Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/0606049

Full security of quantum key distribution from no-signaling constraints

Ll. Masanes·R. Renner·M. Christandl·A. Winter·J. Barrett
View original source ↗Read source document ↗Export metadata ↓

Abstract

We analyze a cryptographic protocol for generating a distributed secret key from correlations that violate a Bell inequality by a sufficient amount, and prove its security against eavesdroppers, constrained only by the assumption that any information accessible to them must be compatible with the non-signaling principle. The claim holds with respect to the state-of-the-art security definition used in cryptography, known as universally-composable security. The non-signaling assumption only refers to the statistics of measurement outcomes depending on the choices of measurements; hence security is independent of the internal workings of the devices --- they do not even need to follow the laws of quantum theory. This is relevant for practice as a correct and complete modeling of realistic devices is generally impossible. The techniques developed are general and can be applied to other Bell inequality-based protocols. In particular, we provide a scheme for estimating Bell-inequality violations when the samples are not independent and identically distributed.

Explore related subjects

quant-phcs.CR

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Ll. Masanes, R. Renner, M. Christandl, A. Winter, J. Barrett. 2014-09-24. Full security of quantum key distribution from no-signaling constraints. https://doi.org/10.1109/tit.2014.2329417

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A quantum central path algorithm for linear optimization

We propose a novel quantum algorithm for solving linear optimization problems by quantum-mechanical simulation of the central path. While interior point methods follow the central path with an iterative algorithm that works with successive linearizations of the perturbed KKT conditions, we perform a simulation working directly with the nonlinear complementarity equations. Using a two-stage quantum eigenpath traversal schedule, this approach yields an algorithm for solving linear optimization problems involving $m$ constraints and $n$ variables to $\varepsilon$-optimality using $\widetilde{O}\!\left((m+n)^{3/2}\,\varepsilon^{-1}+(m+n)^{1/2}\,\varepsilon^{-3/2}\right)$ queries to an oracle that evaluates a potential function. In the standard gate model (i.e., without access to quantum RAM), our algorithm can obtain $\varepsilon$-precise solutions to LO problems using at most $$\widetilde{O}\!\left(\left[\frac{(m+n)^{3/2}}{\varepsilon} + \frac{(m+n)^{1/2}}{\varepsilon^{3/2}}\right] \cdot \mathrm{nnz}(A)\right)$$ elementary gates, where $\mathrm{nnz}(A)$ is the total number of non-zero elements found in the constraint matrix.

quant-ph↗
arXiv2026

Entanglement Scaling of Motzkin Chains under Spiral Hamiltonian-path Embeddings

We investigate how a two-dimensional spatial embedding changes the entanglement observed across geometrically local bipartitions of a one-dimensional quantum spin chain. A $q$-deformed colored Motzkin chain is placed along a spiral-inspired Hamiltonian path that visits $N(L)=Θ(L^2)$ sites of a square-lattice region while retaining a path interaction graph. Straight ambient-space cuts then correspond to unions of $Θ(L)$ disconnected intervals in the chain ordering. We derive the scaling of a height-variation proxy for the leading color-pairing contribution and predict ambient-space entropy scaling proportional to $L^2$, $L$, and $O(1)$ for $q>1$, $q=1$, and $q<1$, respectively. We evaluate this proxy numerically using the matrix-product-state representation and verify its predicted finite-size scaling. The embedded and original Hamiltonians have exactly identical spectra and spectral gaps at fixed chain length. We also describe a sparse tensor-network representation and propose a two-chain junction extension. These results isolate the roles of interaction connectivity, spatial embedding, and subsystem geometry in entanglement scaling.

quant-ph↗
arXiv2026

Brace for impact: ECDLP challenges for quantum cryptanalysis

Precise suites of benchmarks are required to assess the progress of early fault-tolerant quantum computers at economically impactful applications such as cryptanalysis. Appropriate challenges exist for factoring but those for elliptic curve cryptography are either too sparse or inadequate for standard applications of Shor's algorithm. We introduce a difficulty-graded suite of elliptic curve discrete logarithm (ECDLP) challenges that use Bitcoin's curve y^2=x^3+7 mod p while incrementally lowering the prime field from 256 down to 6 bits. For each bit-length, we provide the prime, the prime group order, and two deterministic nothing-up-my-sleeve (NUMS) points in compressed SEC1 form. All challenges are generated by a deterministic, reproducible procedure, and no private challenge scalar is chosen in advance. We calibrate classical cost against Pollard's rho records and quantum cost against resource estimation results for Shor's algorithm. We compile Shor's ECDLP circuit to logical counts and map them to physical resources for various parameters of the surface code, the repetition cat code and the LDPC cat codes. Under explicit and testable assumptions on physical error rates, code distances, and non-Clifford supply, our scenarios place the full 256-bit instance within a 2027--2033 window. The challenge ladder thus offers a transparent ruler to track fault-tolerant progress on a cryptanalytic target of immediate relevance, and it motivates proactive migration of digital assets to post-quantum signatures.

quant-ph↗