Related papers: Are Quantum States Exponentially Long Vectors?
The linear mathematics of quantum mechanics gives many versions of reality instead of the single version we perceive, with the perceived version chosen at random according to a probability law. Because of these peculiarities, the theory…
In the comment(quant-ph/0103003) Eggeling,Vollbrecht and Wolf suspect our method in quant-ph/0102133 is not practical. Here we explain our result and method and show that our example can tell one how to judge a separable state, and so our…
This is an extended abstract for a talk given at the Oberwolfach workshop "The Renormalization Group", March 13th - March 19th, 2011.
This paper offers a critique of the Bayesian interpretation of quantum mechanics with particular focus on a paper by Caves, Fuchs, and Schack containing a critique of the "objective preparations view" or OPV. It also aims to carry the…
In recent results, it has been proven that all sampling methods produce outliers. In this paper, we extend these results to quantum information theory. Projectors of large rank must contain pure quantum states in their images that are…
This is mainly a lecture note taken by myself following Weinberg's book, but also contains some corrections to the abuse of mathematical treatment. This article discusses projective unitary representations of Poincare group on the single…
A discussion of fundamental aspects of quantum theory is presented, stressing the essential role of "events". (Abstract by Erhard Seiler -- see afterword)
In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to…
In this paper we briefly define distance vector routing algorithms, their advantages and possible drawbacks. On these possible drawbacks, currently widely used methods split horizon and poisoned reverse are defined and compared. The count…
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
In the week 3--9, October 2010, the Mathematisches Forschungsinstitut at Oberwolfach hosted a mini workshop Linear Series on Algebraic Varieties. These notes contain a variety of interesting problems which motivated the participants prior…
Genuine high-dimensional entanglement, i.e. the property of having a high Schmidt number, constitutes a resource in quantum communication, overcoming limitations of low-dimensional systems. States with a positive partial transpose (PPT), on…
We make comments on some shortcomings of the non-unitary-invariant and non-bi-invariant complexity in quantum mechanics/field theory and argue that the unitary-invariant and bi-invariant complexity is still a competitive candidate in…
We study odd entanglement entropy (odd entropy in short), a candidate of measure for mixed states holographically dual to the entanglement wedge cross section, in two-dimensional free scalar field theories. Our study is restricted to…
Because of the constraint that the estimators be bona fide physical states, any quantum state tomography scheme - including the widely used maximum likelihood estimation - yields estimators that may have a bias, although they are consistent…
A recent paper of Trandafir and Cabello [Phys. Rev. A, 111, 022408 (2025)] contains a number of errors, inconsistencies, and inefficiencies. They are too numerous to be listed here, so we identify and discuss them in the main body of the…
The vast majority of quantum states and unitaries have circuit complexity exponential in the number of qubits. In a similar vein, most of them also have exponential minimum description length, which makes it difficult to pinpoint examples…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
We introduce new definitions of states and of representations of covariance systems. The GNS-construction is generalized to this context. It associates a representation with each state of the covariance system. Next, states are extended to…
This paper is an answer to the first part of Adrian Kent's One World versus Many : the Inadequacy of Everettian Accounts of Evolution, Probability, and Scientific Confirmation [arXiv:0905.0624]. We take issue with Kent's arguments against…