Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Classical deterministic complexity of Edmonds' Problem and quantum entanglement
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Solving convex programs by random walks
Journal of the ACM (JACM)
Geometry of Quantum States: An Introduction to Quantum Entanglement
Geometry of Quantum States: An Introduction to Quantum Entanglement
The complexity of the consistency and n-representability problems for quantum states
The complexity of the consistency and n-representability problems for quantum states
Algorithms for quantum computation: discrete logarithms and factoring
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Entanglement-breaking channels in infinite dimensions
Problems of Information Transmission
Maximal p-norms of entanglement breaking channels
Quantum Information & Computation
Computational complexity of the quantum separability problem
Quantum Information & Computation
A quasipolynomial-time algorithm for the quantum separability problem
Proceedings of the forty-third annual ACM symposium on Theory of computing
Properties of local quantum operations with shared entanglement
Quantum Information & Computation
On global effects caused by locally noneffective unitary operations
Quantum Information & Computation
Epsilon-net method for optimizations over separable states
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Testing Product States, Quantum Merlin-Arthur Games and Tensor Optimization
Journal of the ACM (JACM)
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Given the density matrix ρ of a bipartite quantum state, the quantum separability prob-lem asks whether ρ is entangled or separable. In 2003, Gurvits showed that this problemis NP-hard if ρ is located within an inverse exponential (with respect to dimension) dis-tance from the border of the set of separable quantum states. In this paper, we extendthis NP-hardness to an inverse polynomial distance from the separable set. The resultfollows from a simple combination of works by Gurvits, Ioannou, and Liu. We applyour result to show (1) an immediate lower bound on the maximum distance between abound entangled state and the separable set (assuming P ≠ NP), and (2) NP-hardnessfor the problem of determining whether a completely positive trace-preserving linearmap is entanglement-breaking.