemented in any system where these experimental tools are available. Furthermore the number of involved interferometers scales logarithmically with the dimension, which is important for practical implementation.

quant-ph↗