Related papers: Probabilistic and approximate universal quantum pu…

Pure quantum states play a central role in applications of quantum information, both as initial states for many algorithms and as resources for quantum error correction. Preparation of highly pure states that satisfy the threshold for…

The inevitable accumulation of errors in near-future quantum devices represents a key obstacle in delivering practical quantum advantages, motivating the development of various quantum error-mitigation methods. Here, we derive fundamental…

We propose a versatile strategy for numerical renormalization group solution of general channel-mixing Kondo and Anderson models beyond previous reach, opening the door toward broad applications in protocol non-perturbative machineries,…

This PHD thesis is concerned with uncertainty relations in quantum probability theory, state estimation in quantum stochastics, and natural bundles in differential geometry. After some comments on the nature and necessity of decoherence in…

Given an ensemble of mixed qubit states, it is possible to increase the purity of the constituent states using a procedure known as state purification. The reverse operation, which we refer to as dilution, reduces the level of purity…

Entanglement purification is a very important element for long-distance quantum communication. Different from all the existing entanglement purification protocols (EPPs) in which two parties can only obtain some quantum systems in a mixed…

In this work we initiate the question of whether quantum devices can provide us with an almost perfect source of classical randomness, and more generally, suffice for classical cryptographic tasks, such as encryption. Indeed, it is well…

We provide a general method to calculate and maximize the purity of a qubit interacting with an anisotropic non-Markovian environment. Counter to intuition, we find that the purity is often maximized by preparing and storing the qubit in a…

Generative quantum machine learning has gained significant attention for its ability to produce quantum states with desired distributions. Among various quantum generative models, quantum denoising diffusion probabilistic models (QuDDPMs)…

Quantum purity amplification (QPA) provides a novel approach to counteracting the pervasive noise that degrades quantum states. We present the optimal QPA protocol for general quantum systems and global noise, resolving a two-decade open…

We demonstrate how insights gained from reformulating the problem of quantum teleportation into one of reversing quantum operations, and designing optimum completely positive maps for teleportation, can enable one to explore optimal…

Since its discovery, the quantum entanglement becomes a promising resource in quantum communication and computation. However, the entanglement is fragile due to the presence of noise in quantum channels. Entanglement purification is a…

Quantum algorithms profit from the interference of quantum states in an exponentially large Hilbert space and the fact that unitary transformations on that Hilbert space can be broken down to universal gates that act only on one or two…

We introduce a quantity called the coherence of purification which can be a measure of total quantumness for a single system. We prove that coherence of purification is always more than the coherence of the system. For a pure state, the…

Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…

We propose a novel optimization scheme designed to find optimally correctable subspace codes for a known quantum noise channel. To each candidate subspace code we first associate a universal recovery map, as if the code was perfectly…

We present a general theory of comparison of quantum channels, concerning with the question of simulability or approximate simulability of a given quantum channel by allowed transformations of another given channel. We introduce a…

We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem…

A fundamental task in quantum information science is to measure nonlinear functionals of quantum states, such as $\mathrm{Tr}(\rho^k O)$. Intuitively, one expects that computing a $k$-th order quantity generally requires $O(k)$ copies of…

Random quantum circuits have played a central role in establishing the computational advantages of near-term quantum computers over their conventional counterparts. Here, we use ensembles of low-depth random circuits with local connectivity…