Related papers: Quantum Pseudorandomness and Classical Complexity
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
We present a polynomial-time quantum algorithm making a single query (in superposition) to a classical oracle, such that for every state $|\psi\rangle$ there exists a choice of oracle that makes the algorithm construct an exponentially…
Although a quantum state requires exponentially many classical bits to describe, the laws of quantum mechanics impose severe restrictions on how that state can be accessed. This paper shows in three settings that quantum messages have only…
Quantum information science explores the frontier of highly complex quantum states, the "entanglement frontier." This study is motivated by the observation (widely believed but unproven) that classical systems cannot simulate highly…
Quantum entanglement and nonlocality are inequivalent notions: There exist entangled states that nevertheless admit local-realistic interpretations. This paper studies a special class of local-hidden-variable theories, in which the linear…
The existence of entangled quantum states gives extra power to quantum computers over their classical counterparts. Quantum entanglement shows up qualitatively at the level of two qubits. We show that if no entanglement is envolved then…
We consider the power of various quantum complexity classes with the restriction that states and operators are defined over a real, rather than complex, Hilbert space. It is well know that a quantum circuit over the complex numbers can be…
The quantum component in uncertainty relation can be naturally characterized by the quantum coherence of a quantum state, which is of paramount importance in quantum information science. Here, we experimentally investigate quantum…
We find a modification to QMA where having one quantum proof is strictly less powerful than having two unentangled proofs, assuming EXP $\ne$ NEXP. This gives a new route to prove QMA(2) = NEXP that overcomes the primary drawback of a…
A pseudorandom quantum state (PRS) is an ensemble of quantum states indistinguishable from Haar-random states to observers with efficient quantum computers. It allows one to substitute the costly Haar-random state with efficiently…
A characteristical property of a classical physical theory is that the observables are real functions taking an exact outcome on every (pure) state; in a quantum theory, at the contrary, a given observable on a given state can take several…
Quantum computing hardware has grown sufficiently complex that it often can no longer be simulated by classical computers, but its computational power remains limited by errors. These errors corrupt the results of quantum algorithms, and it…
A sufficient condition for a quantum state of a system of spin-1/2 particles (spin-1/2s) to admit a local hidden variable (LHV) description i.e. to be classical is the separability of the density matrix characterizing its state, but not all…
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…
We discuss a model for quantum computing with initially mixed states. Although such a computer is known to be less powerful than a quantum computer operating with pure (entangled) states, it may efficiently solve some problems for which no…
One of the most fundamental results in classical cryptography is that the existence of Pseudo-Random Generators (PRG) that expands $k$ bits of randomness to $k+1$ bits that are pseudo-random implies the existence of PRG that expand $k$ bits…
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…
Classical programming languages cannot model essential elements of complex systems such as true random number generation. This paper develops a formal programming language called the lambda-q calculus that addresses the fundamental…
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…
We develop a theory of the algorithmic information in bits contained in an individual pure quantum state. This extends classical Kolmogorov complexity to the quantum domain retaining classical descriptions. Quantum Kolmogorov complexity…