Information storage and transmission under Markovian noise

• URL: http://arxiv.org/abs/2504.10436v2
• Date: Fri, 03 Oct 2025 10:33:40 GMT
• Title: Information storage and transmission under Markovian noise
• Authors: Satvik Singh, Nilanjana Datta,
• Abstract summary: We study the information transmission capacities of quantum Markov semigroups $(Psit)_tin mathbbN$ acting on $d-dimensional quantum systems.<n>We show that, in the limit of $tto infty$, the capacities can be efficiently computed in terms of the structure of the peripheral space of $Psi$.<n>We also establish convergence bounds to show that the infinite-time capacities are reached after time $tgtrsim d2ln (d)$.
• Score: 11.745324895296465
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study the information transmission capacities of quantum Markov semigroups $(\Psi^t)_{t\in \mathbb{N}}$ acting on $d-$dimensional quantum systems. We show that, in the limit of $t\to \infty$, the capacities can be efficiently computed in terms of the structure of the peripheral space of $\Psi$, 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 $t\gtrsim d^2\ln (d)$. 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 device that is experiencing Markovian noise. From a practical standpoint, we show that typically, an $n-$qubit 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 $t\gtrsim n2^{2n}$. In contrast, if the error correction is local, we prove that the memory becomes useless much more quickly, i.e., after time $t\gtrsim \ln(n)$. 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 $(\Psi^l)_{l\in \mathbb{N}}$ of length $l\gtrsim d^2 \ln(d)$, both in the finite block-length and asymptotic regimes.

Related papers

• Singular value transformation for unknown quantum channels [0.7499722271664144]
  We develop a quantum algorithm for transforming a quantum channel's singular values.<n>We show our method applies practically to the problem of learning the $q$-th singular value moments of unknown quantum channels.
  arXiv  Detail & Related papers  (2025-06-30T17:56:07Z)
• Exact Quantum Capacity of Decohering Channels in Arbitrary Dimensions [0.0]
  We derive exact analytical expressions for the quantum capacity of a broad class of decohering quantum channels of the form $Lambda(rho)= (1-x)rho + x D(rho)$, where $D(rho)$ represents a structured decoherence process.<n>These channels are shown to be degradable for all noise parameters and in arbitrary dimensions, yielding closed-form, single-letter capacity formulas.
  arXiv  Detail & Related papers  (2025-06-16T12:06:26Z)
• Achievable rates in non-asymptotic bosonic quantum communication [0.9999629695552193]
  We find easily computable lower bounds on the non-asymptotic capacities of Gaussian channels.<n>We design the first algorithm capable of computing the trace distance between two Gaussian states up to a fixed precision.
  arXiv  Detail & Related papers  (2025-02-08T11:12:26Z)
• Rate-reliability tradeoff for deterministic identification [49.126395046088014]
  We find that for positive exponents linear scaling is restored, now with a rate that is a function of the reliability exponents.<n>We also show that even if only one of the two errors is required to be exponentially small, the linearithmic scaling is lost.
  arXiv  Detail & Related papers  (2025-02-04T15:09:14Z)
• Information transmission under Markovian noise [9.054540533394926]
  We consider an open quantum system undergoing Markovian dynamics. We find upper and lower bounds on the one-shot $epsilon$-error information transmission capacities of $Phin$ for a finite time.
  arXiv  Detail & Related papers  (2024-09-26T11:17:42Z)
• Quantum channels, complex Stiefel manifolds, and optimization [45.9982965995401]
  We establish a continuity relation between the topological space of quantum channels and the quotient of the complex Stiefel manifold. The established relation can be applied to various quantum optimization problems.
  arXiv  Detail & Related papers  (2024-08-19T09:15:54Z)
• Phase Transition in the Quantum Capacity of Quantum Channels [0.0]
  We prove that every quantum channel $Lambda$ in arbitrary dimension, when contaminated by white noise, completely loses its capacity of transmitting quantum states. We also find the quantum capacity of the complement of the depolarizing channel in closed form.
  arXiv  Detail & Related papers  (2024-08-11T09:49:52Z)
• General Communication Enhancement via the Quantum Switch [15.779145740528417]
  We conjecture that $mathcalP_n>0$ is both a necessary and sufficient condition for communication enhancement via the quantum $tt SWITCH$. We then formulate a communication protocol involving the quantum $tt SWITCH$ which enhances the private capacity of the BB84 channel.
  arXiv  Detail & Related papers  (2024-07-03T00:47:13Z)
• The Cost of Entanglement Renormalization on a Fault-Tolerant Quantum Computer [0.042855555838080824]
  We perform a detailed estimate for the prospect of using deep entanglement renormalization ansatz on a fault-tolerant quantum computer. For probing a relatively large system size, we observe up to an order of magnitude reduction in the number of qubits. For estimating the energy per site of $epsilon$, $mathcalOleft(fraclog Nepsilon right)$ $T$ gates and $mathcalOleft(log Nright)$ qubits suffice.
  arXiv  Detail & Related papers  (2024-04-15T18:00:17Z)
• Deterministic identification over channels with finite output: a dimensional perspective on superlinear rates [49.126395046088014]
  We consider the problem in its generality for memoryless channels with finite output, but arbitrary input alphabets.<n>Our main findings are that the maximum length of messages thus identifiable scales superlinearly as $R,nlog n$ with the block length $n$.<n>We show that it is sufficient to ensure pairwise reliable distinguishability of the output distributions to construct a DI code.
  arXiv  Detail & Related papers  (2024-02-14T11:59:30Z)
• Towards large-scale quantum optimization solvers with few qubits [59.63282173947468]
  We introduce a variational quantum solver for optimizations over $m=mathcalO(nk)$ binary variables using only $n$ qubits, with tunable $k>1$. We analytically prove that the specific qubit-efficient encoding brings in a super-polynomial mitigation of barren plateaus as a built-in feature.
  arXiv  Detail & Related papers  (2024-01-17T18:59:38Z)
• Weyl channels for multipartite systems [42.37986459997699]
  Quantum channels describe unitary and non-unitary evolution of quantum systems. We show that these channels are completely characterized by elements drawn of finite cyclic groups.
  arXiv  Detail & Related papers  (2023-10-17T02:45:47Z)
• Spacetime-Efficient Low-Depth Quantum State Preparation with Applications [93.56766264306764]
  We show that a novel deterministic method for preparing arbitrary quantum states requires fewer quantum resources than previous methods. We highlight several applications where this ability would be useful, including quantum machine learning, Hamiltonian simulation, and solving linear systems of equations.
  arXiv  Detail & Related papers  (2023-03-03T18:23:20Z)
• Correspondence between open bosonic systems and stochastic differential equations [77.34726150561087]
  We show that there can also be an exact correspondence at finite $n$ when the bosonic system is generalized to include interactions with the environment. A particular system with the form of a discrete nonlinear Schr"odinger equation is analyzed in more detail.
  arXiv  Detail & Related papers  (2023-02-03T19:17:37Z)
• Exponentially decaying velocity bounds of quantum walks in periodic fields [0.0]
  We consider a class of discrete-time one-dimensional quantum walks, associated with a CMV unitary matrix, in the presence of a local field. We show that for a certain range for $t$, the corresponding velocity can be made arbitrarily small by introducing a periodic local field with a sufficiently large period.
  arXiv  Detail & Related papers  (2023-02-03T17:15:15Z)
• A lower bound on the space overhead of fault-tolerant quantum computation [51.723084600243716]
  The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation. We prove an exponential upper bound on the maximal length of fault-tolerant quantum computation with amplitude noise.
  arXiv  Detail & Related papers  (2022-01-31T22:19:49Z)
• Random quantum circuits transform local noise into global white noise [118.18170052022323]
  We study the distribution over measurement outcomes of noisy random quantum circuits in the low-fidelity regime. For local noise that is sufficiently weak and unital, correlations (measured by the linear cross-entropy benchmark) between the output distribution $p_textnoisy$ of a generic noisy circuit instance shrink exponentially. If the noise is incoherent, the output distribution approaches the uniform distribution $p_textunif$ at precisely the same rate.
  arXiv  Detail & Related papers  (2021-11-29T19:26:28Z)
• Dephasing superchannels [0.09545101073027092]
  We characterise a class of environmental noises that decrease coherent properties of quantum channels by introducing and analysing the properties of dephasing superchannels. These are defined as superchannels that affect only non-classical properties of a quantum channel $mathcalE$. We prove that such superchannels $Xi_C$ form a particular subclass of Schur-product supermaps that act on the Jamiolkowski state $J(mathcalE)$ of a channel $mathcalE$ via a Schur product, $J'=J
  arXiv  Detail & Related papers  (2021-07-14T10:10:46Z)
• Coherent control and distinguishability of quantum channels via PBS-diagrams [59.94347858883343]
  We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS) We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
  arXiv  Detail & Related papers  (2021-03-02T22:56:25Z)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)
• Quasi-polynomial time algorithms for free quantum games in bounded dimension [11.56707165033]
  We give a semidefinite program of size $exp(mathcalObig(T12(log2(AT)+log(Q)log(AT))/epsilon2big)) to compute additive $epsilon$-approximations on the values of two-player free games. We make a connection to the quantum separability problem and employ improved multipartite quantum de Finetti theorems with linear constraints.
  arXiv  Detail & Related papers  (2020-05-18T16:55:08Z)
• Bosonic quantum communication across arbitrarily high loss channels [68.58838842613457]
  A general attenuator $Phi_lambda, sigma$ is a bosonic quantum channel that acts by combining the input with a fixed environment state. We show that for any arbitrary value of $lambda>0$ there exists a suitable single-mode state $sigma(lambda)$. Our result holds even when we fix an energy constraint at the input of the channel, and implies that quantum communication at a constant rate is possible even in the limit of arbitrarily low transmissivity.
  arXiv  Detail & Related papers  (2020-03-19T16:50:11Z)
• Decoding quantum information via the Petz recovery map [16.276576840098254]
  We show that there is a sharp error threshold above which $Qn, epsilon(mathcalN)$ scales as $sqrtn$. Applying our achievability bound to the 50-50 erasure channel, we find that there is a sharp error threshold above which $Qn, epsilon(mathcalN)$ scales as $sqrtn$.
  arXiv  Detail & Related papers  (2015-04-17T06:20:32Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.