Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2604.27042

Onset of superactivation of quantum capacity

Marco Parentin, Bjarne Bergh, Nilanjana Datta, Mark M. Wilde

quant-phSubmitted Apr 29, 2026• Announced Apr 30, 2026• 0 citations
v1 · Apr 29, 2026v2 · May 4, 2026
arXivHTMLPDF

Abstract

Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously unexplored non-asymptotic regime of finitely many channel uses. We give a definition of finite-blocklength superactivation and propose numerical methods that can certify it. Then, focusing on the 50% erasure and positive-partial-transpose channels considered in the original work on superactivation, we show that as few as 17 uses of the joint channel already enable qubit transmission with a fidelity unattainable by any number of uses of either channel alone, demonstrating a strong finite-blocklength form of superactivation and opening the door to experimental demonstration.

Comments
64 pages, 12 figures. See also the accompanying paper from today: Bergh, Parentin: Permutation Invariant Optimization Problems in Quantum Information Theory: A Framework for Channel Fidelity and Beyond

Related papers

Activation and superactivation of single-mode Gaussian quantum channels

Youngrong Lim, Ryuji Takagi, Gerardo Adesso +1 more

Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low, or the thermal noise is high. This means that we can transmit quantum information reliably through very noisy Gaussian channels with the help of another Gaussian channel, whose quantum capacity is also zero. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the nonactivation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.

arXiv:1901.03147•Physical Review A•Mar 25, 2019•17 citations

Private communication via zero-private-capacity quantum channels

Chengkai Zhu, Xin Wang

Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.

quant-pharXiv:2609.10520•Sep 10, 2026•0 citations

Computational Refutation of Quantum Superactivation via Bound Entanglement in Low Dimensions

Yaroslav Murai

Smith and Yard (2008) famously demonstrated that two quantum channels with zero quantum capacity can possess a strictly positive joint capacity, a phenomenon known as superactivation. Their proof relies on the existence of Positive Partial Transpose (PPT) states possessing a strictly positive Devetak-Winter private key rate ($K_{DW} > 0$), explicitly citing a 4x4 construction by Horodecki et al. We present a two-tiered computational refutation of this phenomenon. First, using a high-precision global optimization framework with exact Stinespring purifications, we compute $K_{DW}$ across the full 512-dimensional PPT manifold for d=4x4 and find a strict upper bound of $K_{DW} \le -0.68$ bits, physically breaking the foundational protocol. Second, to address recent theoretical defenses concerning macro-scale finite-blocklength scaling ($N \ge 17$), we deploy a 30-qubit hybrid machine learning simulator (equivalent to $N=15$ joint channels). By evaluating the joint topology under strict causal limits and with omniscient encoder prescience, we demonstrate a complete failure to achieve positive capacity, establishing that superactivation is physically impossible in practical quantum systems.

•May 14, 2026•0 citations

Secure Communication over Zero-Private Capacity Quantum Channels

László Gyöngyösi, Sándor Imre

In this work a new phenomenon called polaractivation is introduced. Polaractivation is based on quantum polar encoding and the result is similar to the superactivation effect — positive capacity can be achieved with zero-capacity quantum channels. However, polaractivation has many advantages over the superactivation: it is limited neither by any preliminary conditions on the quantum channel nor on the maps of other channels involved in the joint channel structure. We prove that the polaractivation works for arbitrary zero-private capacity quantum channels and we demonstrate, that the symmetric private classical capacity of arbitrary zero-private capacity quantum channels is polaractive.

EPiC series in computing•Jan 23, 2018•0 citations

Noise cancellation by superposition of channels and superactivation of quantum capacity: Experimental realization by NMR

Deepika Bhargava, Arijit Chatterjee, Vishal Varma +1 more

Noisy quantum channels degrade quantum resources such as coherence and entanglement and hence pose challenges for realizing quantum technologies. Coherent control of noisy channels allows us to minimize their effects on the quantum system. Here we achieve the cancellation of two noisy quantum channels by superposing their corresponding Stinespring dilation unitaries. We first arrive at conditions under which superposition of channels results in a valid quantum channel. We then consider superposing two dephasing channels and observe their destructive interference, thereby effectively recovering the quantum coherence. On superposing two zero-capacity depolarizing channels, we show superactivation of quantum capacity. We experimentally realize the cancellation of two dephasing channels using a three-qubit NMR register. Furthermore, using a five-qubit NMR register, we realize the cancellation of two depolarization channels and demonstrate superactivation of quantum capacity.

quant-pharXiv:2606.10744•Jun 10, 2026•0 citations

Superadditivity of Quantum Channel Coding Rate With Finite Blocklength Joint Measurements

Hye Won Chung, Saikat Guha, Lizhong Zheng

The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on C[subscript N]/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to C[subscript N]/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C², where V is the respective channel dispersion quantity.

•Aug 1, 2016•8 citations
Superactivation of quantum capacity is the phenomenon whereby two quantum channels, each with zero quantum capacity, can exhibit a strictly positive capacity when used in tandem. In this work, we explore superactivation in the previously unexplored non-asymptotic regime of finitely many channel uses. We give a definition of finite-blocklength superactivation and propose numerical methods that can certify it. Then, focusing on the 50% erasure and positive-partial-transpose channels considered in the original work on superactivation, we show that as few as 17 uses of the joint channel already enable qubit transmission with a fidelity unattainable by any number of uses of either channel alone, demonstrating a strong finite-blocklength form of superactivation and opening the door to experimental demonstration.
Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low, or the thermal noise is high. This means that we can transmit quantum information reliably through very noisy Gaussian channels with the help of another Gaussian channel, whose quantum capacity is also zero. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the nonactivation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.
Private communication over a noisy quantum channel requires reliable transmission to the receiver and secrecy from the environment. Whether two channels with zero private capacity can jointly enable private communication is a longstanding open problem in quantum information theory. Here we resolve this problem by exhibiting a four-level channel and a qubit erasure channel with half erasure probability, each with zero private capacity, whose joint use achieves more than 0.0001903 private bits per product use. The encoding gives the receiver a linear information gain with at most quadratic environmental leakage, enabling privacy through a fixed joint measurement and classical coding. This superactivation, impossible for independent classical memoryless wiretap channels, shows that a channel's private capacity alone does not determine its value for secure communication. The initial activation example was identified through interactions with large language models, and the result has been formalized in Lean 4.
Smith and Yard (2008) famously demonstrated that two quantum channels with zero quantum capacity can possess a strictly positive joint capacity, a phenomenon known as superactivation. Their proof relies on the existence of Positive Partial Transpose (PPT) states possessing a strictly positive Devetak-Winter private key rate (KDW>0K_{DW} > 0KDW​>0), explicitly citing a 4x4 construction by Horodecki et al. We present a two-tiered computational refutation of this phenomenon. First, using a high-precision global optimization framework with exact Stinespring purifications, we compute KDWK_{DW}KDW​ across the full 512-dimensional PPT manifold for d=4x4 and find a strict upper bound of KDW≤−0.68K_{DW} \le -0.68KDW​≤−0.68 bits, physically breaking the foundational protocol. Second, to address recent theoretical defenses concerning macro-scale finite-blocklength scaling (N≥17N \ge 17N≥17), we deploy a 30-qubit hybrid machine learning simulator (equivalent to N=15N=15N=15 joint channels). By evaluating the joint topology under strict causal limits and with omniscient encoder prescience, we demonstrate a complete failure to achieve positive capacity, establishing that superactivation is physically impossible in practical quantum systems.
In this work a new phenomenon called polaractivation is introduced. Polaractivation is based on quantum polar encoding and the result is similar to the superactivation effect — positive capacity can be achieved with zero-capacity quantum channels. However, polaractivation has many advantages over the superactivation: it is limited neither by any preliminary conditions on the quantum channel nor on the maps of other channels involved in the joint channel structure. We prove that the polaractivation works for arbitrary zero-private capacity quantum channels and we demonstrate, that the symmetric private classical capacity of arbitrary zero-private capacity quantum channels is polaractive.
Noisy quantum channels degrade quantum resources such as coherence and entanglement and hence pose challenges for realizing quantum technologies. Coherent control of noisy channels allows us to minimize their effects on the quantum system. Here we achieve the cancellation of two noisy quantum channels by superposing their corresponding Stinespring dilation unitaries. We first arrive at conditions under which superposition of channels results in a valid quantum channel. We then consider superposing two dephasing channels and observe their destructive interference, thereby effectively recovering the quantum coherence. On superposing two zero-capacity depolarizing channels, we show superactivation of quantum capacity. We experimentally realize the cancellation of two dephasing channels using a three-qubit NMR register. Furthermore, using a five-qubit NMR register, we realize the cancellation of two depolarization channels and demonstrate superactivation of quantum capacity.
The maximum rate at which classical information can be reliably transmitted per use of a quantum channel strictly increases in general with N , the number of channel outputs that are detected jointly by the quantum joint-detection receiver (JDR). This phenomenon is known as superadditivity of the maximum achievable information rate over a quantum channel. We study this phenomenon for a pure-state classical-quantum channel and provide a lower bound on C[subscript N]/N, the maximum information rate when the JDR is restricted to making joint measurements over no more than N quantum channel outputs, while allowing arbitrary classical error correction. We also show the appearance of a superadditivity phenomenon-of mathematical resemblance to the aforesaid problem-in the channel capacity of a classical discrete memoryless channel when a concatenated coding scheme is employed, and the inner decoder is forced to make hard decisions on N-length inner codewords. Using this correspondence, we develop a unifying framework for the above two notions of superadditivity, and show that for our lower bound to C[subscript N]/N to be equal to a given fraction of the asymptotic capacity C of the respective channel, N must be proportional to V/C², where V is the respective channel dispersion quantity.