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arxiv: 2512.14819 · v2 · submitted 2025-12-16 · 🪐 quant-ph · nucl-th

The entangling power of non-entangling channels

Julien Pinske , Jan Sperling , Klaus M{\o}lmer This is my paper

Pith reviewed 2026-05-16 21:25 UTC · model grok-4.3

classification 🪐 quant-ph nucl-th
keywords non-entangling channelsSchmidt numberentanglement witnessesquantum channelsdual mapsstochastic LOCCBell inequalities
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The pith

Non-entangling quantum channels increase Schmidt number only if they can generate entanglement with positive probability.

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

The paper shows that a quantum operation unable to produce entanglement on its own can still raise the Schmidt number of an input state, but only when there exists a non-zero probability that the output reveals newly generated entanglement. This contrasts with local operations and classical communication, where even probabilistic application cannot raise Schmidt numbers. The authors define stochastically non-entangling maps as those that never create entanglement even probabilistically. They prove that a channel is non-entangling precisely when its dual map sends entanglement witnesses to witnesses, and they derive Bell-like inequalities that detect entanglement generation by a process.

Core claim

There are processes that cannot generate entanglement but may nevertheless amplify entanglement already present in a system. A non-entangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some non-zero probability. This is in stark contrast to stochastic LOCC. A channel is non-entangling if and only if its dual map is witness-preserving. This leads to a Schmidt number for channels quantifying probabilistic entanglement generation and to Bell-like inequalities whose violation signals that a process generates entanglement.

What carries the argument

The witness-preserving property of the dual map, which is equivalent to a channel being non-entangling, together with the requirement that any Schmidt-number increase demands a positive probability of entanglement generation.

If this is right

  • Certain non-entangling operations become entangling when one selects on specific measurement outcomes.
  • Stochastically non-entangling maps are those that cannot generate entanglement even probabilistically.
  • A Schmidt number can be assigned to quantum channels to measure their capacity for probabilistic entanglement generation.
  • Bell-like inequalities can be constructed whose violation directly indicates that a given process generates entanglement.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The distinction between non-entangling and stochastically non-entangling maps may guide the design of quantum networks where local control must avoid creating entanglement.
  • The dual-map characterization offers a practical test for whether an unknown quantum process can generate entanglement.
  • Similar witness-preserving conditions might classify operations in infinite-dimensional or continuous-variable settings once suitable witnesses are defined.

Load-bearing premise

The analysis uses standard finite-dimensional quantum systems together with the usual definitions of entanglement witnesses and Schmidt number.

What would settle it

An explicit example of a non-entangling channel that raises the Schmidt number of some state while having zero probability of generating entanglement on any measurement outcome would falsify the central claim.

Figures

Figures reproduced from arXiv: 2512.14819 by Jan Sperling, Julien Pinske, Klaus M{\o}lmer.

Figure 1
Figure 1. Figure 1: FIG. 1. Hierarchy of quantum channels. The set of channels [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Separable states [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Entanglement test for the witness [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Entanglement test for the witness [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
read the original abstract

There are processes that cannot generate entanglement but may, nevertheless, amplify entanglement already present in a system. Here, we show that a non-entangling operation can increase the Schmidt number of a quantum state only if it can generate entanglement with some non-zero probability. This is in stark contrast to the case where the parties of a quantum network are only able to control their joint state by local operations and classical communication (LOCC). There, being able to apply operations probabilistically (stochastic LOCC) does not increase the Schmidt number. Our findings show that certain non-entangling operations become entangling when selecting on specific measurement outcomes. This naturally leads us to the class of stochastically non-entangling maps, being those that cannot generate entanglement even probabilistically. Intrigued by this finding, we devise a Schmidt number for quantum channels that quantifies whether a channel can generate entanglement probabilistically. Moreover, we show that a channel is non-entangling if and only if its dual map is witness-preserving -- it takes entanglement witnesses to witnesses. Based on this finding, we derive Bell-like inequalities whose violation signals that a process generates entanglement.

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 / 2 minor

Summary. The paper claims that non-entangling quantum operations can increase the Schmidt number of an input state only if they generate entanglement with non-zero probability. This stands in contrast to stochastic LOCC, where probabilistic application does not increase Schmidt number. The work introduces the class of stochastically non-entangling maps, defines a Schmidt number for quantum channels that quantifies probabilistic entanglement generation, proves that a channel is non-entangling if and only if its dual map preserves entanglement witnesses, and derives Bell-like inequalities whose violation detects entanglement-generating processes.

Significance. If the central claims hold, the results sharpen the distinction between different classes of non-entangling operations and provide new operational characterizations of entanglement generation. The equivalence between non-entangling channels and witness-preserving dual maps, together with the channel Schmidt number and the derived inequalities, offers concrete tools for analyzing quantum processes beyond standard LOCC. These contributions are grounded in standard finite-dimensional quantum channel theory and could inform resource theories of entanglement.

major comments (2)
  1. The central equivalence (non-entangling channel iff dual is witness-preserving) is load-bearing for the later inequalities. The abstract states it follows from the adjoint relation, but the manuscript should explicitly verify that the dual preserves the cone of separable states in both directions, including the case of non-unital maps.
  2. The definition of the Schmidt number for quantum channels (introduced to quantify probabilistic entanglement generation) relies on an optimization over input states and output Schmidt numbers. The paper should clarify whether this quantity is monotonic under composition with non-entangling maps and provide a concrete example where it is strictly positive for a stochastically non-entangling channel.
minor comments (2)
  1. Notation for the dual map and the witness-preserving property should be introduced with an explicit equation in the preliminaries section to avoid ambiguity when the Bell-like inequalities are derived.
  2. The contrast with stochastic LOCC is stated clearly in the abstract; a short paragraph recalling the standard definition of stochastic LOCC instruments would help readers who are not specialists in entanglement theory.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. We address each point below and will revise the manuscript to incorporate explicit verifications and clarifications where appropriate.

read point-by-point responses

  1. Referee: The central equivalence (non-entangling channel iff dual is witness-preserving) is load-bearing for the later inequalities. The abstract states it follows from the adjoint relation, but the manuscript should explicitly verify that the dual preserves the cone of separable states in both directions, including the case of non-unital maps.

    Authors: We agree that an explicit bidirectional verification strengthens the presentation, particularly for non-unital maps. In the revised manuscript we will add a self-contained proof in the main text or an appendix. The argument proceeds from the adjoint relation by showing that if the channel maps separable states to separable states, then its dual maps witnesses to witnesses, and conversely; the non-unital case is handled by extending the input space with an ancillary system and verifying positivity preservation on the extended separable cone using the Choi-Jamiolkowski isomorphism. revision: yes

  2. Referee: The definition of the Schmidt number for quantum channels (introduced to quantify probabilistic entanglement generation) relies on an optimization over input states and output Schmidt numbers. The paper should clarify whether this quantity is monotonic under composition with non-entangling maps and provide a concrete example where it is strictly positive for a stochastically non-entangling channel.

    Authors: We will add a proposition establishing monotonicity: the channel Schmidt number is non-increasing under left or right composition with any non-entangling map, because such maps cannot increase the maximum output Schmidt number achievable over probabilistic branches. By definition the channel Schmidt number vanishes exactly on the stochastically non-entangling class. We will therefore supply a concrete example of a non-entangling channel with strictly positive channel Schmidt number (a suitably chosen mixture of a separable-preserving map and a weakly entangling Kraus branch) to illustrate the distinction, together with an explicit calculation of the optimizing input state and output Schmidt numbers. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper's central results follow from standard finite-dimensional quantum channel theory, the adjoint relation between CP maps, and the definition of entanglement witnesses as functionals positive on separable states. The equivalence 'non-entangling channel iff dual is witness-preserving' is a direct consequence of these definitions rather than a reduction to fitted parameters or self-referential quantities. The new Schmidt number for channels is introduced by explicit definition to quantify probabilistic entanglement generation and does not rely on prior self-citations for its validity. No load-bearing step reduces by construction to an input or to a self-citation chain; the contrast with stochastic LOCC is derived from the differing Kraus-operator restrictions and remains externally falsifiable.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The claims rest on standard definitions of quantum channels, entanglement witnesses, and Schmidt rank in finite dimensions. No free parameters are introduced. The new concepts (stochastically non-entangling maps, channel Schmidt number) are defined rather than postulated as physical entities.

axioms (1)
  • standard math Standard quantum mechanics in finite dimensions with completely positive trace-preserving maps and the usual definition of entanglement witnesses.
    Invoked throughout the abstract for all statements about non-entangling operations and dual maps.
invented entities (2)
  • Stochastically non-entangling maps no independent evidence
    purpose: Class of maps that cannot generate entanglement even probabilistically.
    Defined directly from the main finding; no independent evidence beyond the definition.
  • Schmidt number for quantum channels no independent evidence
    purpose: Quantifies whether a channel can generate entanglement probabilistically.
    New measure devised from the result; no external validation shown.

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