Quantum marginals from pure doubly excited states

Abstract

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 that constrain the polytope for the entire quantum system. The outer bound is sharp. The inner polytope stems only from doubly excited states. We find all quantum systems, where the bounds coincide giving the entire polytope. We show, that those systems are: i) any system of two particles ii) $L$ qubits, iii) three fermions on $N\le 7$ levels, iv) any number of bosons on any number of levels and v) fermionic Fock space on $N\le 5$ levels. The methods we use come from symplectic geometry and representation theory of compact Lie groups. In particular, we study the images of proper momentum maps, where our method describes momentum images for all representations that are spherical.

arXiv comment35 pages, 2 figures

References in corpus (34)

• Quantum entanglement
• Universal Quantum Computation with the nu=5/2 Fractional Quantum Hall State
• Quantum marginal problem and N-representability
• N-representability is QMA-complete
• Entanglement Polytopes: Multiparticle Entanglement from Single-Particle Information
• The Pauli principle revisited
• Pinning of Fermionic Occupation Numbers
• One-qubit reduced states of a pure many-qubit state: polygon inequalities
• Geometry of quantum systems: density states and entanglement
• Quasi-pinning and entanglement in the lithium isoelectronic series
• Convexity of momentum map, Morse index, and quantum entanglement
• Quasipinning and its relevance for $N$-Fermion quantum states
• Critical sets of the total variance of state detect all SLOCC entanglement classes
• Eigenvalue Distributions of Reduced Density Matrices
• Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6
• Natural Orbitals and Occupation Numbers for Harmonium: Fermions vs. Bosons
• Symplectic geometry of entanglement
• Quasipinning and selection rules for excitations in atoms and molecules
• Hubbard model: Pinning of occupation numbers and role of symmetries
• Classical simulation of fermionic linear optics augmented with noisy ancillas
• Entanglement in fermionic Fock space
• A universal framework for entanglement detection
• Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension
• Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle
• Fraction of isospectral states exhibiting quantum correlations
• Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• The lowest excited configuration of harmonium
• How many invariant polynomials are needed to decide local unitary equivalence of qubit states?
• Embedding qubits into fermionic Fock space, peculiarities of the four-qubit case
• Membership in moment polytopes is in NP and coNP
• Bipartite entanglement, spherical actions and geometry of local unitary orbits
• Critical points of the linear entropy for pure L-qubit states
• Universal Subspaces for Local Unitary Groups of Fermionic Systems

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• Foundation of one-particle reduced density matrix functional theory for excited states
• Generalized Pauli constraints in small atoms
• Asymptotic properties of entanglement polytopes for large number of qubits
• Locally Maximally Entangled States of Multipart Quantum Systems
• Role of the pair potential for the saturation of generalized Pauli constraints
• On the time evolution of fermionic occupation numbers
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Implications of pinned occupation numbers for natural orbital expansions. II: Rigorous derivation and extension to non-fermionic systems
• Solving one-body ensemble N-representability problems with spin
• Refining ensemble $N$-representability of one-body density matrices from partial information