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arXiv:2504.10436 · PRX Quantum

Information Storage and Transmission under Markovian Noise

Satvik Singh, Nilanjana Datta

Published Feb 18, 2026• 0 citations
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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.

DOI
10.1103/8rnj-667b

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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.
Given a quantum Markovian noise model, we study the maximum dimension of a classical or quantum system that can be stored for arbitrarily large time. We show that, unlike the fixed time setting, in the limit of infinite time, the classical and quantum capacities are characterized by efficiently computable properties of the peripheral spectrum of the quantum channel. In addition, the capacities are additive under tensor product, which implies in the language of Shannon theory that the one-shot and the asymptotic i.i.d. capacities are the same. We also provide an improved algorithm for computing the structure of the peripheral subspace of a quantum channel, which might be of independent interest.
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We consider an open quantum system undergoing Markovian dynamics, the latter being modelled by a discrete-time quantum Markov semigroup (Φn)n∈N(Φ^n)_{n \in {\mathbb{N}}}(Φn)n∈N​, resulting from the action of sequential uses of a quantum channel ΦΦΦ, with n∈Nn \in {\mathbb{N}}n∈N being the discrete time parameter. We find upper and lower bounds on the one-shot εεε-error information transmission capacities of ΦnΦ^nΦn for a finite time n∈Nn\in \mathbb{N}n∈N and ε∈[0,1)ε\in [0,1)ε∈[0,1) in terms of the structure of the peripheral space of the channel ΦΦΦ. We consider transmission of (i)(i)(i) classical information (both in the unassisted and entanglement-assisted settings); (ii)(ii)(ii) quantum information and (iii)(iii)(iii) private classical information.
Quantum memory systems are vital in quantum information processing for dependable storage and retrieval of quantum states. Inspired by classical reliability theories that synthesize reliable computing systems from unreliable components, we formalize the problem of reliable storage of quantum information using noisy components. We introduce the notion of stable quantum memories and define the storage rate as the ratio of the number of logical qubits to the total number of physical qubits as well as the circuit complexity of the decoder, which includes both quantum gates and measurements. We demonstrate that a strictly positive storage rate can be achieved by constructing a quantum memory system with quantum expander codes. Moreover, by reducing the reliable storage problem to reliable quantum communication, we provide upper bounds on the achievable storage capacity. In the case of physical qubits corrupted by noise satisfying hypercontractivity conditions, we provide a tighter upper bound on storage capacity using an entropy dissipation argument. Furthermore, observing that the time complexity of the decoder scales nontrivially with the number of physical qubits, achieving asymptotic rates may not be possible due to the induced dependence of the noise on the number of physical qubits. In this constrained nonasymptotic setting, we derive upper bounds on storage capacity using finite blocklength communication bounds. Finally, we numerically analyze the gap between upper and lower bounds in both asymptotic and nonasymptotic cases, and provide suggestions to tighten the gap.
We show that it is possible to transmit and preserve information at short time scales over an n-fold composition of quantum channels (Ξn)n∈N(Ξ^n)_{n \in \mathbb{N}}(Ξn)n∈N​ modelled as a discrete quantum Markov semigroup, long enough to generate entanglement at some finite nnn. This is achieved by interspersing the action of noise with quantum error correction in succession. We show this by means of a non-trivial lower bound on the one-shot quantum capacity in the sequential setting as a function of nnn, in an attempt to model a linear quantum network and assess its capabilities to distribute entanglement. Intriguingly, the rate of transmission of such a network turns out to be a property of the spectrum of the channels composed in sequence, and the maximum possible error in transmission can be bounded as a function of the noise model only. As an application, we derive an exact error bound for the infinite dimensional pure-loss channel believed to be the dominant source of noise in networks precluding the distribution of entanglement. We exemplify our results by analysing the amplitude damping channel and its bosonic counterpart.
We show that the capacity of a quantum channel demarcates a phase transition: while reliable transmission below capacity is always possible, any attempt to transmit information above it fails catastrophically. Specifically, we prove exponential strong converse theorems for unassisted quantum and classical communication over arbitrary finite-dimensional memoryless quantum channels. At rates beyond the respective capacity, the entanglement-generation fidelity and the success probability for classical communication decay exponentially with the number of channel uses. This rules out transmission above capacity even when one tolerates arbitrarily large errors. Our proof follows the classical Arimoto strategy, augmented by a crucial new ingredient: integral representations of Rényi information measures that lead to asymptotic continuity bounds for Rényi capacities.