Related papers: Private Quantum Subsystems and Quasiorthogonal Ope…
We consider some basic problems associated with quantum mechanics of systems having a time-dependent Hilbert space. We provide a consistent treatment of these systems and address the possibility of describing them in terms of a…
This paper is an expanded and more detailed version of our recent work in which the Operator Quantum Error Correction formalism was introduced. This is a new scheme for the error correction of quantum operations that incorporates the known…
In conventional quantum mechanics, quantum no-deleting and no-cloning theorems indicate that two different and nonorthogonal states cannot be perfectly and deterministically deleted and cloned, respectively. Here, we investigate the quantum…
It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is…
Quantum physics has revealed many interesting formal properties associated with the algebra of two operators, A and B, satisfying the partial commutation relation AB-BA=1. This study surveys the relationships between classical combinatorial…
In this paper, we study differentially private mechanisms for functions whose outputs lie in a Euclidean Jordan algebra. Euclidean Jordan algebras capture many important mathematical structures and form the foundation of linear programming,…
The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the…
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 investigate the notion of a subgroup of a quantum group. We suggest a general definition, which takes into account the work that has been done for quantum homogeneous spaces. We further restrict our attention to reductive subgroups,…
Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…
We give an algorithm to solve the quantum hidden subgroup problem for maximal cyclic non-normal subgroups of the affine group of a finite field (if the field has order $q$ then the group has order $q(q-1)$) with probability $1-\varepsilon$…
Quantum technologies hold the promise of not only faster algorithmic processing of data, via quantum computation, but also of more secure communications, in the form of quantum cryptography. In recent years, a number of protocols have…
We present a security analysis of the recently introduced Quantum Private Query (QPQ) protocol. It is a cheat sensitive quantum protocol to perform a private search on a classical database. It allows a user to retrieve an item from the…
In this article we consider partial abelianization of associative algebra with respect to a subalgebra. This notion is a generalization of usual abelianization of associative algebra and has an application in Quantum Mechanics and Quantum…
We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
We construct an algebra of pseudodifferential operators on each groupoid in a class that generalizes differentiable groupoids to allow manifolds with corners. We show that this construction encompasses many examples. The subalgebra of…
A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on…
We propose a new fractional statistics for arbitrary dimensions, based on an extension of Pauli's exclusion principle, to allow for finite multi-occupancies of a single quantum state. By explicitly constructing the many-body Hilbert space,…
In this second paper, we develop the full mathematical structure of the algebra of the pseudo-observables, in order to solve the quantum measurement problem. Quantum state vectors are recovered but as auxiliary pseudo-observables storing…