Related papers: Approximate k-uniform states: definition, construc…
We establish connections between state tomography, pseudorandomness, quantum state synthesis, and circuit lower bounds. In particular, let $\mathfrak{C}$ be a family of non-uniform quantum circuits of polynomial size and suppose that there…
Haar random states are fundamental objects in quantum information theory and quantum computing. We study the density matrix resulting from sampling $t$ copies of a $d$-dimensional quantum state according to the Haar measure on the…
We investigate the maximum purity that can be achieved by k-uniform mixed states of N parties. Such N-party states have the property that all their k-party reduced states are maximally mixed. A scheme to construct explicitly k-uniform…
We prove a quantum information-theoretic conjecture due to Ji, Liu and Song (CRYPTO 2018) which suggested that a uniform superposition with random \emph{binary} phase is statistically indistinguishable from a Haar random state. That is, any…
Masking information into quantum correlations is a cornerstone of many quantum information applications. While there exist the no-hiding and no-masking theorems, approximate quantum information masking (AQIM) offers a promising means of…
We introduce several classes of quantum combinatorial designs, namely quantum Latin squares, cubes, hypercubes and a notion of orthogonality between them. A further introduced notion, quantum orthogonal arrays, generalizes all previous…
An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge…
Understanding the complexity of quantum states and circuits is a central challenge in quantum information science, with broad implications in many-body physics, high-energy physics and quantum learning theory. A common way to model the…
We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix…
The existence of pseudorandom unitaries (PRUs) -- efficient quantum circuits that are computationally indistinguishable from Haar-random unitaries -- has been a central open question, with significant implications for cryptography,…
We consider the problem of efficiently simulating random quantum states and random unitary operators, in a manner which is convincing to unbounded adversaries with black-box oracle access. This problem has previously only been considered…
Estimation of quantum states and measurements is crucial for the implementation of quantum information protocols. The standard method for each is quantum tomography. However, quantum tomography suffers from systematic errors caused by…
Computing many-body ground state energies and resolving electronic structure calculations are fundamental problems for fields such as quantum chemistry or condensed matter. Several quantum computing algorithms that address these problems…
Measurement based (MB) quantum computation allows for universal quantum computing by measuring individual qubits prepared in entangled multipartite states, known as graph states. Unless corrected for, the randomness of the measurements…
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with…
In this paper we consider the problem of unambiguous discrimination between a set of linearly independent pure quantum states. We show that the design of the optimal measurement that minimizes the probability of an inconclusive result can…
We show how to efficiently generate pseudo-random states suitable for quantum information processing via cluster-state quantum computation. By reformulating pseudo-random algorithms in the cluster-state picture, we identify a strategy for…
A common requirement of quantum simulations and algorithms is the preparation of complex states through sequences of 2-qubit gates. For a generic quantum state, the number of gates grows exponentially with the number of qubits, becoming…
This thesis discusses the young fields of quantum pseudo-randomness and quantum learning algorithms. We present techniques for derandomising algorithms to decrease randomness resource requirements and improve efficiency. One key object in…
Hyperuniform many-particle systems are characterized by a structure factor $S({\mathbf{k}})$ that is precisely zero as $|\mathbf{k}|\rightarrow0$; and stealthy hyperuniform systems have $S({\mathbf{k}})=0$ for the finite range $0 <…