Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · quant-ph/0310088

Superselection rules and quantum protocols

Alexei Kitaev·Dominic Mayers·John Preskill
View original source ↗Read source document ↗Export metadata ↓

Abstract

We show that superselection rules do not enhance the information-theoretic security of quantum cryptographic protocols. Our analysis employs two quite different methods. The first method uses the concept of a reference system -- in a world subject to a superselection rule, unrestricted operations can be simulated by parties who share access to a reference system with suitable properties. By this method, we prove that if an n-party protocol is secure in a world subject to a superselection rule, then the security is maintained even if the superselection rule is relaxed. However, the proof applies only to a limited class of superselection rules, those in which the superselection sectors are labeled by unitary irreducible representations of a compact symmetry group. The second method uses the concept of the format of a message sent between parties -- by verifying the format, the recipient of a message can check whether the message could have been sent by a party who performed charge-conserving operations. By this method, we prove that protocols subject to general superselection rules (including those pertaining to nonabelian anyons in two dimensions) are no more secure than protocols in the unrestricted world. However, the proof applies only to two-party protocols. Our results show in particular that, if no assumptions are made about the computational power of the cheater, then secure quantum bit commitment and strong quantum coin flipping with arbitrarily small bias are impossible in a world subject to superselection rules.

Explore related subjects

quant-phhep-th

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Alexei Kitaev, Dominic Mayers, John Preskill. 2004-03-11. Superselection rules and quantum protocols. https://doi.org/10.1103/physreva.69.052326

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

KEEP EXPLORING

Related papers

arXiv2026

Quantum-to-classical transition and the emergence of trajectory level Darwinism with measurements distributed in time: a path integral approach

We present a formulation for the emergence of classical dynamics in a quantum world using a path integral approach that incorporates continuous measurements. It complements decoherence and coarse-grained measurement frameworks. The formulation provides the joint statistics of a sequence of measurements, with each Feynman path picking up a random phase proportional to the measurement strength, and we give conditions under which trajectories near classical paths dominate the probability amplitude. Information proliferates across the environment, a key feature of quantum Darwinism, via plane-wave probe scattering. In the continuous limit, momentum kicks from the probes add a further phase to each trajectory--the origin of the back-action force. We provide conditions under which measurements yield enough ``which-path'' information while keeping the wave packet localized. This describes the quantum-to-classical transition at the level of individual measurement records, complementing the ensemble description by density matrices. The same scattering that decoheres a trajectory also heats it, tying decoherence and measurement back-action together. This bounds how redundantly a classical trajectory can be recorded before back-action randomizes it into Brownian motion. The bound is not restrictive for macroscopic systems. For a trapped particle, it is set by the resolution in units of the zero-point motion and collapses to a single record where the semiclassical description of the orbit fails; for a free coordinate it marks the loss of deterministic objectivity even while the classical action remains large. In both cases, it delimits the regime in which objective classical trajectories exist. The crossover is driven by photon recoil, already resolved in levitated optomechanics; the bound recasts it as the point where a redundantly recorded trajectory, still objective, stops being deterministic.

quant-ph↗
arXiv2026

Toward fault-tolerant quantum computation exploiting quantum spatial distribution and gauge symmetry

We explore how the integrated use of quantum spatial distribution (QSD), or more specifically, a superposition of both spin and position states of particles, and gauge symmetry (GS) revealed by Poulin's stabilizer formalism enhances quantum error correction. The study employs $3+2$ particles on nested squares proposed in the companion paper (arXiv:2504.07941), where three of them encode Shor's nine-qubit code and the remaining two detect errors in this code through their spin state measurements. The first result is that the GS offers resilience against three types of noise acting on a particle: arbitrary decoherence of its spin or position state, and dephasing of both states, which completely or partly destroys its QSD. To show that, we formulate a noise model unifying the above noise sources and prove the correctability of this unified model under our error-correcting scheme. The second result is that the QSD, together with the GS, provides architectural flexibility, allowing us to stack the error-correcting systems both vertically and horizontally. Indeed, we present implementations of the error detection (stabilizer measurement), logical Hadamard and Toffoli gates, and a quantum adder with the required interactions only between nearest-neighbor and next-nearest-neighbor particles. Here, our treatment of the dynamics of particles, each having spin and position degrees of freedom, under nontrivial noise and gate operations indicates that the stabilizer formalism is a powerful tool for describing quantum many-body dynamics.

quant-ph↗
arXiv2026

Multi-Objective Optimization with Quantum-Annealing-Inspired Algorithms

Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of a practical quantum advantage remains elusive. Recent studies have reported that both gate-based quantum circuits and quantum annealers can outperform state-of-the-art classical heuristics on multi-objective optimization (MO-MaxCut) problems. However, these studies did not fully account for the substantial pre- and postprocessing overheads intrinsic to quantum solvers, leading to incomplete comparisons between quantum and classical approaches. In this work, we re-examine the same benchmark suite using GPU-based quantum-annealing-inspired algorithms (QAIAs), which generate probabilistic samples analogously to quantum processors and thus serve as formidable classical contenders. Our results show that QAIAs can sample candidate solutions approximately two orders of magnitude faster than the previously studied quantum processors, based on the reported sampling and device-access times. On the instances for which a complete pipeline can be compared, the measured end-to-end QAIA runtime, including model construction, sampling and Pareto filtering, is about an order of magnitude shorter than that of the exact objective-space baselines DCM and DPA-a, and the QAIA pipeline outperforms the tested evolutionary multi-objective heuristics under an equal wall-clock budget.

quant-ph↗