Informational geometric analysis of superactivation of asymptotic quantum capacity of zero-capacity optical quantum channels

We introduce Partially Coherent Direct Sum (PCDS) quantum channels, as a generalization of the already known Direct Sum quantum channels. We derive necessary and sufficient conditions to identify the subset of those maps which are degradable, and provide a simplified expression for their quantum capacities. Interestingly, the special structure of PCDS allows us to extend the computation of the quantum capacity formula also for quantum channels which are explicitly not degradable (nor antidegradable). We show instances of applications of the results to dephasing channels, amplitude damping channels and combinations of the two.

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Quantum Advantage for Shared Randomness Generation

Quantum ◽

10.22331/q-2021-10-27-569 ◽

2021 ◽

Vol 5 ◽

pp. 569

Author(s):

Tamal Guha ◽

Mir Alimuddin ◽

Sumit Rout ◽

Amit Mukherjee ◽

Some Sankar Bhattacharya ◽

...

Keyword(s):

Message Passing ◽

State Of The Art ◽

Quantum Systems ◽

Quantum Channels ◽

Noisy Channels ◽

Information Theoretic ◽

Classical Counterpart ◽

Zero Capacity ◽

Set Up ◽

Noise Robust

Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.

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An upper bound on quantum capacity of unital quantum channels

2017 IEEE Information Theory Workshop (ITW) ◽

10.1109/itw.2017.8277947 ◽

2017 ◽

Author(s):

Anurag Anshu

Keyword(s):

Upper Bound ◽

Quantum Channels ◽

Quantum Capacity

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Algorithmic solution to superactivation of zero-capacity optical quantum channels

2010 Photonics Global Conference ◽

10.1109/pgc.2010.5705957 ◽

2010 ◽

Cited By ~ 1

Author(s):

L. Gyongyosi ◽

S. Imre

Keyword(s):

Quantum Channels ◽

Algorithmic Solution ◽

Zero Capacity

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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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On the Mathematical Boundaries of Communication with Zero-Capacity Quantum Channels

10.29007/7h1q ◽

2018 ◽

Author(s):

Laszlo Gyongyosi ◽

Sandor Imre

Keyword(s):

Information Theory ◽

Quantum Information ◽

21St Century ◽

Quantum Information Theory ◽

Quantum Mechanical ◽

Quantum Channels ◽

Classical Systems ◽

Quantum Relative Entropy ◽

Mathematical Properties ◽

Zero Capacity

In the first decade of the 21st century, many revolutionary properties of quantum channels were discovered. These phenomena are purely quantum mechanical and completely unimaginable in classical systems. Recently, the most important discovery in Quantum Information Theory was the possibility of transmitting quantum information over zero-capacity quantum channels. In this work we prove that the possibility of superactivation of quantum channel capacities is determined by the mathematical properties of the quantum relative entropy function.

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On Classification of Quantum Channels

Open Systems & Information Dynamics ◽

10.1023/a:1011365917780 ◽

2001 ◽

Vol 08 (01) ◽

pp. 73-88

Author(s):

Satoshi Iriyama ◽

Noboru Watanabe

Keyword(s):

Laser Beam ◽

Coherent State ◽

Optical Communication ◽

Quantum Communication ◽

Quantum Channels ◽

Squeezed State ◽

Quantum Capacity ◽

Communication Processes ◽

Mutual Entropy

Quantum mutual entropy and quantum capacity are rigorously defined by Ohya, and they are quite useful in the study of quantum communication processes [4, 7, 8, 9,10]. Mathematical models of optical communication processes are described by a quantum channel and optical states, and quantum capacity is one of the most important criteria to measure the efficiency of information transmission [4,7,8]. In actual optical communication, a laser beam is used for a signal, and it is denoted mathematically by a coherent state. Further, optical communication using a squeezed state, which is expected to be more efficient than that using a coherent state is proposed. In this paper, we define several quantum channels, that is, a squeezed channel and a coherent channel and so on. We compare them by calculating quantum capacity.

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