Polaractivation of Zero-Capacity Optical Quantum Channels

2012 ◽  
Author(s):  
Laszlo Gyongyosi ◽  
Sandor Imre
Keyword(s):  
Quantum Channels ◽  
Zero Capacity

scholarly journals Quantum Advantage for Shared Randomness Generation

Quantum ◽  
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.

scholarly journals 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.

scholarly journals 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.

scholarly journals Jordan products of quantum channels and their compatibility

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Mark Girard ◽  
Martin Plávala ◽  
Jamie Sikora
Keyword(s):  
Quantum State ◽  
Sufficient Conditions ◽  
The Other ◽  
Independent Interest ◽  
Quantum Channels ◽  
Semidefinite Programs ◽  
Jordan Product ◽  
Marginal Problem ◽  
Jordan Products ◽  
Product Of Matrices

AbstractGiven two quantum channels, we examine the task of determining whether they are compatible—meaning that one can perform both channels simultaneously but, in the future, choose exactly one channel whose output is desired (while forfeiting the output of the other channel). Here, we present several results concerning this task. First, we show it is equivalent to the quantum state marginal problem, i.e., every quantum state marginal problem can be recast as the compatibility of two channels, and vice versa. Second, we show that compatible measure-and-prepare channels (i.e., entanglement-breaking channels) do not necessarily have a measure-and-prepare compatibilizing channel. Third, we extend the notion of the Jordan product of matrices to quantum channels and present sufficient conditions for channel compatibility. These Jordan products and their generalizations might be of independent interest. Last, we formulate the different notions of compatibility as semidefinite programs and numerically test when families of partially dephasing-depolarizing channels are compatible.

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