Related papers: Are Quantum States Exponentially Long Vectors?

This is an extended abstract of my talk at the Oberwolfach-Workshop "Representation Theory of Finite-Dimensional Algebras" (February 6 - 12, 2005). It gives self-contained and simplified definitions of quantum cluster algebras introduced…

This is an extended abstract of my talk at the Oberwolfach Workshop "Algebraic Groups" (April 22 - 28, 2007). It is based on a joint work with H.Derksen and J.Weyman (arXiv:0704.0649v2 [math.RA]).

The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…

Do correctness and completeness of quantum mechanics jointly imply that quantum state vectors are necessarily in one-to-one correspondence with elements of the physical reality? In terms of category theory, such a correspondence would stand…

I consider the "Quantum Bayesian" view of quantum theory as expounded in a 2006 paper of Caves, Fuchs, and Schack. I argue that one can accept a generally personalist, decision-theoretic view of probability, including probability as…

The development of quantum information theory has renewed interest in the idea that the state vector does not represent the state of a quantum system, but rather the knowledge or information that we may have on the system. I argue that this…

It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing…

Recently, it has been argued that quantum mechanics is complete, and that quantum states vectors are necessarily in one-to-one correspondence with the elements of reality, under the assumptions that quantum theory is correct and that…

A class of vector states on a von Neumann algebra is constructed. These states belong to a deformed exponential family. One specific deformation is considered. It makes the exponential function asymptotically linear. Difficulties arising…

Significant advances in the development of computing devices based on quantum effects and the demonstration of their use to solve various problems have rekindled interest in the nature of the "quantum computational advantage." Although…

I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is…

A foundational question in quantum computational complexity asks how much more useful a quantum state can be in a given task than a comparable, classical string. Aaronson and Kuperberg showed such a separation in the presence of a quantum…

In this paper we propose the idea that there is a corresponding relation between quantum states and points of the complex projective space, given that the number of dimensions of the Hilbert space is finite. We check this idea through…

The paper discusses objections against non-hidden variable versions of the epistemic conception of quantum states - the view that quantum states do not describe the properties of quantum systems but reflect, in some way to be specified, the…

Arguments have been raised that the system--observer cut of quantum mechanics can be shifted arbitrarily close to, or even into, the conscious observer. Here I show that this view leads to {\it observable} contradictions (despite our…

A projective quantum logic in terms of relative states is developed, emphasizing the importance of information transfer between a system under study and its environment. The need for accounting for the historical evolution of system is…

In recent years, the entanglement spectra of quantum states have been identified to be highly valuable for improving our understanding on many problems in quantum physics, such as classification of topological phases, symmetry-breaking…

The status of the quantum state is perhaps the most controversial issue in the foundations of quantum theory. Is it an epistemic state (state of knowledge) or an ontic state (state of reality)? In realist models of quantum theory, the…

In recent works, \v{C}aslav Brukner and Jacques Pienaar have raised interesting objections to the relational interpretation of quantum mechanics. We answer these objections in detail and show that, far from questioning the viability of the…

This talk deals with the old problem of formulatingn a covariant quantum theory of superstrings, ``covariant'' here meaning having manifest Lorentz symmetry and supersymmetry. The advantages and disadvantages of several quantization methods…