# Trade-off relations for operation entropy of complementary quantum channels

@article{Czartowski2019TradeoffRF, title={Trade-off relations for operation entropy of complementary quantum channels}, author={Jakub Czartowski and Daniel Braun and Karol Życzkowski}, journal={International Journal of Quantum Information}, year={2019} }

The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi–Jamiołkowski state, characterizes the coupling of the principal system with the environment. For any quantum channel acting on a state of a given size, one defines the complementary channel, which sends the input state into the state of the environment after the operation. Making use of subadditivity of entropy, we show that for any dimension the sum of both entropies is bounded from below. This…

## 3 Citations

### Completely synchronizing quantum channels

- Physics
- 2021

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide…

### Perfect quantum-state synchronization

- PhysicsPhysical Review A
- 2021

We investigate the most general mechanisms that lead to perfect synchronization of the quantum states of all subsystems of an open quantum system starting from an arbitrary initial state. We provide…

### Relating Compatibility and Divisibility of Quantum Channels

- BiologyInternational Journal of Theoretical Physics
- 2022

Two key concepts in quantum information: compatibility and divisibility of quantum channels are connected and it is shown that, for degradable channels, compatibility implies Divisibility, and that, in turn, for anti-degradability channels,divisibility implies compatibility.

## References

SHOWING 1-10 OF 25 REFERENCES

### Entropic trade-off relations for quantum operations

- Physics, Computer Science
- 2013

It is proved that for any map acting on a N--dimensional quantum system the sum of both entropies is not smaller than ln N, and the corresponding R\'enyi entropIES are investigated, providing an upper bound for their sum and entanglement of the bi-partite quantum state associated with the channel.

### ENTROPIC CHARACTERIZATION OF QUANTUM OPERATIONS

- Computer Science
- 2011

It is conjecture that for any channel Φ1 acting on a finite dimensional system, there exists a class of channels Φ2 sufficiently close to a unitary map such that additivity of minimal output entropy for Ψ1 ⊗ Ψ2 holds.

### Composition of quantum states and dynamical subadditivity

- Mathematics, Computer Science
- 2008

A composition of quantum states of a bipartite system which is based on the reshuffling of density matrices is introduced, and strong dynamical subadditivity of a concatenation of three bistochastic maps is established.

### Quantum channels and their entropic characteristics

- Computer Science, PhysicsReports on progress in physics. Physical Society
- 2012

A survey of the main properties of quantum channels and of their entropic characterization, with a variety of examples for finite-dimensional quantum systems, and the remarkable role of specific quantum correlations—entanglement—as a novel communication resource is stressed.

### The private classical capacity and quantum capacity of a quantum channel

- Physics, Computer ScienceIEEE Transactions on Information Theory
- 2005

Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement.

### The private classical information capacity and quantum information capacity of a quantum channel

- Computer Science, Physics
- 2003

### Coherifying quantum channels

- Physics
- 2017

Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is…

### On Duality between Quantum Maps and Quantum States

- MathematicsOpen Syst. Inf. Dyn.
- 2004

The concept of the dynamical matrix and the Jamiołkowski isomorphism are explored and an analogous relation is established between the classical maps and an extended space of the discrete probability distributions.

### Quantum Entropy and Its Use

- Physics
- 1993

I Entropies for Finite Quantum Systems.- 1 Fundamental Concepts.- 2 Postulates for Entropy and Relative Entropy.- 3 Convex Trace Functions.- II Entropies for General Quantum Systems.- 4 Modular…

### Selfcomplementary Quantum Channels

- PhysicsOpen Syst. Inf. Dyn.
- 2016

A parametrization of a large class of selfcomplementary channels is provided and it is shown that time evolution under selfcom complementary channels is highly non-Markovian.