On the one-shot zero-error classical capacity of classical-quantum channels assisted by quantum non-signalling correlations

Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling correlations, minimized over all classicalquantum channels with a confusability graph G, is exactly log ϑ(G), where ϑ(G) is the celebrated Lov´asz theta function. In this paper, we show that the one-shot capacity for a classical-quantum channel, induced from a circulant graph G defined by equal-sized cyclotomic cosets, is logbϑ(G)c, which further implies that its asymptotic capacity is log ϑ(G). This type of graphs include the cycle graphs of odd length, the Paley graphs of prime vertices, and the cubit residue graphs of prime vertices. Examples of other graphs are also discussed. This gives Lov´asz ϑ function another operational meaning in zero-error classical-quantum communication.

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Performance characterization of Pauli channels assisted by indefinite causal order and post-measurement

Quantum Information and Computation ◽

10.26421/qic20.15-16-1 ◽

2020 ◽

Vol 20 (15&16) ◽

pp. 1261-1280

Author(s):

Francisco Delgado ◽

Carlos Cardoso-Isidoro

Keyword(s):

Quantum Channel ◽

Communication Channel ◽

Quantum Communication ◽

Quantum Channels ◽

Causal Order ◽

Combined Process ◽

Performance Characterization ◽

Output State ◽

Transmission Of Information

Indefinite causal order has introduced disruptive procedures to improve the fidelity of quantum communication by introducing the superposition of { orders} on a set of quantum channels. It has been applied to several well characterized quantum channels as depolarizing, dephasing and teleportation. This work analyses the behavior of a parametric quantum channel for single qubits expressed in the form of Pauli channels. Combinatorics lets to obtain affordable formulas for the analysis of the output state of the channel when it goes through a certain imperfect quantum communication channel when it is deployed as a redundant application of it under indefinite causal order. In addition, the process exploits post-measurement on the associated control to select certain components of transmission. Then, the fidelity of such outputs is analysed to characterize the generic channel in terms of its parameters. As a result, we get notable enhancement in the transmission of information for well characterized channels due to the combined process: indefinite causal order plus post-measurement.

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Towards joint reconstruction of noise and losses in quantum channels

Quantum Measurements and Quantum Metrology ◽

10.1515/qmetro-2016-0005 ◽

2016 ◽

Vol 3 (1) ◽

Author(s):

F. Piacentini ◽

A. Avella ◽

P. Traina ◽

L. Lolli ◽

E. Taralli ◽

...

Keyword(s):

Quantum Channel ◽

Quantum Communication ◽

Photon Number ◽

Practical Implementation ◽

Quantum Metrology ◽

Quantum Channels ◽

Transmission Losses ◽

Single Measurement ◽

Joint Reconstruction

AbstractThe calibration of a quantum channel, i.e. the determination of the transmission losses affecting it, is definitely one of the principal objectives in both the quantum communication and quantum metrology frameworks. Another task of the utmost relevance is the identification, e.g. by extracting its photon number distribution, of the noise potentially present in the channel.Here we present a protocol, based on the response of a photon-number-resolving detector at different quantum efficiencies, able to accomplish both of these tasks at once, providing with a single measurement an estimate of the transmission losses as well as the photon statistics of the noise present in the exploited quantum channel.We show and discuss the experimental results obtained in the practical implementation of such protocol, with different kinds and levels of noise.

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Explicit Construction of Optimal Witnesses for Input-Output Correlations Attainable by Quantum Channels

Open Systems & Information Dynamics ◽

10.1142/s1230161220500171 ◽

2020 ◽

Vol 27 (04) ◽

pp. 2050017

Author(s):

Michele Dall’Arno ◽

Sarah Brandsen ◽

Francesco Buscemi

Keyword(s):

Quantum Channel ◽

Explicit Construction ◽

Quantum Channels ◽

Input Output ◽

Noisy Channels ◽

Completely Positive ◽

Communication Games ◽

Single Use ◽

Classical Quantum ◽

Communication Resource

Given a quantum channel — that is, a completely positive trace-preserving linear map — as the only communication resource available between two parties, we consider the problem of characterizing the set of classical noisy channels that can be obtained from it by means of suitable classical-quantum encodings and quantum-classical decodings, respectively, on the sender’s and the receiver’s side. We consider various classes of linear witnesses and compute their optimum values in closed form for several classes of quantum channels. The witnesses that we consider here are formulated as communication games, in which Alice’s aim is to exploit a single use of a given quantum channel to help Bob guess some information she has received from an external referee.

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Secure Communication over Zero-Private Capacity Quantum Channels

10.29007/pcxv ◽

2018 ◽

Author(s):

Laszlo Gyongyosi ◽

Sandor Imre

Keyword(s):

Quantum Channel ◽

Secure Communication ◽

Channel Structure ◽

Quantum Channels ◽

Private Capacity ◽

Classical Capacity ◽

Zero Capacity ◽

Joint Channel ◽

Positive Capacity

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.

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INFORMATION TRANSMISSION VIA ENTANGLED QUANTUM STATES IN GAUSSIAN CHANNELS WITH MEMORY

International Journal of Quantum Information ◽

10.1142/s021974990600189x ◽

2006 ◽

Vol 04 (03) ◽

pp. 439-452 ◽

Cited By ~ 3

Author(s):

NICOLAS J. CERF ◽

JULIEN CLAVAREAU ◽

JÉRÉMIE ROLAND ◽

CHIARA MACCHIAVELLO

Keyword(s):

Quantum Channel ◽

Quantum States ◽

Gaussian Channel ◽

Hard Problem ◽

Quantum Channels ◽

Classical Capacity ◽

Gaussian Channels ◽

Memoryless Channels ◽

Entangled Quantum States ◽

With Memory

Gaussian quantum channels have recently attracted a growing interest, since they may lead to a tractable approach to the generally hard problem of evaluating quantum channel capacities. However, the analysis performed so far has always been restricted to memoryless channels. Here, we consider the case of a bosonic Gaussian channel with memory, and show that the classical capacity can be significantly enhanced by employing entangled input symbols instead of product symbols.

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Classical capacity of a Bayesian inference quantum channel employing photon counting detectors

Proceedings of the 4th International Symposium on Applied Sciences in Biomedical and Communication Technologies - ISABEL '11 ◽

10.1145/2093698.2093859 ◽

2011 ◽

Author(s):

F. Daneshgaran ◽

M. T. Delgado ◽

M. Mondin ◽

I. Bari

Keyword(s):

Bayesian Inference ◽

Quantum Channel ◽

Photon Counting ◽

Classical Capacity ◽

Photon Counting Detectors

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Fundamental limitations on distillation of quantum channel resources

Nature Communications ◽

10.1038/s41467-021-24699-0 ◽

2021 ◽

Vol 12 (1) ◽

Author(s):

Bartosz Regula ◽

Ryuji Takagi

Keyword(s):

Lower Bounds ◽

Quantum Channel ◽

Quantum Communication ◽

Fault Tolerant ◽

State Of The Art ◽

Quantum Systems ◽

Noisy Channels ◽

General Transformation ◽

Fundamental Limitations ◽

Strong Converse

AbstractQuantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

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Optimal teleportation via noisy quantum channels without additional qubit resources

npj Quantum Information ◽

10.1038/s41534-021-00426-x ◽

2021 ◽

Vol 7 (1) ◽

Author(s):

Dong-Gil Im ◽

Chung-Hyun Lee ◽

Yosep Kim ◽

Hyunchul Nha ◽

M. S. Kim ◽

...

Keyword(s):

Quantum Computing ◽

Quantum Teleportation ◽

Quantum Communication ◽

Quantum Noise ◽

Single Copy ◽

Entangled State ◽

Quantum Network ◽

Quantum Channels ◽

Maximally Entangled State ◽

Near Term

AbstractQuantum teleportation exemplifies how the transmission of quantum information starkly differs from that of classical information and serves as a key protocol for quantum communication and quantum computing. While an ideal teleportation protocol requires noiseless quantum channels to share a pure maximally entangled state, the reality is that shared entanglement is often severely degraded due to various decoherence mechanisms. Although the quantum noise induced by the decoherence is indeed a major obstacle to realizing a near-term quantum network or processor with a limited number of qubits, the methodologies considered thus far to address this issue are resource-intensive. Here, we demonstrate a protocol that allows optimal quantum teleportation via noisy quantum channels without additional qubit resources. By analyzing teleportation in the framework of generalized quantum measurement, we optimize the teleportation protocol for noisy quantum channels. In particular, we experimentally demonstrate that our protocol enables to teleport an unknown qubit even via a single copy of an entangled state under strong decoherence that would otherwise preclude any quantum operation. Our work provides a useful methodology for practically coping with decoherence with a limited number of qubits and paves the way for realizing noisy intermediate-scale quantum computing and quantum communication.

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