Quantum Lower Bounds by Quantum Arguments

Quantum Lower Bounds by Quantum Arguments1

Quantum lower bounds by entropy numbers

We use entropy numbers in combination with the polynomial method to derive a new general lower bound for the n-th minimal error in the quantum setting of information-based complexity. As an application, we improve some lower bounds on quantum approximation of embeddings between finite dimensional Lp spaces and of Sobolev embeddings.

Quantum lower bounds for fanout

We consider the resource bounded quantum circuit model with circuits restricted by the number of qubits they act upon and by their depth. Focusing on natural universal sets of gates which are familiar from classical circuit theory, several new lower bounds for constant depth quantum circuits are proved. The main result is that parity (and hence fanout) requires log depth quantum circuits, when ...

Lower Bounds for Quantum Search and Derandomization

We prove lower bounds on the error probability of a quantum algorithm for searching through an unordered list of N items, as a function of the number T of queries it makes. In particular, if T ∈ O( √ N) then the error is lower bounded by a constant. If we want error ≤ 1/2 then we need T ∈ Ω(N) queries. We apply this to show that a quantum computer cannot do much better than a classical computer...

Lower bounds for Quantum Oblivious Transfer

Oblivious transfer is a fundamental primitive in cryptography. While perfect information theoretic security is impossible, quantum oblivious transfer protocols can limit the dishonest players’ cheating. Finding the optimal security parameters in such protocols is an important open question. In this paper we show that every 1-out-of-2 oblivious transfer protocol allows a dishonest party to cheat...