# Chain-Rules for Channel Capacity

@article{Jain2021ChainRulesFC, title={Chain-Rules for Channel Capacity}, author={Rahul Jain}, journal={2021 IEEE International Symposium on Information Theory (ISIT)}, year={2021}, pages={262-267} }

We show some chain-rules for the capacity11In some sense, the maximum amount of information that can be conveyed through the channel. of classical-quantum and quantum channels. We use the concept of Nash-Equilibrium in game-theory, and its existence in suitably defined games, to arrive at the chain-rules.

## References

SHOWING 1-10 OF 33 REFERENCES

### Communication complexity of remote state preparation with entanglement

- Computer Science, MathematicsQuantum Inf. Comput.
- 2006

This work considers the problem of remote state preparation, in the presence of entanglement and in the scenario of single use of the channel, and studies the communication complexity of this problem.

### New Results in the Simultaneous Message Passing Model via Information Theoretic Techniques

- Computer Science2009 24th Annual IEEE Conference on Computational Complexity
- 2009

The gap between the $\smp$ model and the one-way model in communication complexity is investigated and a partial function is investigated that is exponentially more expensive in the former if quantum communication with entanglement is allowed, compared to the latter even in the deterministic case.

### Interactive compression to external information

- Computer ScienceSTOC
- 2018

It is shown that every communication protocol that communicates C bits and reveals I bits of information about the participants’ private inputs to an observer that watches the communication, can be simulated by a new protocol that communicating at most poly(I) · loglog(C) bits.

### An Interactive Information Odometer and Applications

- Computer Science, MathematicsSTOC
- 2015

It is shown that the odometer allows to reduce interactive compression to the regime where I=O(log C), thereby opening a potential avenue for improving the compression result of [BBCR10] and to new direct sum and product theorems in communication complexity.

### Interactive compression for product distributions

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2015

The interactive compression problem is studied, and a protocol is given that is the first simulation protocol whose communication complexity is bounded by a polynomial in the information cost of the original protocol.

### Compressing Interactive Communication under Product Distributions

- Computer Science2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
- 2016

This work focuses on the case when the participants' inputs are distributed independently and shows how to compress the communication to O(I log2 I) bits, with no dependence on the original communication cost.

### Interactive information complexity

- Computer Science, MathematicsSTOC '12
- 2012

It is shown that IC(f) is equal to the amortized (randomized) communication complexity of f, and this connection implies that a non-trivial exchange of information is required when solving problems that have non-Trivial communication complexity.

### A Course in Game Theory

- Economics
- 1994

A Course in Game Theory presents the main ideas of game theory at a level suitable for graduate students and advanced undergraduates, emphasizing the theory's foundations and interpretations of its…

### New Strong Direct Product Results in Communication Complexity

- Computer Science, MathematicsElectron. Colloquium Comput. Complex.
- 2011

It is proved that the new complexity measure gives a tight lower bound of Ω(n) for the set-disjointness problem on n-bit inputs (this strengthens the linear lower bound on the rectangle/corruption bound for set- Disjoints shown by Razborov [1992]).

### Prior entanglement, message compression and privacy in quantum communication

- Computer Science20th Annual IEEE Conference on Computational Complexity (CCC'05)
- 2005

It is shown that the first message of P can be compressed to 0(k) classical bits using prior entanglement if it carries at most k bits of information about the sender's input, which implies a general direct sum result for one-round and simultaneous quantum protocols.