Related papers: The Quantum Marginal Problem
This paper studies projections of uniform random elements of (co)adjoint orbits of compact Lie groups. Such projections generalize several widely studied ensembles in random matrix theory, including the randomized Horn's problem, the…
The boundary operator is a linear operator that acts on a collection of high-dimensional binary points (simplices) and maps them to their boundaries. This boundary map is one of the key components in numerous applications, including…
It is virtually impossible to directly solve the Schr\"odinger equation for a many-electron wave function due to the exponential growth in degrees of freedom with increasing particle number. The two-body reduced density matrix (2-RDM)…
The spectral variant of the quantum marginal problem asks: Given prescribed spectra for a set of overlapping quantum marginals, does there exist a compatible joint state? The main idea of this work is a symmetry-reduced semidefinite…
The quantum many-body problem can be rephrased as a variational determination of the two-body reduced density matrix, subject to a set of N-representability constraints. The mathematical problem has the form of a semidefinite program. We…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a…
In a recent preprint by Deutsch et al. [1995] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on $n$ qubits by 2-qubit unitary operations. We address that comment by proving strong lower…
Non-commutative polynomial optimization (NPO) problems seek to minimize the state average of a polynomial of some operator variables, subject to polynomial constraints, over all states and operators, as well as the Hilbert spaces where…
We study non-hermitian many-body physics in the interacting Hatano-Nelson model with open boundary condition. The violation of reciprocity, resulting from an imaginary vector potential, induces the non-hermitian skin-effect and causes…
In prior work, we have shown how the basic concepts and terms of quantum mechanics relate to factorizations and marginals of complex-valued quantum mass functions, which are generalizations of joint probability mass functions. In this…
Employing the quadratic fermionic Hamiltonians for the collective and internal subsystems with a linear coupling, we studied the role of fermionic statistics on the dynamics of the collective motion. The transport coefficients are discussed…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
We discuss the possibility of observing quantum nonlocality using the so-called mode entanglement, analyzing the differences between different types of particles in this context. We first discuss the role of coherent states in such…
We study quantum many-body systems with a global U(1) conservation law, focusing on a theory of $N$ interacting fermions with charge conservation, or $N$ interacting spins with one conserved component of total spin. We define an effective…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
It has been conjectured that the Pauli exclusion principle alone may be responsible for a particular geometric arrangement of confined systems of identical fermions even when there is no interaction between them. These geometric structures,…
We give an exact solution to the nonlinear optimization problem of approximating a Hermitian matrix by positive semi-definite matrices. Our algorithm was then used to judge whether a quantum state is entangled or not. We show that the exact…
It is a hard and important problem to find the criterion of the set of positive-definite matrixes which can be written as reduced density operators of a multi-partite quantum state. This problem is closely related to the study of many-body…
The possible spectra of one-particle reduced density matrices that are compatible with a pure multipartite quantum system of finite dimension form a convex polytope. We introduce a new construction of inner- and outer-bounding polytopes…
We shall revisit the conventional treatment of open quantum devices based on the Wigner-Function formalism. Our analysis will show that the artificial spatial separation between device active region and external reservoirs -properly defined…