# No-Go Theorems for Quantum Resource Purification: New Approach and Channel Theory

@article{Fang2020NoGoTF, title={No-Go Theorems for Quantum Resource Purification: New Approach and Channel Theory}, author={Kun Fang and Zi-Wen Liu}, journal={PRX Quantum}, year={2020} }

It is recently shown that there exist fundamental limits to the accuracy and efficiency of purifying generic noisy resource states in any well-behaved quantum resource theory [Fang/Liu, Phys. Rev. Lett. 125, 060405 (2020)]. Here, we develop a novel and powerful method for analyzing the limitations of quantum resource purification, which not only leads to improved bounds that rule out exact purification for a broader range of noisy states and are tight in certain cases, but also allow us to…

## 20 Citations

### Fundamental limitations on quantum channel manipulation

- Computer Science
- 2020

Comprehensive lower bounds for the overhead of any physical distillation protocol in terms of required channel uses are introduced, imposing strong limitations on the practical efficiency and cost of channel manipulation protocols.

### One-Shot Manipulation of Dynamical Quantum Resources.

- Computer SciencePhysical review letters
- 2021

We develop a unified framework to characterize one-shot transformations of dynamical quantum resources in terms of resource quantifiers, establishing universal conditions for exact and approximate…

### Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes

- Physics
- 2021

Quantum error correction and symmetries play central roles in quantum information science and physics. It is known that quantum error-correcting codes covariant with respect to continuous symmetries…

### Tight constraints on probabilistic convertibility of quantum states

- Computer ScienceQuantum
- 2022

The monotone is used to tightly characterise single-shot probabilistic distillation in broad types of resource theories, allowing an exact analysis of the trade-offs between the probabilities and errors in distilling maximally resourceful states.

### Probabilistic Transformations of Quantum Resources.

- Computer SciencePhysical review letters
- 2022

This work introduces a new resource monotone that obeys a very strong type of monotonicity that can rule out all transformations, probabilistic or deterministic, between states in any quantum resource theory, and strengthens previous findings and extends recent no-go theorems.

### No second law of entanglement manipulation after all

- PhysicsNature Physics
- 2023

Many fruitful analogies have emerged between the theories of quantum entanglement and thermodynamics, motivating the pursuit of an axiomatic description of entanglement akin to the laws of…

### Quantum NETwork: from theory to practice

- Computer ScienceArXiv
- 2022

This work aims to provide an up-to-date review of the field of quantum networks from both theoretical and experimental perspectives, contributing to a better understanding of the building blocks required for the establishment of a global quantum internet.

### Method for Quantum Denoisers Using Convolutional Neural Network

- PhysicsComputational intelligence and neuroscience
- 2022

In many applications of quantum information science, high-dimensional entanglement is needed. Quantum teleportation is used for transferring information from one place to another using…

### Projective robustness for quantum channels and measurements and their operational significance

- MathematicsLaser Physics Letters
- 2022

Recently, the projective robustness of quantum states was introduced in (Regula 2022 Phys. Rev. Lett. 128 110505). This demonstrates that the projective robustness is a useful resource monotone and…

### Relation between quantum coherence and quantum entanglement in quantum measurements

- PhysicsPhysical Review A
- 2022

Quantum measurement is a class of quantum channels that sends quantum states to classical states. We set up resource theories of quantum coherence and quantum entanglement for quantum measurements…

## References

SHOWING 1-10 OF 94 REFERENCES

### Fundamental limitations on quantum channel manipulation

- Computer Science
- 2020

Comprehensive lower bounds for the overhead of any physical distillation protocol in terms of required channel uses are introduced, imposing strong limitations on the practical efficiency and cost of channel manipulation protocols.

### No-Go Theorems for Quantum Resource Purification.

- Computer SciencePhysical review letters
- 2020

It is proved fundamental limitations on how effectively generic noisy resources can be purified enforced by the laws of quantum mechanics, which universally apply to any reasonable kind of quantum resource.

### Resource theory of asymmetric distinguishability for quantum channels

- Computer SciencePhysical Review Research
- 2019

Two special cases of the general channel box transformation problem, known as distinguishability distillation and dilution, are considered, and it is proved that the exact distinguishability cost is equal to the channel max-relative entropy and the distillable distinguishability isequal to the amortized channel relative entropy.

### One-Shot Operational Quantum Resource Theory.

- Computer SciencePhysical review letters
- 2019

This work analyzes, from a resource-nonspecific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation.

### Quantum coding with finite resources

- Computer ScienceNature communications
- 2016

This work finds approximate and exact characterizations of this trade-off for various channels of interest, including dephasing, depolarizing and erasure channels, and develops several bounds that are valid for general quantum channels and can be computed for small instances.

### Quantifying the magic of quantum channels

- Computer Science, PhysicsNew Journal of Physics
- 2019

A resource theory for magic quantum channels is developed to characterize and quantify the quantum ‘magic’ or non-stabilizerness of noisy quantum circuits, and two efficiently computable magic measures for quantum channels are introduced.

### Reversible Framework for Quantum Resource Theories.

- MathematicsPhysical review letters
- 2015

The general structure of QRTs is discussed, and it is shown that under a few assumptions, a QRT is asymptotically reversible if its set of allowed operations is maximal, that is, if the allowed operations are the set of all operations that do not generate (asymptotical) a resource.

### Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages)

- Physics
- 2005

We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state |0>, and qubit measurement in the computational basis.…

### Strong Converse Exponents for a Quantum Channel Discrimination Problem and Quantum-Feedback-Assisted Communication

- Computer ScienceArXiv
- 2014

It is shown that the most general adaptive discrimination strategies provide no asymptotic advantage over non-adaptive tensor-power strategies in this channel discrimination setting, and a strong converse theorem is established for the quantum-feedback-assisted capacity of a channel.

### Theoretical framework for quantum networks

- Physics, Computer Science
- 2009

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such…