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  • Open Access

Information Storage and Transmission under Markovian Noise

Satvik Singh1,2,* and Nilanjana Datta2,†

  • *Contact author: satvik.singh@tum.de
  • †Contact author: n.datta@damtp.cam.ac.uk
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PRX Quantum 7, 020312 – Published 21 April, 2026

DOI: https://doi.org/10.1103/8rnj-667b

Abstract

We study the information transmission capacities of quantum Markov semigroups acting on finite-dimensional quantum systems. We show that, in the limit of infinite time, the capacities can be efficiently computed in terms of the structure of the peripheral space of the semigroup, are strongly additive, and satisfy the strong converse property. We also establish convergence bounds to show that the infinite-time capacities are reached after time scaling quadratically with the system dimension. From a data storage perspective, our analysis provides tight bounds on the number of bits or qubits that can be reliably stored for long times in a quantum memory experiencing Markovian noise. From a practical standpoint, we show that typically, a quantum memory with Markovian noise acting independently and identically on all qubits and a fixed time-independent global error correction mechanism becomes useless for storage after time scaling exponentially with the number of qubits. In contrast, if the error correction is local, the memory becomes useless much more quickly, i.e., after time scaling logarithmically with the number of qubits. In the setting of point-to-point communication between two spatially separated parties, our analysis provides efficiently computable bounds on the optimal rate at which bits or qubits can be reliably transmitted via long Markovian communication channels, both in the finite block-length and asymptotic regimes.

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Popular Summary

Quantum information is extremely fragile, and protecting it from noise is a key challenge in building reliable quantum computers. Consequently, this problem has been analyzed from different perspectives, most notably from the viewpoint of designing concrete error-correcting codes to develop a fault-tolerant quantum memory. In contrast, in this work, we adopt a Shannon-theoretic perspective in order to understand the ultimate limits of data-storage in noisy quantum memories. In this framework, all physical and computational restrictions on how the information is encoded/decoded inside the memory are eliminated, which leads to the most general bounds on a memory’s storage capacity that are allowed by quantum physics. Although it is unclear if the error-correcting codes associated with these bounds are efficiently implementable, they nevertheless help us understand the ultimate limits of error correction; in addition, they serve as critical benchmarks against which other codes can be compared.

In this Shannon-theoretic setting, we provide explicit, efficiently computable, and tight bounds on the maximum number of bits/qubits that can be reliably stored for “long” times in an open quantum memory undergoing Markovian noise. We also derive bounds on the timescale at which these long-time formulas become applicable, thus providing insight on typical memory lifetimes. Interestingly, we show that while global error-correction can yield lifetimes scaling at most exponentially with the number of qubits in memory, local error-correction can only yield lifetimes scaling at most logarithmically with the number of qubits in memory. From the viewpoint of point-to-point communication between two spatially separated parties, our analysis provides efficiently computable bounds on the optimal rate at which bits/qubits can be reliably transmitted via “long” Markovian communication channels, both in the finite block-length and asymptotic regimes.

Article Text

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PRX Quantum 7, 020312– Published 21 April, 2026
  • Received 7 October 2025
  • Accepted 18 February 2026
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