A quantum channel describes the general evolution of quantum systems, which is therefore a critical issue for quantum simulation and a fundamental element of quantum information. To realize quantum channels, an efficient method is to randomly implement Kraus operators, which does not require any ancillary quantum system. For open systems, it is natural to extend the method from implementation of unitary Kraus operators to nonunitary ones. However, when some Kraus operators are not proportional to unitary ones, this method becomes probabilistic even if the channel is trace preserving. In this paper, to overcome this drawback, we propose an algorithm to deterministically realize arbitrary trace-preserving channels with only one ancillary qubit and finite iterations of evolutions of the combined states of the system and the ancilla. Moreover, to show the validity of the method, we experimentally realize conventional and modified Landau-Streater channels based on the algorithm. Our results shed light on quantum simulation of quantum channels for open systems.
A quantum channel describes the general evolution of quantum systems, which is therefore a critical issue for quantum simulation and a fundamental element of quantum information. To realize quantum channels, an efficient method is to randomly implement Kraus operators, which does not require any ancillary quantum system. For open systems, it is natural to extend the method from implementation of unitary Kraus operators to nonunitary ones. However, when some Kraus operators are not proportional to unitary ones, this method becomes probabilistic even if the channel is trace preserving. In this paper, to overcome this drawback, we propose an algorithm to deterministically realize arbitrary trace-preserving channels with only one ancillary qubit and finite iterations of evolutions of the combined states of the system and the ancilla. Moreover, to show the validity of the method, we experimentally realize conventional and modified Landau-Streater channels based on the algorithm. Our results shed light on quantum simulation of quantum channels for open systems.
Quantum channels describe general transformations of the state of a physical system and play a fundamental role in many fields. It promises wide range of applications, because any physical process can be represented as a quantum channel transforming an initial state into a final state. The evolution of system undergoing a quantum channel is not necessary unitary which makes it unrealisable without ancillary system. Inspired by the method performing non-unitary operator by the linear combination of unitary operations, we proposed a quantum algorithm for the simulation of universal single-qubit channel, described by a convex combination of two generalized extreme channels corresponding to four Kraus operators, and is scalable to arbitrary higher dimension. We demonstrate the whole algorithm experimentally using the universal IBM cloud quantum computer and study properties of different qubit quantum channels. We illustrate the quantum capacity of the general qubit quantum channels, which quantifies the amount of quantum information that can be protected. There is a general agreement between the theoretical predictions and the experiments, which strongly supported our method. By realizing arbitrary qubit channel, this work provides a universal way to explore various properties of quantum channel and novel prospect of quantum communication.
The Solovay-Kitaev theorem allows us to approximate any single-qubit gate to arbitrary accuracy with a finite sequence of fundamental operations from a universal set of gates. Inspired by this decomposition, we present a quantum channel simulator capable of implementing any completely positive trace-preserving map. Our realization consists of one ancillary qubit, encoded in the transverse mode of a laser beam (orbital degree of freedom), one qubit system, encoded in its polarization (spin), one spin-orbit CNOT gate, and four single-qubit operations performed with prisms and polarization components. Our results describe the implementation of arbitrary single-qubit channels on the photon polarization using the transverse mode as the ancillary qubit.
We propose and theoretically study a method for the stochastic realization of arbitrary quantum channels on multimode single-photon qudits. In order for our method to be undemanding in its implementation, we restrict our analysis to linear-optical techniques, vacuum ancillary states, and nonadaptive schemes, but we allow for random switching between different optical networks. With our method it is possible to deterministically implement random-unitary channels and to stochastically implement general channels. We provide an expression for the optimal probability of success of our scheme and calculate this quantity for specific examples such as the qubit amplitude-damping channel. The success probability is shown to be related to the entanglement properties of the Choi-Jamio\l{}kowski state isomorphic to the channel.
Quantum control has been a cornerstone of quantum information science, driving major advances in quantum computing, quantum communication, and quantum sensing. Over the years, it has enabled the implementation of arbitrary completely positive and trace-preserving (CPTP) maps; an important next step is to extend control to Hermitian-preserving and trace-preserving (HPTP) maps, which underpin applications such as entanglement detection, quantum error mitigation, quantum simulation, and quantum machine learning. Here we present an efficient and fully constructive method for implementing arbitrary HPTP maps. Unlike existing methods that decompose an HPTP map into multiple CPTP maps or approximate it using bipartite Hamiltonians with large Hilbert spaces, our approach compiles a target HPTP map into a single executable CPTP map whose Kraus rank is guaranteed to be no larger than the intrinsic rank of the target HPTP map plus one, followed by simple classical post-processing. Numerical results for inverse noise channels used in quantum error mitigation, including bosonic photon loss, confirm substantial reductions in resources and highlight scalability in higher-dimensional settings. Together with our numerical benchmarks, these results validate the efficiency and versatility of the proposed framework, opening a route to broader quantum-information applications enabled by HPTP processing.
The main topic of this thesis is linear optics and the implementation of quantum operations (measurements, quantum channels, and unitary rotations) on optical systems. \nIn the opening chapter the basic notions needed to understand the rest of the thesis will be explained. \nThese notions include defining a quantum state, measurement, quantum channel and the linear optics tool set. \n \nThe work in this thesis takes both fundamental and practical approaches to studying linear optical networks. \nFor instance in the first chapter a proof is provided that shows that any unitary on a single mode Fock state can be realised with linear optics. \nThe proof is constructive, however the approach to realising the unitary is not suitable for experimental implementation \nbecause it requires complicated ancilla states. \nAs in the KLM proposal the procedure works only stochastically however by allowing the size of the ancilla to grow \nthe probability of failure can be made arbitrarly small. \n \nFurthermore we investigate the realisation of arbitrary channels in a specific encoding that we call a d-rail encoding. \nThe only ancilla state that we allow is a vacuum ancilliary state and further restrictions were considered (e.g. photon counting). \nA proof is provided that using these resources only random unitaries can be applied deterministically using linear optics. An expression for the optimal probability of success for realising \nmore general channels with these resources is also discussed. \n \nAs a final topic we also investigate the realisation of a quantum non-demolition measurement onto the dual rail qubit space. \nThe investigation is a blend of both fundamental and practical approaches. \nTo begin we employ a modified KLM-like procedure and show that the scheme can be realised perfectly but stochastically. \nThe probability that the proper measurement is made can be made arbitrarly close to one using a suitably large ancilla state. \nIn addition we consider an existing scheme \\cite{gisin10a} which uses practical sources (two single photon sources) to perform the measurement. \nThe scheme does not realise the true measurement but instead has a free parameter in it which is the transmittiviy of a beamsplitter. The measurement will project onto a space that has a vacuum component. By adjusting the transmittivity of this beamsplitter the vacuum component can be made arbitrarly small but only at the expense of the probability of success of the procedure. \nIn this thesis a modification that can be made to eliminate the vacuum component without changing the sources is introduced. The modification is surprisingly simple and only involves the addition of a single beamsplitter. In the proposal for the original amplifier it was used in simulations for DIQKD that included device imperfections. \nTo show the improvement of our modification these DIQKD simulations are reproduced using the modified amplifier and its results are compared to the results of the original amplifier.
This work presents a new protocol for simulating quantum systems based on quantum state preparation, with various applications such as the simulation of quantum channels and the implementation of general measurements. In general, these applications are modeled by quantum operations and involve completely positive trace-preserving (CPTP) maps. These maps correspond to sets of operators known as Kraus operators, when applied to the simulation of quantum channels, and general measurement operators, when applied to the implementation of non-selective measurements. In the literature, especially when the experimental platform is circuit-based quantum computing, these operators are employed to adjust the parameters of unitary matrices, which are the ones that actually operate in the experiment. To do this, it is necessary to solve a system of nonlinear equations numerically. The new protocol avoids these complications by applying the operators directly over the analytical description of the quantum systems to be simulated. Through the use of isometries and purifications, it models the quantum operations of interest to the experimentalist, whether they are quantum channels or general measurements, enabling the use of software libraries for symbolic algebra to perform exact and automated manipulation of the state vector, with complex amplitudes, to be prepared for simulation. The algebraic manipulation of the state vector provides greater flexibility in experimental planning, as it can be used on any quantum simulation platform. More specifically, it is not restricted to circuit-based quantum computing. Finally, the use of the new protocol is illustrated in the simulation of one-qubit channels, qudits, Lorentz transformations, mixed-state simulations, POVM implementation, and the certification of quantum contextuality via POVMs.