Related papers: Weak approximate unitary designs and applications …
We consider process tomography for unitary quantum channels. Given access to an unknown unitary channel acting on a $\textsf{d}$-dimensional qudit, we aim to output a classical description of a unitary that is $\varepsilon$-close to the…
The union-find decoder is a leading algorithmic approach to the correction of quantum errors on the surface code, achieving code thresholds comparable to minimum-weight perfect matching (MWPM) with amortised computational time scaling…
We propose a new cryptographic protocol. It is suggested to encode information in ordinary binary form into many-qubit entangled states with the help of a quantum computer. A state of qubits (realized, e.g., with photons) is transmitted…
Quantum computers promise to solve important problems faster than conventional computers. However, unleashing this power has been challenging. In particular, design automation runs into (1) the probabilistic nature of quantum computation…
We investigate the approximate quantum state sharing protocol based on random unitary channels, which is secure against any exterior or interior attackers in principle. Although the protocol leaks small information for a security parameter…
This paper addresses the problem of designing universal quantum circuits to transform $k$ uses of a $d$-dimensional unitary input-operation into a unitary output-operation in a probabilistic heralded manner. Three classes of protocols are…
We derive the effective channel for a logical qubit protected by an arbitrary quantum error-correcting code, and derive the map between channels induced by concatenation. For certain codes in the presence of single-bit Pauli errors, we…
Recently, Yamaguchi and Kempf [Phys. Rev. Lett. 136:010801, arXiv:2501.02757] proved that encrypted qubits can be cloned. In this work, we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum…
We establish fundamental mathematical limits on universal approximation theorem (UAT) system alignment by proving that catastrophic failures are an inescapable feature of any useful computational system. Our central thesis is that for any…
Unitary t-designs have a wide variety of applications in quantum information theory, such as quantum data encryption and randomised benchmarking. However, experimental realisations of t-designs are subject to noise. Here we investigate the…
We construct an optimal quantum universal variable-length code that achieves the admissible minimum rate, i.e., our code is used for any probability distribution of quantum states. Its probability of exceeding the admissible minimum rate…
Fault-tolerant quantum computing typically requires the transpilation of arbitrary quantum circuits into a finite, universal gate set, such as Clifford+T. As a baseline, Diagonal approximation can be used for synthesizing single-qubit Pauli…
We derive a new entropic quantum uncertainty relation involving min-entropy. The relation is tight and can be applied in various quantum-cryptographic settings. Protocols for quantum 1-out-of-2 Oblivious Transfer and quantum Bit Commitment…
We present for the first time, a bidirectional Quantum Key Distribution protocol with minimal encoding operations derived from the use of two `nonorthogonal' unitary transformations selected from two mutually unbiased unitary bases; which…
The main aim of this work is to present an explicit construction of a 2-design of ${\rm U}(2)$, relying only on a tool that belongs to every physicists toolbox: the theory of angular momentum. Unitary designs are a rich and fundamental…
Random unitary matrices sampled from the uniform Haar ensemble have a number of important applications both in cryptography and in the simulation of a variety of fundamental physical systems. Since the Haar ensemble is very expensive to…
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…
A major line of questions in quantum information and computing asks how quickly locally random circuits converge to resemble global randomness. In particular, approximate k-designs are random unitary ensembles that resemble random circuits…
Topological quantum computing promises intrinsic fault tolerance by encoding quantum information in non-Abelian anyons, where quantum gates are implemented via braiding. While braiding operations are robust against local perturbations, a…
We address the question of existence of private quantum channel for qubits encoded in polarization degrees of freedom of a photon, that remains secure even if multi-photon (instead of single-photon) pulse is emitted. We show that random…