“Squashed entanglement”: An additive entanglement measure

By Matthias Christandl, Andreas J. Winter. 2003

448 citations recorded by the source corpus.

In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call “squashed entanglement”: it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes-type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.

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

View Paper: https://www.semanticscholar.org/paper/3701c3fbceef1a61aca82fac06cb7b144555a431

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Citations in the corpus

Multiboundary wormholes and holographic entanglement (2014, background): “Since ⩽ E I 2 D [57], this means that the distillable entanglement of any subsystem of size n 2 or smaller is negligible.”
Continuity of quantum conditional information (2003, background): “ntity is the smallest conditional mutual information computed over the set of all ﬁnite dimensional extensions of the state: E sq(ρ12) := inf ρ123 1 2 S(ρ13|ρ3)−S(ρ123|ρ23) . It was introduced in [1] and shown to vanish on separable states and to be additive. Continuity in the state, however, rema”
The mother of all protocols: restructuring quantum information’s family tree (2006, background): “So, where E sq ( ϕ AB ) is the squashed entanglement of ϕ AB , deﬁned as the inﬁmum of I ( A ; B E ) over extensions ϕ ABE of ϕ AB [26].”
Quantum Conditional Mutual Information and Approximate Markov Chains (2014, background): “where the infimum ranges over all non-negative extensions ρACE of ρAC [17].”
Entanglement certification from theory to experiment (2018, background): “[238] Matthias Christandl and Andreas Winter, ““squashed”
Aspects of Generic Entanglement (2004, background): “Even in the bipartite, asymptotic case, there are many different mixedstate “entanglement measures,” most of which are poorly understood, both individually and in relation to each other; see [3, 6, 12, 21, 26, 50] and references therein.”
Holographic mutual information is monogamous (2011, background): “One way to formulate that question rigorously involves a third (and final!) entanglement measure, known as the squashed entanglement [36].”
Faithful Squashed Entanglement (2010, background): “for every state ρAB1 B2 . This, together with the bound Esq(ρA:B) ≤ log |A| [ 6 ]i mplies that the squashed entanglement of any k-extendible state must be smaller than k −1 log |A|, which combined with Corollary 1 gives Corollary 2.”
A canonical purification for the entanglement wedge cross-section (2019, background): “For example this is the quantity that goes into the squashed entanglement [50] - which is found after minimizing over possible extensions like A?.”
Entanglement of purification through holographic duality (2017, background): “This leads to the squashed entanglement E sq ( ρ AB ) [28, 29] deﬁned by Here ) is the quantum conditional mutual information, which is non-negative due to the strong subadditivity of von Neumann entropy.”
Fundamental rate-loss tradeoff for optical quantum key distribution (2014, methodology): “The first inequality follows from monotonicity of the squashed entanglement under LOCC.”