Related papers: A distribution testing oracle separation between Q…
Algorithms with unitary oracles can be nested, which makes them extremely versatile. An example is the phase estimation algorithm used in many candidate algorithms for quantum speed-up. The search for new quantum algorithms benefits from…
The class MA consists of languages that can be efficiently verified by classical probabilistic verifiers using a single classical certificate, and the class QMA consists of languages that can be efficiently verified by quantum verifiers…
A typical oracle problem is finding which software program is installed on a computer, by running the computer and testing its input-output behaviour. The program is randomly chosen from a set of programs known to the problem solver. As…
We describe a general framework for regarding oracle-assisted quantum algorithms as tools for discriminating between unitary transformations. We apply this to the Deutsch-Jozsa problem and derive all possible quantum algorithms which solve…
In this paper we consider a quantum computational variant of nondeterminism based on the notion of a quantum proof, which is a quantum state that plays a role similar to a certificate in an NP-type proof. Specifically, we consider quantum…
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Kernel methods are ubiquitous in classical machine learning, and recently their formal similarity with quantum mechanics has been established. To grasp the potential advantage of quantum machine learning, it is necessary to understand the…
A dynamical quantum model assigns an eigenstate to a specified observable even when no measurement is made, and gives a stochastic evolution rule for that eigenstate. Such a model yields a distribution over classical histories of a quantum…
Quantum sampling, a fundamental subroutine in numerous quantum algorithms, involves encoding a given probability distribution in the amplitudes of a pure state. Given the hefty cost of large-scale quantum storage, we initiate the study of…
It is an established fact that for many of the interesting problems quantum algorithms based on queries of the standard oracle bring no significant improvement in comparison to known classical algorithms. It is conceivable that there are…
We demonstrate that a necessary precondition for unconditionally secure quantum key distribution is that sender and receiver can use the available measurement results to prove the presence of entanglement in a quantum state that is…
Mahadev [SIAM J. Comput. 2022] introduced the first protocol for classical verification of quantum computation based on the Learning-with-Errors (LWE) assumption, achieving a 4-message interactive scheme. This breakthrough naturally raised…
Existing protocols for classical verification of quantum computation (CVQC) consume the prover's witness state, requiring a new witness state for each invocation. Because QMA witnesses are not generally clonable, destroying the input…
We investigate quantum analogues of collision resistance and obtain separations between quantum ``one-way'' and ``collision-resistant'' primitives. 1. Our first result studies one-wayness versus collision-resistance defined over quantum…
We present several new examples of speed-ups obtainable by quantum algorithms in the context of property testing. First, motivated by sampling algorithms, we consider probability distributions given in the form of an oracle $f:[n]\to[m]$.…
Quantum Darwinism is a compelling theory that describes the quantum-to classical transition as the emergence of objectivity of quantum systems. Spectrum broadcast structure and strong quantum Darwinism are two extensions of this theory with…
Quantum key distribution is widely thought to offer unconditional security in communication between two users. Unfortunately, a widely accepted proof of its security in the presence of source, device and channel noises has been missing.…
We study the long-standing open question on the power of unique witnesses in quantum protocols, which asks if $\textsf{UniqueQMA}$, a variant of $\textsf{QMA}$ whose accepting witness space is 1-dimensional, contains $\mathsf{QMA}$ under…
We initiate the study of quantum Interactive Oracle Proofs (qIOPs), a generalization of both quantum Probabilistically Checkable Proofs and quantum Interactive Proofs, as well as a quantum analogue of classical Interactive Oracle Proofs. In…
We consider the problem of testing the dimension of uncharacterised classical and quantum systems in a prepare-and-measure setup. Here we assume the preparation and measurement devices to be independent, thereby making the problem…