Related papers: Learning quantum graph states with product measure…
Let $H$ be a fixed $k$-vertex graph with $m$ edges and minimum degree $d >0$. We use the learning graph framework of Belovs to show that the bounded-error quantum query complexity of determining if an $n$-vertex graph contains $H$ as a…
Accurate control of quantum states is crucial for quantum computing and other quantum technologies. In the basic scenario, the task is to steer a quantum system towards a target state through a sequence of control operations. Determining…
Real-world data is often times associated with irregular structures that can analytically be represented as graphs. Having access to this graph, which is sometimes trivially evident from domain knowledge, provides a better representation of…
The entanglement of graph states up to eight qubits is calculated in the regime of iteration calculation. The entanglement measures could be the relative entropy of entanglement, the logarithmic robustness or the geometric measure. All 146…
In this work, we consider the fundamental task of quantum state certification: given copies of an unknown quantum state $\rho$, test whether it matches some target state $\sigma$ or is $\epsilon$-far from it. For certifying $d$-dimensional…
Suppose that there is a family of $n$ random points $X_v$ for $v \in V$, independently and uniformly distributed in the square $\left[-\sqrt{n}/2,\sqrt{n}/2\right]^2$ of area $n$. We do not see these points, but learn about them in one of…
Graph states play an important role in quantum information theory through their connection to measurement-based computing and error correction. Prior work has revealed elegant connections between the graph structure of these states and…
Distinguishing sets of quantum states shared by two parties using only local operations and classical communication measurements is a fundamental topic in quantum communication and quantum information theory. We introduce a graph-theoretic…
In quantum computing and quantum information processing, graph states are a specific type of quantum states which are commonly used in quantum networking and quantum error correction. A recurring problem is finding a transformation from a…
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…
Distance measures provide the foundation for many popular algorithms in Machine Learning and Pattern Recognition. Different notions of distance can be used depending on the types of the data the algorithm is working on. For graph-shaped…
While quantum state tomography is notoriously hard, most states hold little interest to practically-minded tomographers. Given that states and unitaries appearing in Nature are of bounded gate complexity, it is natural to ask if efficient…
We consider the problem of learning low-degree quantum objects up to $\varepsilon$-error in $\ell_2$-distance. We show the following results: $(i)$ unknown $n$-qubit degree-$d$ (in the Pauli basis) quantum channels and unitaries can be…
Graph states are ubiquitous in quantum information with diverse applications ranging from quantum network protocols to measurement based quantum computing. Here we consider the question whether one graph (source) state can be transformed…
Quantum state learning is a fundamental problem in physics and computer science. As near-term quantum devices are error-prone, it is important to design error-resistant algorithms. Apart from device errors, other unexpected factors could…
In a previous version of this document we misinterpreted the runtime of a part of the described algorithm. Indeed, the runtime is not better than the Grover-Algorithm. We therefor withdraw this work. We present a novel algorithmic approach…
In this work we are interested the problem of testing quantum entanglement. More specifically, we study the separability problem in quantum property testing, where one is given $n$ copies of an unknown mixed quantum state $\varrho$ on…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
Quantum graph state is a special class of nonlocal state among multiple quantum particles, underpinning several nonclassical and promising applications such as quantum computing and quantum secret sharing. Recently, establishing quantum…
We show how to optimally discriminate between K distinct quantum states, of which N copies are available, using one-at-a-time interactions with each of the N copies. While this task (famously) requires joint measurements on all N copies, we…