Simple sufficient condition for subspace to be completely or genuinely entangled

Abstract

We introduce a simple sufficient criterion, which allows one to tell whether a subspace of a bipartite or multipartite Hilbert space is entangled. The main ingredient of our criterion is a bound on the minimal entanglement of a subspace in terms of entanglement of vectors spanning that subspace expressed for geometrical measures of entanglement. The criterion is applicable to both completely and genuinely entangled subspaces. We explore its usefulness in several important scenarios. Further, an entanglement criterion for mixed states following directly from the condition is stated. As an auxiliary result we provide a formula for the generalized geometric measure of entanglement of the $d$--level Dicke states.

arXiv commenttitle slightly changed, appendix B fixed; journal ref. added

References in corpus (34)

• Geometric measure of entanglement and applications to bipartite and multipartite quantum states
• Unextendible Product Bases and Bound Entanglement
• Multipartite entanglement, quantum-error-correcting codes, and entangling power of quantum evolutions
• Multipartite entanglement in spin chains
• Detection of multipartite entanglement in the vicinity of symmetric Dicke states
• Homodyne-detector-blinding attack in continuous-variable quantum key distribution
• On the dimension of subspaces with bounded Schmidt rank
• The Entanglement of Superpositions
• Entanglement criteria for Dicke states
• Entanglement and local information access for graph states
• Generic local distinguishability and completely entangled subspaces
• A completely entangled subspace of maximal dimension
• On quantum advantage in dense coding
• Quantum Codes of Maximal Distance and Highly Entangled Subspaces
• Genuinely entangled subspace with all-encompassing distillable entanglement across every bipartition
• From unextendible product bases to genuinely entangled subspaces
• Connecting the generalized robustness and the geometric measure of entanglement
• Generalized Geometric Measure of Entanglement for Multiparty Mixed States
• Bounds on Negativity of Superpositions
• Device-Independent Certification of Genuinely Entangled Subspaces
• Constructions of k-uniform and absolutely maximally entangled states beyond maximum distance codes
• Matrix permanent and quantum entanglement of permutation invariant states
• Bounds on the multipartite entanglement of superpositions
• Tight bounds on the concurrence of quantum superpositions
• On the concurrence of superpositions of many states
• Self-testing maximally-dimensional genuinely entangled subspaces within the stabilizer formalism
• Entanglement of subspaces in terms of entanglement of superpositions
• Entanglement of genuinely entangled subspaces and states: exact, approximate, and numerical results
• Genuine Multipartite Entanglement of Superpositions
• An approach to constructing genuinely entangled subspaces of maximal dimension
• Forbidden regimes in the distribution of bipartite quantum correlations due to multiparty entanglement
• Evaluation of two different entanglement measures on a bound entangled state
• The Bound of Entanglement of Superpositions with More Than Two Components
• Mixture of entangled pure states with maximally mixed one-qudit reduced density matrices

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• Construction of genuinely entangled multipartite subspaces from bipartite ones by reducing the total number of separated parties
• Negative result about the construction of genuinely entangled subspaces from unextendible product bases
• Computing linear sections of varieties: quantum entanglement, tensor decompositions and beyond
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• Bounding Real Tensor Optimizations via the Numerical Range