# The Capacity of the Quantum Channel with General Signal States

@article{Holevo1998TheCO, title={The Capacity of the Quantum Channel with General Signal States}, author={Alexander S. Holevo}, journal={IEEE Trans. Inf. Theory}, year={1998}, volume={44}, pages={269-273} }

It is shown that the capacity of a classical-quantum channel with arbitrary (possibly mixed) states equals the maximum of the entropy bound with respect to all a priori distributions. This completes the recent result of Hausladen, Jozsa, Schumacher, Westmoreland, and Wootters (1996), who proved the equality for the pure state channel.

## 964 Citations

### Transition behavior in the channel capacity of two-quibit channels with memory

- Computer Science
- 2004

It is proved that a general upper bound on the maximal mutual information of quantum channels is saturated in the case of Pauli channels with an arbitrary degree of memory and for a subset of such channels, the optimal signal states are identified.

### Quantum Gaussian channels

- Physics, Computer Science2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060)
- 2000

The aim of this paper is explicit calculation of the classical capacity of quantum Gaussian channels, in particular, of those using squeezed states, based on a general formula for the entropy of quantumGaussian state and on the recently proved coding theorem for quantum communication channels.

### Classical capacities of compound quantum channels

- Computer Science2008 IEEE Information Theory Workshop
- 2008

The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-Quantum channels.

### Efficient Accessible Bounds to the Classical Capacity of Quantum Channels.

- Computer SciencePhysical review letters
- 2019

A method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements, reconstruction of sets of conditional probabilities, and classical optimization is presented.

### Capacities of Quantum Erasure Channels

- Physics
- 1997

The quantum analog of the classical erasure channel provides a simple example of a channel whose asymptotic capacity for faithful transmission of intact quantum states, with and without the…

### Strong converse to the quantum channel coding theorem

- Computer ScienceIEEE Trans. Inf. Theory
- 1999

A lower bound on the probability of decoding error for a quantum communication channel is presented, from which the strong converse to the quantum channel coding theorem is immediately shown. The…

### Zero-error capacity of quantum channels and noiseless subsystems

- Computer Science2006 International Telecommunications Symposium
- 2006

If the authors have a noiseless subsystem state p supported by a projector P, then any quantum state with components in the subspace Pperp is adjacent to p, and this result has some interesting implications for the quantum states of the optimum (S,V) for which the zero-error capacity is reached.

### Classical Capacity of Classical-Quantum Arbitrarily Varying Channels

- MathematicsIEEE Transactions on Information Theory
- 2007

We prove that the average error classical capacity C(W) of a classicalquantum arbitrarily varying channel (cq-AVC) W equals 0 or else the random code capacity C (Ahlswede's dichotomy). We also…

### Generalized relative entropies and the capacity of classical-quantum channels

- Computer Science
- 2009

Lower and upper bounds on the information transmission capacity of one single use of a classical-quantum channel are provided and a quantity obtained by replacing the relative entropy with the recently introduced max-relative entropy in the definition of the divergence radius of a channel is provided.

## References

SHOWING 1-10 OF 27 REFERENCES

### On Reliability Function of Quantum Communication Channel

- Computer Science
- 1997

Bounds for the reliability function of a quantum pure state channel are given and an alternative proof of the coding theorem for quantum noiseless channel is suggested, which would make no use of the notion of typical subspace.

### Ultimate information carrying limit of quantum systems.

- PhysicsPhysical review letters
- 1993

The possible amount of information transfer between any source and any user via a quantum system is bounded through the quantum entropy function, which shows that infinite information transfer implies infinite entropy.

### On Quantum Communication Channels with Constrained Inputs

- Computer Science
- 1997

The purpose of this work is to extend the result of previous papers to quantum channels with additive constraints onto the input signal, by showing that the capacity of such channel is equal to the supremum of the entropy bound with respect to all apriori distributions satisfying the constraint.

### Sending classical information via noisy quantum channels

- Computer Science
- 1997

This paper extends previous results about the classical information capacity of a noiseless quantum-mechanical communication channel to situations in which the final signal states are mixed states,…

### Classical information capacity of a quantum channel.

- Computer SciencePhysical review. A, Atomic, molecular, and optical physics
- 1996

If the sender uses a block coding scheme consisting of a choice of code words that respects the a priori probabilities of the letter states, and the receiver distinguishes whole words rather than individual letters, then the information transmitted can be made arbitrarily close to H and never exceeds H, providing a precise information-theoretic interpretation of von Neumann entropy in quantum mechanics.

### Optimal detection of quantum information.

- PhysicsPhysical review letters
- 1991

The most efficient set of operations of that type that the authors were able to design falls short of a single combined measurement, performed on both system together.

### A new proof of the quantum noiseless coding theorem

- Physics
- 1994

An account of the quantum noiseless coding theorem, including a new proof based on a simplified block coding scheme, and an illustrative example of quantum coding.

### Entropy inequalities

- Mathematics
- 1970

Some inequalities and relations among entropies of reduced quantum mechanical density matrices are discussed and proved. While these are not as strong as those available for classical systems they…

### Introduction to photon communication

- Physics
- 1995

Elements of the Mathematical Formulation of the Quantum Theory.- Performance Criteria: Detection, Information.- Direct Detection Processing.- Phase Operator.- Conclusion.