Related papers: A distribution testing oracle separation between Q…
For any function $f: X \times Y \to Z$, we prove that $Q^{*\text{cc}}(f) \cdot Q^{\text{OIP}}(f) \cdot (\log Q^{\text{OIP}}(f) + \log |Z|) \geq \Omega(\log |X|)$. Here, $Q^{*\text{cc}}(f)$ denotes the bounded-error communication complexity…
The determination of a quantum observable from the first and second moments of its measurement outcome statistics is investigated. Operational conditions for the moments of a probability measure are given which suffice to determine the…
Nonclassical states of light are necessary resources for quantum technologies such as cryptography, computation and the definition of metrological standards. Observing signatures of nonclassicality generally requires inferring either the…
Oracle quantum programs are a fundamental class of quantum programs that serve as a critical bridge between quantum computing and classical computing. Many important quantum algorithms are built upon oracle quantum programs, making it…
Quantum data access and quantum processing can make certain classically intractable learning tasks feasible. However, quantum capabilities will only be available to a select few in the near future. Thus, reliable schemes that allow…
Random quantum circuits continue to inspire a wide range of applications in quantum information science and many-body quantum physics, while remaining analytically tractable through probabilistic methods. Motivated by an interest in…
Any Quantum Key Distribution (QKD) protocol consists first of sequences of measurements that produce some correlation between classical data. We show that these correlation data must violate some Bell inequality in order to contain…
We construct a classical oracle relative to which $\mathsf{P} = \mathsf{NP}$ but quantum-computable quantum-secure trapdoor one-way functions exist. This is a substantial strengthening of the result of Kretschmer, Qian, Sinha, and Tal (STOC…
The power of quantum computers is still somewhat speculative. While they are certainly faster than classical ones at some tasks, the class of problems they can efficiently solve has not been mapped definitively onto known classical…
Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective for most classical machine learning algorithms. This ceases to be true in quantum learning, where many settings do not admit, neither an SQ analog nor a quantum…
The states accepted by a quantum circuit are known as the witnesses for the quantum circuit's satisfiability. The assumption BQP does not equal QMA implies that no efficient algorithm exists for constructing a witness for a quantum circuit…
The multiple-quantum operator algebra formalism has been exploited to construct generally an unsorted quantum search algorithm. The exponential propagator and its corresponding effective Hamiltonian are constructed explicitly that describe…
We initiate the study of parameterized complexity of $\textsf{QMA}$ problems in terms of the number of non-Clifford gates in the problem description. We show that for the problem of parameterized quantum circuit satisfiability, there exists…
The class QMA plays a fundamental role in quantum complexity theory and it has found surprising connections to condensed matter physics and in particular in the study of the minimum energy of quantum systems. In this paper, we further…
We consider ontological models of a quantum system, assuming that not all probability distributions over the space $\Lambda$ of ontic states are preparable, only those belonging to a certain set C. We assume further that every POVM with a…
Originally, quantum probability theory was developed to analyze statistical phenomena in quantum systems, where classical probability theory does not apply, because the lattice of measurable sets is not necessarily distributive. On the…
The framework of distribution testing is currently ubiquitous in the field of property testing. In this model, the input is a probability distribution accessible via independently drawn samples from an oracle. The testing task is to…
We consider the problem of secure key distribution among $n$ trustful agents: the goal is to distribute an identical random bit-string among the $n$ agents over a noisy channel such that eavesdroppers learn little about it. We study the…
In this paper, the space complexity of nonuniform quantum computations is investigated. The model chosen for this are quantum branching programs, which provide a graphic description of sequential quantum algorithms. In the first part of the…
In this paper we study the separation between the deterministic (classical) query complexity ($D$) and the exact quantum query complexity ($Q_E$) of several Boolean function classes using the parity decision tree method. We first define the…