Largest separable balls around the maximally mixed bipartite quantum state

By Leonid Gurvits, Howard Barnum. 2002

228 citations recorded by the source corpus.

For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral ${l}_{p}$ norms for $1l~pl~\ensuremath{\infty},$ of separable (unentangled) matrices around the identity matrix. This implies a simple and intuitively meaningful geometrical sufficient condition for separability of bipartite density matrices: that their purity $\mathrm{tr}{\ensuremath{\rho}}^{2}$ not be too large. Theoretical and experimental applications of these results include algorithmic problems such as computing whether or not a state is entangled, and practical ones such as obtaining information about the existence or nature of entanglement in states reached by nuclear magnetic resonance quantum computation implementations or other experimental situations.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/eac330ce3dac1602b49888765c5e567b0b0aea58

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In Artificial Intelligence

In Atomic and Molecular Physics, and Optics

Citations in the corpus

Geometry of Quantum States: Index (2007, background): “Separability of the maximal ball for higher dimensions was established by Gurvits and Barnum [380], who later estimated the radius of the separable ball for multipartite systems [381].”
The role of quantum information in thermodynamics—a topical review (2015, background): “Another pathway was pursued by [132–134], where with NMR quantum computation in”
Strong Converse for the Classical Capacity of Entanglement-Breaking and Hadamard Channels via a Sandwiched Rényi Relative Entropy (2013, background): “That the interior of the set of entanglement-breaking channels is non-empty then follows from [27].”
Random matrix techniques in quantum information theory (2015, background): “olumes can be expressed, up to a factor, from the probability that a quantum state is separable, under the induced measure nk;nk, see Remark4.5. The rst result in this direction is quite remarkable [GB02]. It has many interesting corollaries, one of them being that the set SEPof separable states ha”
Sparse Methods for Direction-of-Arrival Estimation (2016, background): “Formally, the result is stated in the following theorem, a proof of which (inspired by [123]) is also provided; note that the proof suggests a way of computing the decomposition.”
Classical complexity and quantum entanglement (2004, unknown): “The following result was recently proved in [20].”