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arxiv: 2409.10393 · v2 · submitted 2024-09-16 · 🪐 quant-ph

Multicopy quantum state teleportation with application to storage and retrieval of quantum programs

Fr\'ed\'eric Grosshans , Micha{\l} Horodecki , Mio Murao , Tomasz M{\l}ynik , Marco T\'ulio Quintino , Micha{\l} Studzi\'nski , Satoshi Yoshida This is my paper

Pith reviewed 2026-05-23 20:25 UTC · model grok-4.3

classification 🪐 quant-ph
keywords multicopy teleportationquantum state teleportationquditsquantum program storagegroup representation theorysuccess probability boundquantum channels
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The pith

The maximal success probability for multicopy teleportation of an unknown qudit without correction is k/[d(k-1+d)].

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

This paper analyzes multicopy state teleportation where Alice holds k identical copies of an arbitrary unknown d-dimensional state and shares a maximally entangled pair with Bob, who cannot correct. Alice performs a joint measurement on her entanglement half and the k copies to teleport one exact copy. The authors prove the maximum success probability is p(d,k) = k/[d(k-1+d)] and give an explicit protocol achieving it. They apply this to boost the success rate of storing and retrieving arbitrary quantum programs or channels using multiple copies of the target state. The proofs draw on group representation theory.

Core claim

We prove that the maximal probability of success for teleporting the exact state |ψ⟩ to Bob is p(d,k)=k/[d(k-1+d)] and present an explicit protocol to attain this performance. By utilising k copies of an arbitrary target state |ψ⟩, the multicopy state teleportation protocol enhances the success probability of storage and retrieval of quantum programs.

What carries the argument

The multicopy state teleportation task, in which Alice jointly measures her half of a shared maximally entangled state together with k copies of the unknown state to send one exact copy to Bob without correction.

If this is right

  • The bound p(d,k) gives the optimal performance for this asymmetric teleportation task.
  • An explicit protocol achieves the bound p(d,k).
  • The same approach improves the success probability for universal storage and retrieval of quantum channels.
  • Methods from group representation theory are used to derive the bound and may apply to related quantum tasks.

Where Pith is reading between the lines

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

  • This bound may limit the performance of other quantum communication protocols that lack a correction step from the receiver.
  • Multiple copies could be used in similar ways to enhance other tasks involving unknown quantum states, such as discrimination or estimation.
  • The group representation theory techniques might provide exact bounds for asymmetric versions of other quantum information protocols.

Load-bearing premise

The protocol assumes Alice and Bob share a maximally entangled two-qudit state and that Alice can perform an arbitrary joint measurement on her half plus the k copies of the unknown state.

What would settle it

Observing a success probability higher than k/[d(k-1+d)] in an experiment with specific values of d and k, or a mathematical construction of a better protocol, would show the bound is not maximal.

Figures

Figures reproduced from arXiv: 2409.10393 by Fr\'ed\'eric Grosshans, Marco T\'ulio Quintino, Micha{\l} Horodecki, Micha{\l} Studzi\'nski, Mio Murao, Satoshi Yoshida, Tomasz M{\l}ynik.

Figure 1
Figure 1. Figure 1: Pictorial illustration of the teleportation scenario considered in this work. Alice and Bob share one [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) The task of storage and retrieval of quantum programs, which can be used to universally retrieve [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Panel A presents five possible Young frames for [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

This work considers a teleportation task for Alice and Bob in a scenario where Bob cannot perform corrections. In particular, we analyse the task of \textit{multicopy state teleportation}, where Alice has $k$ identical copies of an arbitrary unknown $d$-dimensional qudit state $\vert\psi\rangle$ to teleport a single copy of $\vert\psi\rangle$ to Bob using a maximally entangled two-qudit state shared between Alice and Bob without Bob's correction. Alice may perform a joint measurement on her half of the entangled state and the $k$ copies of $\vert\psi\rangle$. We prove that the maximal probability of success for teleporting the exact state $\vert\psi\rangle$ to Bob is $p(d,k)=\frac{k}{d(k-1+d)}$ and present an explicit protocol to attain this performance. Then, by utilising $k$ copies of an arbitrary target state $\vert\psi\rangle$, we show how the multicopy state teleportation protocol can be employed to enhance the success probability of storage and retrieval of quantum programs, which aims to universally retrieve the action of an arbitrary quantum channel that is stored in a state. Our proofs make use of group representation theory methods, which may find applications beyond the problems addressed in this work.

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 manuscript analyzes multicopy quantum state teleportation where Alice holds k identical copies of an unknown d-dimensional qudit state |ψ⟩ and shares a maximally entangled two-qudit pair with Bob, who cannot perform corrections. Alice performs a joint measurement on her half of the entangled state plus the k copies to teleport one exact copy of |ψ⟩ to Bob. Using group representation theory, the paper proves that the maximal success probability is p(d,k)=k/[d(k-1+d)] and supplies an explicit protocol attaining this bound. The protocol is then applied to improve the success probability of storage and retrieval of quantum programs (universal retrieval of an arbitrary channel stored in a state).

Significance. If the bound and protocol hold, the result supplies a tight, representation-theoretic characterization of multicopy teleportation without correction that recovers the standard 1/d² value at k=1, confirming internal consistency. The explicit protocol and the extension to quantum-program storage/retrieval constitute concrete strengths; the group-representation approach may be reusable for related tasks such as port-based teleportation or channel discrimination.

major comments (2)
  1. [§3] §3 (or the section containing the optimality proof): the upper-bound derivation via irreducible representations of the unitary group must be shown to be tight; explicitly state which representation appears in the measurement and how its multiplicity directly produces the factor k/[d(k-1+d)] without additional optimization.
  2. [Application section] Application section (storage/retrieval): the claimed improvement in success probability when the multicopy protocol is substituted for single-copy teleportation should be quantified for concrete (d,k) pairs and compared with the baseline single-copy figure; the reduction in the number of required program copies must be stated explicitly.
minor comments (2)
  1. [Introduction] Define the precise Hilbert-space dimensions and the form of the shared maximally entangled state at the beginning of the main text; the abstract assumes familiarity with the standard two-qudit Bell state.
  2. [Notation] Notation: use a consistent symbol for the success probability (p(d,k) in the abstract, possibly P elsewhere) and ensure all group-theoretic objects (e.g., the specific irrep labels) are introduced before their first use in equations.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment and the recommendation of minor revision. We address each major comment below and will update the manuscript accordingly.

read point-by-point responses

  1. Referee: [§3] §3 (or the section containing the optimality proof): the upper-bound derivation via irreducible representations of the unitary group must be shown to be tight; explicitly state which representation appears in the measurement and how its multiplicity directly produces the factor k/[d(k-1+d)] without additional optimization.

    Authors: We agree that additional explicitness will strengthen the presentation. In the revised manuscript we will identify the specific irreducible representation of U(d) (the one corresponding to the highest-weight vector in the symmetric subspace of the k-fold tensor product) that enters the measurement operators. We will show that the multiplicity of this irrep in the decomposition of the relevant Hilbert space is exactly k, which, when combined with the dimension d of the fundamental representation, directly produces the success probability k/[d(k-1+d)] via the standard projection formula; no further optimization is required because the protocol saturates the bound obtained from representation theory. revision: yes

  2. Referee: [Application section] Application section (storage/retrieval): the claimed improvement in success probability when the multicopy protocol is substituted for single-copy teleportation should be quantified for concrete (d,k) pairs and compared with the baseline single-copy figure; the reduction in the number of required program copies must be stated explicitly.

    Authors: We accept the suggestion. The revised application section will include explicit numerical comparisons, for example for (d=2,k=2) the success probability rises from the single-copy value 1/4 to 1/3, and for (d=3,k=2) from 1/9 to 2/12=1/6. We will also state the corresponding reduction in the number of program copies needed to reach a target success probability, showing that the multicopy protocol achieves the same performance with strictly fewer stored copies than the single-copy baseline. revision: yes

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The derivation of the bound p(d,k)=k/[d(k-1+d)] proceeds from the task definition (shared maximally entangled pair, Alice's joint measurement on k copies plus her entanglement half, no Bob correction) via group representation theory, yielding both the upper bound and an explicit attaining protocol. The k=1 case recovers the standard 1/d² value without adjustment, and no step reduces by construction to a fitted parameter, self-referential definition, or load-bearing self-citation chain. The result is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the standard postulates of quantum mechanics for states and measurements plus methods of group representation theory for the optimality proof; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • standard math Standard postulates of quantum mechanics for states, measurements, and entanglement
    Invoked for the definition of the teleportation task and success probability.
  • domain assumption Tools and results from group representation theory
    Stated as the method used for the proofs of the bound and protocol.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. A resource theory of asynchronous quantum information processing

    quant-ph 2025-04 unverdicted novelty 7.0

    Introduces resource theories for asynchronous port-based teleportation with free classical and quantum pre-processing, computes tight fidelity bounds for isotropic, graph, and symmetrized EPR states, and proves the st...

Reference graph

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