Restricting quantum communication inputs to full permutation invariance limits gains from correlating signals sent through a communications channel. Optimised coherent information, measuring reliably transmitted data, converges towards its maximum value after only a finite number of channel uses. Limitations exist on how effectively quantum communications can use connections spanning several instances of a transmission channel when employing specific symmetrical input states.

Demonstrating these limits makes optimisation problems concerning quantum channel capacity more manageable; suggesting they may be understood by analysing only one instance of channel usage under such conditions. The work expands upon existing knowledge regarding mathematical properties relating to norms and measures governing reliable data transfer, offering alternative proofs through symmetry reduction techniques. Constraints have been identified on optimising quantum communications utilising symmetrical inputs, specifically when correlating signals sent through a transmission channel.

Optimised coherent information, akin to measuring message clarity despite noise, converges towards its maximum value after just a finite number of channel uses. Improvements gained from linking multiple instances of a communication channel are limited by these symmetries, simplifying calculations needed to determine quantum capacity which represents the maximum rate at which reliable data can be transmitted over noisy connections like bandwidth for radio signals but with qubits. Findings suggest analysing only one instance of channel usage may suffice under such conditions.

Simplifying Quantum Systems via De Finetti Reduction and Permutation Invariance

De Finetti reduction formed the basis of this investigation, representing a mathematical technique enabling replacement of complex multi-particle states with simpler single-particle descriptions under specific symmetry conditions. This approach resembles understanding average behaviour across many shuffled items instead of tracking each one individually.

The team exploited permutation invariance, where rearranging inputs does not alter outcomes, to apply this reduction effectively, simplifying intricate quantum systems by leveraging inherent symmetries within them. Consequently, key quantities related to reliable data transmission through noisy channels could be bounded, allowing analysis focusing on just a single use of that channel rather than considering infinite repetitions.

Finite Channel Use Optimisation Bounds Coherent Information Transmission

Researchers at Perimeter Institute for Theoretical Physics and University of Waterloo have demonstrated optimised coherent information, a measure of reliable data transmission, converges towards its maximum value after only a finite number of channel uses. Previously, optimising quantum communication required consideration of arbitrarily large blocks; however, the new findings challenge this necessity. The team proved that for every finite-dimensional memoryless channel, qsym n (N) ≤Q(N) + O(log n/√n), representing an excess coherent information which diminishes as ‘n’ increases, signifying optimisation effectively reduces to analysing just one instance of channel use.

Permutationally invariant states enable rapid optimisation of quantum channel capacity

These findings offer a pathway toward simplifying calculations needed to determine how much information quantum channels can reliably transmit. Restricting input states to exhibit full permutation invariance, where rearranging qubits doesn’t alter outcomes, is crucial for this simplification; however, it raises questions about whether these results accurately reflect performance with more complex or naturally occurring signals lacking such strict symmetries.

Despite acknowledging the limitation that restricting quantum signals to full permutation invariance is necessary, this work provides valuable insight into streamlining complex calculations within quantum information theory. By demonstrating symmetrical inputs allow optimisation to converge rapidly, behaving as if only one transmission step yields maximum efficiency, practical tools are offered and optimised coherent information reaches its peak after examining a limited number of channel uses rather than an infinite series.

The research demonstrated that optimised coherent information converges towards its maximum value following a finite number of channel uses. This means calculating the capacity of quantum channels does not necessarily require analysing infinitely long data streams, simplifying previously complex computations. Researchers found restricting input states to full permutation invariance allowed for rapid optimisation, effectively reducing analysis to single instances of channel use. The team also established the fidelity tends to zero at any fixed rate above the single-use coherent-information maximum

👉 More information
🗞 From Permutation Symmetry to Communication Bounds and Additivity
✍️ Zahra Baghali Khanian (Affiliation: Perimeter Institute for Theoretical Physics); Debbie Leung and Graeme Smith (University of Waterloo)
🧠 ArXiv: https://arxiv.org/abs/2610.02176

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