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:2509.08965 · Physical Review Letters

Retrocausal Capacity of a Quantum Channel: Communicating through Noisy Closed Timelike Curves

Kaiyuan Ji, Seth Lloyd, Mark M. Wilde

Published Apr 14, 2026• 1 citation
arXivHTMLPDF

Abstract

We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve mathematically represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-information and its regularized Doeblin information. This endows these information measures with a novel operational interpretation. Furthermore, our characterization can be generalized beyond quantum channels to all completely positive maps. This imposes information-theoretic limits on transmitting messages via postselected-teleportation-like mechanisms with arbitrary initial- and final-state boundary conditions, including those considered in various black-hole final-state models.

DOI
10.1103/znyd-npk5

Related papers

Postselected communication over quantum channels

Kaiyuan Ji, Bartosz Regula, Mark M. Wilde

The single-letter characterization of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, “inconclusive” measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterization of postselected capacities in the setting of entanglement assistance as well as the more general nonsignaling assistance, establishing that they are both equal to the channel’s projective mutual information — a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation-based protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel’s ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves.

arXiv:2308.02583•International Journal of Quantum Information•Apr 30, 2024•2 citations

One-shot capacity bounds on the simultaneous transmission of classical and quantum information

Salek, F, Anshu, A, Min-Hsiu Hsieh +2 more

© 1963-2012 IEEE. We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

•Apr 1, 2020•12 citations

One-Shot Capacity Bounds on the Simultaneous Transmission of Classical and Quantum Information

Farzin Salek, Anurag Anshu, Min-Hsiu Hsieh +2 more

We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.

arXiv:1809.07104•IEEE Transactions on Information Theory•Oct 7, 2019•12 citations

Randomized Partial Decoupling Unifies One-Shot Quantum Channel Capacities

Eyuri Wakakuwa, Yoshifumi Nakata

We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive the direct and converse bounds for the one-shot capacity region. The bounds are represented in terms of the smooth conditional entropies and the error tolerance, and coincide in the asymptotic limit of infinitely many uses of the channel. The direct and converse bounds for various communication tasks are obtained as corollaries, both for one-shot and asymptotic scenarios. The proof is based on the randomized partial decoupling theorem, which is a generalization of the decoupling theorem. Thereby we provide a unified decoupling approach to the one-shot quantum channel coding, by fully incorporating classical communication, quantum communication and shared entanglement.

•Apr 27, 2020•4 citations

Relativistic quantum communication: Energy cost and channel capacities

Ian Bernardes Barcellos, André G. S. Landulfo

We consider the communication of classical and quantum information between two arbitrary observers in asymptotically flat spacetimes (possibly containing black holes) and investigate what the energy cost is for such information transmission. By means of localized two-level quantum systems, sender and receiver can use a quantum scalar field as a communication channel. As we have already shown in a previous paper, such a channel has nonvanishing classical capacity as well as entanglement-assisted classical and quantum capacities. Here we will show that the change in the expectation value of the energy of the system during the communication process can be separated in (i) a contribution coming from the particle creation due to the change of the spacetime, (ii) a contribution associated with the energy needed to switch on or off each qubit, and (iii) a term which comes from the communication process itself. For the quantum channel considered here, we show that the extra energy cost needed for communication vanishes. As a result, if one has already created a system of qubits for some specific task (e.g., quantum computation), one can also reliably convey information between its parts with no extra energy cost. We conclude the paper by illustrating the form of the channel capacities and energy contributions in two paradigmatic cases in Minkowski spacetime: (i) sender and receiver in inertial motion and (ii) sender in inertial motion while the receiver is uniformly accelerated.

arXiv:2109.13896•Physical review. D/Physical review. D.•Nov 22, 2021•17 citations

Capacities of Gaussian Quantum Channels With Passive Environment Assistance

Samad Khabbazi Oskouei, Stefano Mancini, Andreas Winter

Passive environment-assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders). Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions. In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas. Concerning classical communication, we prove a general coding theorem for the classical capacity under an energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.

arXiv:2101.00602•IEEE Transactions on Information Theory•Oct 25, 2021•10 citations
We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve mathematically represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-information and its regularized Doeblin information. This endows these information measures with a novel operational interpretation. Furthermore, our characterization can be generalized beyond quantum channels to all completely positive maps. This imposes information-theoretic limits on transmitting messages via postselected-teleportation-like mechanisms with arbitrary initial- and final-state boundary conditions, including those considered in various black-hole final-state models.
The single-letter characterization of the entanglement-assisted capacity of a quantum channel is one of the seminal results of quantum information theory. In this paper, we consider a modified communication scenario in which the receiver is allowed an additional, “inconclusive” measurement outcome, and we employ an error metric given by the error probability in decoding the transmitted message conditioned on a conclusive measurement result. We call this setting postselected communication and the ensuing highest achievable rates the postselected capacities. Here, we provide a precise single-letter characterization of postselected capacities in the setting of entanglement assistance as well as the more general nonsignaling assistance, establishing that they are both equal to the channel’s projective mutual information — a variant of mutual information based on the Hilbert projective metric. We do so by establishing bounds on the one-shot postselected capacities, with a lower bound that makes use of a postselected teleportation-based protocol and an upper bound in terms of the postselected hypothesis testing relative entropy. As such, we obtain fundamental limits on a channel’s ability to communicate even when this strong resource of postselection is allowed, implying limitations on communication even when the receiver has access to postselected closed timelike curves.
© 1963-2012 IEEE. We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.
We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.
We analyze a task in which classical and quantum messages are simultaneously communicated via a noisy quantum channel, assisted with a limited amount of shared entanglement. We derive the direct and converse bounds for the one-shot capacity region. The bounds are represented in terms of the smooth conditional entropies and the error tolerance, and coincide in the asymptotic limit of infinitely many uses of the channel. The direct and converse bounds for various communication tasks are obtained as corollaries, both for one-shot and asymptotic scenarios. The proof is based on the randomized partial decoupling theorem, which is a generalization of the decoupling theorem. Thereby we provide a unified decoupling approach to the one-shot quantum channel coding, by fully incorporating classical communication, quantum communication and shared entanglement.
We consider the communication of classical and quantum information between two arbitrary observers in asymptotically flat spacetimes (possibly containing black holes) and investigate what the energy cost is for such information transmission. By means of localized two-level quantum systems, sender and receiver can use a quantum scalar field as a communication channel. As we have already shown in a previous paper, such a channel has nonvanishing classical capacity as well as entanglement-assisted classical and quantum capacities. Here we will show that the change in the expectation value of the energy of the system during the communication process can be separated in (i) a contribution coming from the particle creation due to the change of the spacetime, (ii) a contribution associated with the energy needed to switch on or off each qubit, and (iii) a term which comes from the communication process itself. For the quantum channel considered here, we show that the extra energy cost needed for communication vanishes. As a result, if one has already created a system of qubits for some specific task (e.g., quantum computation), one can also reliably convey information between its parts with no extra energy cost. We conclude the paper by illustrating the form of the channel capacities and energy contributions in two paradigmatic cases in Minkowski spacetime: (i) sender and receiver in inertial motion and (ii) sender in inertial motion while the receiver is uniformly accelerated.
Passive environment-assisted communication takes place via a quantum channel modeled as a unitary interaction between the information carrying system and an environment, where the latter is controlled by a passive helper, who can set its initial state such as to assist sender and receiver, but not help actively by adjusting her behaviour depending on the message. Here we investigate the information transmission capabilities in this framework by considering Gaussian unitaries acting on Bosonic systems. We consider both quantum communication and classical communication with helper, as well as classical communication with free classical coordination between sender and helper (conferencing encoders). Concerning quantum communication, we prove general coding theorems with and without energy constraints, yielding multi-letter (regularized) expressions. In the search for cases where the capacity formula is computable, we look for Gaussian unitaries that are universally degradable or anti-degradable. However, we show that no Gaussian unitary yields either a degradable or anti-degradable channel for all environment states. On the other hand, restricting to Gaussian environment states, results in universally degradable unitaries, for which we thus can give single-letter quantum capacity formulas. Concerning classical communication, we prove a general coding theorem for the classical capacity under an energy constraint, given by a multi-letter expression. Furthermore, we derive an uncertainty-type relation between the classical capacities of the sender and the helper, helped respectively by the other party, showing a lower bound on the sum of the two capacities. Then, this is used to lower bound the classical information transmission rate in the scenario of classical communication between sender and helper.