Related papers: Quantum Proofs
$\text{MIP}^\ast$ is the class of languages decidable by an efficient classical verifier interacting with multiple quantum provers that share entangled qubits but cannot communicate. Notably, $\text{MIP}^\ast$ was proved to equal…
Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways,…
The quest for quantum computers is motivated by their potential for solving problems that defy existing, classical, computers. The theory of computational complexity, one of the crown jewels of computer science, provides a rigorous…
During the last ten years, superconducting circuits have passed from being interesting physical devices to becoming contenders for near-future useful and scalable quantum information processing (QIP). Advanced quantum simulation experiments…
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 consider the problem of testing and learning from data in the presence of resource constraints, such as limited memory or weak data access, which place limitations on the efficiency and feasibility of testing or learning. In particular,…
The main contribution of this paper is the introduction of a dynamic logic formalism for reasoning about information flow in composite quantum systems. This builds on our previous work on a complete quantum dynamic logic for single systems.…
We prove that the complexity class QIP, which consists of all problems having quantum interactive proof systems, is contained in PSPACE. This containment is proved by applying a parallelized form of the matrix multiplicative weights update…
Quantum Image Processing (QIP)is an exciting new field showing a lot of promise as a powerful addition to the arsenal of Image Processing techniques. Representing image pixel by pixel using classical information requires an enormous amount…
We show that every language in QMA admits a classical-verifier, quantum-prover zero-knowledge argument system which is sound against quantum polynomial-time provers and zero-knowledge for classical (and quantum) polynomial-time verifiers.…
Complexity theory traditionally studies the hardness of solving classical computational problems. In the quantum setting, it is also natural to consider a different notion of complexity, namely the complexity of physically preparing a…
We introduce two models of space-bounded quantum interactive proof systems, ${\sf QIPL}$ and ${\sf QIP_{\rm U}L}$. The ${\sf QIP_{\rm U}L}$ model, a space-bounded variant of quantum interactive proofs (${\sf QIP}$) introduced by Watrous (CC…
We prove that QIP(2), the class of problems having two-message quantum interactive proof systems, is a subset of PSPACE. This relationship is obtained by means of an efficient parallel algorithm, based on the multiplicative weights update…
We show that the class QMA does not change even if we restrict Arthur's computing ability to only Clifford gate operations (plus classical XOR gate). The idea is to use the fact that the preparation of certain single-qubit states, so called…
If two classical provers share an entangled state, the resulting interactive proof system is significantly weakened [quant-ph/0404076]. We show that for the case where the verifier computes the XOR of two binary answers, the resulting proof…
The enormous theoretical potential of Quantum Information Processing (QIP) is driving the pursuit for its practical realization by various physical techniques. Currently Nuclear Magnetic Resonance (NMR) has been the forerunner by…
In classical complexity theory, the two definitions of probabilistically checkable proofs -- the constraint satisfaction and the nonlocal games version -- are computationally equal in power. In the quantum setting, the situation is far less…
The general-purpose interactive theorem-proving assistant called Prove-It was used to verify the Quantum Phase Estimation (QPE) algorithm, specifically claims about its outcome probabilities. Prove-It is unique in its ability to express…
Faster algorithms, novel cryptographic mechanisms, and alternative methods of communication become possible when the model underlying information and computation changes from a classical mechanical model to a quantum mechanical one. Quantum…
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent…