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arxiv: 2510.09834 · v2 · submitted 2025-10-10 · 🪐 quant-ph · cs.IT· math.IT

Quantum Action-Dependent Channels

Michael Korenberg , Uzi Pereg This is my paper

Pith reviewed 2026-05-18 07:20 UTC · model grok-4.3

classification 🪐 quant-ph cs.ITmath.IT
keywords quantum action-dependent channelachievable rateschannel side informationquantum memorydepolarizationno-cloning theoremquantum communication
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The pith

The paper derives achievable rates for reliable message transmission over quantum action-dependent channels with causal or non-causal side information.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies a quantum channel model in which the transmitter first performs an action that modifies the environment and then sends an encoded message. It generalizes the classical action-dependent channel while respecting the no-cloning theorem by letting the transmitter share entanglement with the environment rather than possess a copy of its state. Achievable rates are obtained for both causal and non-causal channel side information. The results are illustrated with a memory-storage example involving depolarization and selective rewriting, showing how preparatory actions affect transmission performance.

Core claim

The central claim is that achievable rates for reliable message transmission can be derived for the quantum action-dependent channel, where the transmitter first shocks the environment and then encodes the message, either with causal or non-causal channel side information. Because Alice cannot clone the environment state, the model instead allows her to share entanglement with it. The rates are demonstrated in a case study of memory storage with depolarization and selective rewriting.

What carries the argument

The quantum action-dependent channel, defined by an initial transmitter action that affects the environment before message encoding, with entanglement sharing replacing any environment copy.

Load-bearing premise

The transmitter can share entanglement with the channel environment during the initial action without violating no-cloning or needing an environment copy.

What would settle it

A concrete calculation for the depolarizing memory example in which the derived achievable rate cannot be attained under standard quantum mechanics would falsify the rates.

Figures

Figures reproduced from arXiv: 2510.09834 by Michael Korenberg, Uzi Pereg.

Figure 1
Figure 1. Figure 1: Coding over a quantum action-dependent channel. Here Alice acts as the Action encoder, encoding the message [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Effect of pinching on a quantum state. Left: Matrix representation of B. Off-diagonal blocks (regions labeled C and C† ) indicate non-commutativity with A. Right: After applying the pinching map EA, the modified state EA(B) is block-diagonal in the eigenbasis of A (off-diagonal blocks are zero). Now EA(B) commutes with A, enabling a measurement comparison of their spectra. and the conditional entropy as H(… view at source ↗
read the original abstract

We study communication over a quantum action-dependent channel, where the transmitter first performs an action that "shocks" the channel environment, and subsequently encodes a message into a transmission sent through the channel. This two-stage interaction arises in various settings, including rewriting over defective memory and quantum effects such as measurement-induced state collapse. Our model can be viewed as a quantum generalization of Weissman's classical action-dependent channel (2010). Here, however, Alice cannot have a copy of the environment state due to the no-cloning theorem. Instead, she may share entanglement with this environment. We derive achievable rates for reliable message transmission via the quantum action-dependent channel, with either causal or non-causal channel side information (CSI). As a case study, we analyze memory storage with depolarization and selective rewriting, demonstrating how action-dependent control influences performance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces a quantum generalization of action-dependent channels, in which the transmitter first performs an initial action that interacts with ('shocks') the channel environment and may share entanglement with it (owing to the no-cloning theorem), then encodes a message for transmission. Achievable rates are derived for reliable communication under both causal and non-causal channel side information at the transmitter; a case study applies the model to memory storage involving depolarization and selective rewriting.

Significance. If the rate derivations correctly incorporate the quantum resources associated with the initial action and entanglement sharing, the results would furnish a useful framework for quantum communication in settings with environmental control and side information, extending Weissman's classical model while respecting no-cloning. The case study supplies a concrete illustration of how action-dependent operations affect performance in a physically motivated scenario.

major comments (2)
  1. The derivation of achievable rates (both causal and non-causal CSI cases) must explicitly account for any ebits consumed or generated during the initial action and entanglement-sharing step with the environment; without this accounting the stated rates risk overstating the net capacity, as the interface between the action and the subsequent encoding is the least secure link in the construction.
  2. The model definition requires a precise specification of how the initial action produces an environment state with which Alice shares entanglement while remaining consistent with no-cloning and without implicitly assuming free or unlimited entanglement; this clarification is load-bearing for the validity of the subsequent rate expressions.
minor comments (1)
  1. Notation for the quantum action-dependent channel and the two CSI scenarios should be introduced with explicit definitions of the relevant quantum mutual information quantities and the precise role of the shared entanglement.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript on quantum action-dependent channels and for the constructive major comments. We address each point below, indicating the changes we will make to strengthen the presentation of the model and rate derivations.

read point-by-point responses

  1. Referee: The derivation of achievable rates (both causal and non-causal CSI cases) must explicitly account for any ebits consumed or generated during the initial action and entanglement-sharing step with the environment; without this accounting the stated rates risk overstating the net capacity, as the interface between the action and the subsequent encoding is the least secure link in the construction.

    Authors: We agree that an explicit accounting of ebit consumption or generation is required for the rates to represent net capacity. Our current derivations express achievable rates in terms of quantum mutual informations that incorporate the shared entanglement between Alice and the environment after the initial action. However, the manuscript does not separately quantify the entanglement cost of that action step. In the revision we will introduce a net-rate definition that subtracts the ebit rate consumed (or adds any ebits generated) by the action, and we will recompute the achievable rates for both the causal and non-causal CSI cases under this accounting. revision: yes

  2. Referee: The model definition requires a precise specification of how the initial action produces an environment state with which Alice shares entanglement while remaining consistent with no-cloning and without implicitly assuming free or unlimited entanglement; this clarification is load-bearing for the validity of the subsequent rate expressions.

    Authors: The abstract and introduction note that Alice cannot clone the environment state and may instead share entanglement with it. We acknowledge that the precise mathematical description of the action map and the resulting joint state is not fully formalized in the current text. In the revised manuscript we will add a dedicated model section that defines the initial action as a completely positive trace-preserving map (or isometry) acting on Alice’s input and the environment, explicitly constructs the post-action entangled state, and states that any entanglement is generated by this map itself rather than assumed to be freely available. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of achievable rates

full rationale

The paper derives achievable rates for reliable transmission over the quantum action-dependent channel by generalizing Weissman's classical model to the quantum setting, replacing environment copying with entanglement sharing due to no-cloning. The rate expressions rely on standard quantum mutual information quantities for both causal and non-causal CSI cases, without any reduction to fitted parameters, self-definitional constructs, or load-bearing self-citations. The two-stage interaction (initial action shocking the environment followed by message encoding) is modeled explicitly with physically consistent assumptions, and the derivation chain remains independent of its own outputs, grounded in established quantum information theory techniques.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Relies on standard quantum channel formalism and no-cloning theorem; no new free parameters or invented entities introduced in abstract.

axioms (1)
  • standard math Standard quantum information axioms including no-cloning theorem and entanglement sharing
    Invoked to justify why Alice shares entanglement rather than copying the environment state.

pith-pipeline@v0.9.0 · 5661 in / 1067 out tokens · 27106 ms · 2026-05-18T07:20:35.908244+00:00 · methodology

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Reference graph

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