Distillation of secret key and entanglement from quantum states

By Igor Devetak, Andreas J. Winter. Proceedings of the Royal Society A, 2003

961 citations recorded by the source corpus.

We study and solve the problem of distilling a secret key from quantum states representing correlation between two parties (Alice and Bob) and an eavesdropper (Eve) via one–way public discussion: we prove a coding theorem to achieve the ‘wire–tapper’ bound, the difference of the mutual information Alice–Bob and that of Alice–Eve, for so–called classical–quantum–quantum–correlations, via one–way public communication. This result yields information–theoretic formulae for the distillable secret key, giving ‘ultimate’ key rate bounds if Eve is assumed to possess a purification of Alice and Bob's joint state. Specializing our protocol somewhat and making it coherent leads us to a protocol of entanglement distillation via one–way LOCC (local operations and classical communication) which is asymptotically optimal: in fact we prove the so–called ‘hashing inequality’, which says that the coherent information (i.e. the negative conditional von Neumann entropy) is an achievable Einstein–Podolsky–Rosen rate. This result is known to imply a whole set of distillation and capacity formulae, which we briefly review.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/f6f567181b8cc7994362a0ba4e139f6959f56d83

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Citations in the corpus

Holographic mutual information is monogamous (2011, background): “Specifically, the distillable entanglement quantifies the rate at which standard entangled states |00〉AB + |11〉AB that can be extracted from the state ρ⊗n AB in the limit of many copies [32, 35].”
Distributing Secret Keys with Quantum Continuous Variables: Principle, Security and Implementations (2015, background): “…the asymptotic limit on inﬁnitely long keys, and the goal was to compute the corresponding asymptotic collective key rate K asympt coll , given by [27,28]: where I ( A ; B ) is the mutual information between Alice and Bob’s measurements outcomes and χ ( B ; E ) is the Holevo information between…”
Experimental investigation of the entanglement-assisted entropic uncertainty principle (2010, background): “It is known that − H (A|B) gives the lower bound of the one-way distillable entanglemen”
The mother of all protocols: restructuring quantum information’s family tree (2006, background): “…determination of the classical capacity of a quantum channel [1, 2], the capacities of entanglement-assisted channels [3, 4], the quantum capacity of a quantum channel [5, 6, 7], and the best ways to use noisy entanglement to extract pure entanglement [8] or to help send classical information [9].”
Quantum, classical, and total amount of correlations in a quantum state (2004, background): “…distillable secret key and distillable entanglement (which are decreasing in this order): (for the second quantity, the common randomness CR( ρ ) in a state, see [18]; for the third and fourth, the distillable key K ( ρ ) and the distillable entanglement E D ( ρ ), see the recent results in [19]).”
The security of practical quantum key distribution (2008, methodology): “The generic bound for the secret key fraction achievable using one-way post-processing (Devetak-Winter bound) is given by (21) with IAE = max Eve χ(A : E) (collective attacks) (23) and IBE defined in the analog way (Devetak and Winter, 2005).”
Aspects of Generic Entanglement (2004, background): “One can also quantify the amount of secret key K(σ) distillable against an eavesdropper holding the purification of the state (see [8, 10, 11 ] and references therein), and the distillable “common randomness” CR(σ ) [2, 9] (discounting at the end of the protocol the amount of communication used).”
Fundamental limits of repeaterless quantum communications (2015, neutral): “ck) associated with the one-way key distillation of Alice and Bob’s copies (˜ρn 0 AB) ⊗m is equal to the conditional (Shannon) entropy S(A|B) between the two classical ﬁnite-dimensional systems Aand B[S8]. This overhead is bounded by log2 dimHA,B = ln 0 classical bits per block, so that it scales at”
Faithful Squashed Entanglement (2010, background): “Measure Esq [6] ED [18, 19] KD [20, 21] EC [18, 22] EF [18] ER [23] E∞ R [24] EN [25] normalisation y y y y y y y y faithfulness y Cor.”