Postselection technique for quantum channels with applications to quantum cryptography.

By Matthias Christandl, Robert T. König, Renato Renner. Physical Review Letters, 2008

320 citations recorded by the source corpus.

We propose a general method for studying properties of quantum channels acting on an n-partite system, whose action is invariant under permutations of the subsystems. Our main result is that, in order to prove that a certain property holds for an arbitrary input, it is sufficient to consider the case where the input is a particular de Finetti-type state, i.e., a state which consists of n identical and independent copies of an (unknown) state on a single subsystem. Our technique can be applied to the analysis of information-theoretic problems. For example, in quantum cryptography, we get a simple proof for the fact that security of a discrete-variable quantum key distribution protocol against collective attacks implies security of the protocol against the most general attacks. The resulting security bounds are tighter than previously known bounds obtained with help of the exponential de Finetti theorem.

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

View Paper: https://www.semanticscholar.org/paper/6af99495d7ab01b625edec8f4e036a2d87448c67

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Citations in the corpus

Quantum Conditional Mutual Information and Approximate Markov Chains (2014, methodology): “The second is an extension of the method of de Finetti reductions [14,15,45,46] (Sect.”
Advances in quantum cryptography (2019, unknown): “[493] M.”
Quantum Cryptography (2006, unknown): “in [21, 49, 51], security against general attacks is proven directly with the help of Proposition 1.”
Secure quantum key distribution with realistic devices (2020, background): “…can be extended to the case of coherent attack by further analysis (Coles et al., 2017; Tomamichel et al., 2012), such as the de Finetti theorem (Renner, 2007), the post-selection technique (Christandl et al., 2009) and uncertainty relation for smooth entropies (Tomamichel and Renner, 2011).”
Continuous‐Variable Quantum Key Distribution with Gaussian Modulation—The Theory of Practical Implementations (2017, methodology): “unately, the author notes that both the usual de Finetti method and the post-selection method (another method to derive security against coherent attacks from security against collective attacks, see [54]) fall short on providing useful nite-size key estimates against coherent (general) attacks. How”
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory (2009, methodology): “The Post-Selection Technique was introduced in [34] and is a tool in order to estimate the closeness of two completely positive and trace preserving (CPTP) maps that act symmetrically on an n -partite system, in the metric induced by the diamond norm, the dual of the completely bounded norm [35].”
Tight finite-key analysis for quantum cryptography (2011, methodology): “It therefore avoids various estimates, including the de Finetti Theorem [24] and the Post-Selection technique [25], that have previously led to too pes-simistic bounds.”