Related papers: Succinct quantum proofs for properties of finite g…
Ring signatures are a powerful primitive that allows a member to sign on behalf of a group, without revealing their identity. Recently, ring signatures have received additional attention as an ingredient for post-quantum deniable…
Randomness is a key feature of quantum physics. Heisenberg's uncertainty principle reveals the existence of an intrinsic noise, usually explored through Gaussian squeezed states. Due to their insufficiency for quantum advantage, the focus…
Quantum state discrimination plays a central role in defining the possible and impossible operations through a restricted class of quantum operations. A seminal result by Bennett et al. [Phys. Rev. A 59, 1070 (1999)] demonstrates the…
We prove tight lower bounds for the following variant of the counting problem considered by Aaronson, Kothari, Kretschmer, and Thaler (2020). The task is to distinguish whether an input set $x\subseteq [n]$ has size either $k$ or…
We introduce a general method for the construction of quasiprobability representations for arbitrary notions of quantum coherence. Our technique yields a nonnegative probability distribution for the decomposition of any classical state.…
We study the computational complexity of quantum state isomorphism problems under group actions: given two quantum circuits that prepare pure or mixed states, decide whether the two states are related by a group action. This can be seen as…
The hardness to solve an unstructured quantum search problem by a standard quantum search algorithm mainly originates from the low efficiency to amplify the amplitude of the marked state by the oracle unitary operation associated with other…
Quantum mechanics provides a statistical description about nature, and thus would be incomplete if its statistical predictions could not be accounted for by some realistic models with hidden variables. There are, however, two powerful…
Bit commitment schemes are at the basis of modern cryptography. Since information-theoretic security is impossible both in the classical and the quantum regime, we need to look at computationally secure commitment schemes. In this paper, we…
Quantum computation with quantum data that can traverse closed timelike curves represents a new physical model of computation. We argue that a model of quantum computation in the presence of closed timelike curves can be formulated which…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…
We present authorized quantum computation, where only a user with a non-cloneable quantum authorization key can perform a unitary operation created by an authenticated programmer. The security of our authorized quantum computation is based…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
We study how the choices made when designing an oracle affect the complexity of quantum property testing problems defined relative to this oracle. We encode a regular graph of even degree as an invertible function $f$, and present $f$ in…
Various techniques have been used in recent years for verifying quantum computers, that is, for determining whether a quantum computer/system satisfies a given formal specification of correctness. Barrier certificates are a recent novel…
The rank of a finite algebraic structure with a single binary operation is the minimum number of elements needed to express every other element under the closure of the operation. In the case of groups, the previous best algorithm for…
Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the…
The quantum PCP (QPCP) conjecture states that all problems in QMA, the quantum analogue of NP, admit quantum verifiers that only act on a constant number of qubits of a polynomial size quantum proof and have a constant gap between…
We investigate the intersection problem for finite semigroups, which asks for a given set of regular languages, represented by recognizing morphisms to finite semigroups, whether there exists a word contained in their intersection. We…
Quantum computational pseudorandomness has emerged as a fundamental notion that spans connections to complexity theory, cryptography and fundamental physics. However, all known constructions of efficient quantum-secure pseudorandom objects…