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The complexity class NP is quintessential and ubiquitous in theoretical computer science. Two different approaches have been made to define "Quantum NP," the quantum analogue of NP: NQP by Adleman, DeMarrais, and Huang, and QMA by Knill,…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
An universal approximation technique for analysis of different characteristics of states of composite infinite-dimensional quantum systems is proposed and used to prove general results concerning the properties of correlation and…
Quantum information and computation provide a fascinating twist on the notion of proofs in computational complexity theory. For instance, one may consider a quantum computational analogue of the complexity class \class{NP}, known as QMA, in…
Quantum measurement is essential to both the foundations and practical applications of quantum information science. Among many possible models of quantum measurement, feedback measurements that dynamically update their physical structure…
We summarize a recently proposed resolution of the quantum measurement problem. It stems from an insight into entanglement demonstrated in a 1991 experiment involving photon momenta. This experiment shows that, when two superposed quantum…
It is shown that determining whether a quantum computation has a non-zero probability of accepting is at least as hard as the polynomial time hierarchy. This hardness result also applies to determining in general whether a given quantum…
Complexity theory typically focuses on the difficulty of solving computational problems using classical inputs and outputs, even with a quantum computer. In the quantum world, it is natural to apply a different notion of complexity, namely…
We probe the quantum speed limit (QSL) of an electron when it is trapped in a non-uniform magnetic field. We show that the QSL increases to a large value, but within the regime of causality, by choosing a proper variation in magnetic…
We study the existence of non-separable compact spaces that support a measure and are small from the topological point of view. In particular, we show that under Martin's axiom there is a non-separable compact space supporting a measure…
The ability of quantum states to be in superposition is one of the key features that sets them apart from the classical world. This `coherence' is rigorously quantified by resource theories, which aim to understand how such properties may…
Thermodynamically consistent measurements can either preserve statistics (unbiased) or preserve marginal states (non-invasive) but not both. Here we show the existence of metrological tasks which unequally favor each of the aforementioned…
QMA and QCMA are possible quantum analogues of the complexity class NP. In QCMA the verifier is a quantum program and the proof is classical. In contrast, in QMA the proof is also a quantum state. We show that two known QMA-complete…
In the framework of mutually unbiased bases (MUBs), a measurement in one basis gives \emph{no information} about the outcomes of measurements in another basis. Here, we relax the no-information condition by allowing the $d$ outcomes to be…
We study three variants of multi-prover quantum Merlin-Arthur proof systems. We first show that the class of problems that can be efficiently verified using polynomially many quantum proofs, each of logarithmic-size, is exactly MQA (also…
We improve previous work on the consistency strength of mutually stationary sequences of sets concentrating on points with divergent cofinality building on previous work by Adolf, Cox and Welch. Specifically, we have greatly reduced our…
Quantum measurement of a solid-state qubit by a mesoscopic detector is of fundamental interest in quantum physics and an essential issue in quantum computing. In this work, by employing a unified quantum master equation approach constructed…
In his book `Mathematical Foundations of Quantum Mechanics', von Neumann asserted the following: the Compton-Simon experiment showed that the state vector must collapse upon measurement of any self-adjoint operator. Comparing von Neumann's…
We propose to experimentally test non-deterministic time evolution in quantum mechanics by consecutive measurements of non-commuting observables on the same prepared state. While in the standard theory the measurement outcomes are…
J. v. Neumann justified the collapse postulate by the empirical fact of the repeatability of a measurement at a single quantum system. However, in his quantum mechanical treatment of the measurement process repeatability emerges without…