Related papers: Symmetry implies independence
Essential properties of semiclassical approximation for quantum mechanics are viewed as axioms of an abstract semiclassical mechanics. Its symmetry properties are discussed. Semiclassical systems being invariant under Lie groups are…
Quantum coherence is important in quantum mechanics, and its essence is from superposition principle. We study the coherence of any two pure states and that of their arbitrary superposition, and obtain the relationship between them. In the…
We show that the quantum description of measurement based on decoherence fixes the bug in quantum theory discussed in [D. Frauchiger and R. Renner, {\em Quantum theory cannot consistently describe the use of itself}, Nat. Comm. {\bf 9},…
Noether's theorem is a fundamental result in physics stating that every symmetry of the dynamics implies a conservation law. It is, however, deficient in several respects: (i) it is not applicable to dynamics wherein the system interacts…
We introduce and analyze a task that we call symmetrization, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is…
De Finetti theorems show how sufficiently exchangeable states are well-approximated by convex combinations of i.i.d. states. Recently, it was shown that in many quantum information applications a more relaxed de Finetti reduction (i.e. only…
Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…
Symmetry principles are fundamental in physics, and while they are well understood within Lagrangian mechanics, their impact on quantum channels has a range of open questions. The theory of asymmetry grew out of information-theoretic work…
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…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
A general algebraic approach, incorporating both invariance groups and dynamic symmetry algebras, is developed to reveal hidden coherent structures (closed complexes and configurations) in quantum many-body physics models due to symmetries…
Determining the relationship between composite systems and their subsystems is a fundamental problem in quantum physics. In this paper we consider the spectra of a bipartite quantum state and its two marginal states. To each spectrum we can…
Variance is a ubiquitous quantity in quantum information theory. Given a basis, we consider the averaged variances of a fixed diagonal observable in a pure state under all possible permutations on the components of the pure state and call…
The first law of thermodynamics imposes not just a constraint on the energy-content of systems in extreme quantum regimes, but also symmetry-constraints related to the thermodynamic processing of quantum coherence. We show that this…
Group theory is extremely successful in characterizing the symmetries in quantum systems, which greatly simplifies and unifies our treatments of quantum systems. Here we introduce the concept of the symmetry for a quantum Boltzmann machine…
Problem of classification of all the set of entangled states is considered. Invariance of entangled states relative to transformations from a group of symmetry of qubit space leads to classification of all states of the system through…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
We present a method for describing and characterizing the state of N particles that may be distinguishable in principle but not in practice due to experimental limitations. The technique relies upon a careful treatment of the exchange…
We introduce an algebraic framework for interacting quantum systems that enables studying complex phenomena, characterized by the coexistence and competition of various broken symmetry states of matter. The approach unveils the hidden unity…
The generalized definition of symmetry is formulated. Application of this definition for symmetric analysis of theoretical physics equations is considered. The version of electrodynamics is constructed permitting the faster-than-light…