# Coherence and entanglement measures based on Rényi relative entropies

@article{Zhu2017CoherenceAE, title={Coherence and entanglement measures based on R{\'e}nyi relative entropies}, author={Huangjun Zhu and Masahito Hayashi and Lin Chen}, journal={Journal of Physics A}, year={2017}, volume={50}, pages={475303} }

We study systematically resource measures of coherence and entanglement based on Renyi relative entropies, which include the logarithmic robustness of coherence, geometric coherence, and conventional relative entropy of coherence together with their entanglement analogues. First, we show that each Renyi relative entropy of coherence is equal to the corresponding Renyi relative entropy of entanglement for any maximally correlated state. By virtue of this observation, we establish a simple… Expand

#### 19 Citations

Coherence measures based on coherence eigenvalue and their applications

- Computer Science, Mathematics
- Quantum Inf. Process.
- 2019

By proposing a new coherence witness which is related to coherence eigenvalue, a bound to robustness of coherence is obtained and it is found that the convex roof coherence measure is equal to the geometric measure based on fidelity. Expand

Using and reusing coherence to realize quantum processes

- Computer Science, Physics
- Quantum
- 2018

It is found that in general a quantum channel can be implemented without employing a maximally coherent resource state, and it is proved that every pure coherent state in dimension larger than 2 turns out to be a valuable resource to implement some coherent unitary channel. Expand

Entanglement manipulation beyond local operations and classical communication

- Physics, Computer Science
- 2020

This paper demonstrates that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and shows that any two states can be interconverted by any polytope approximation to the set of separable channels. Expand

Brief report Robustness of coherence for multipartite quantum states

- Mathematics, Physics
- Pramana
- 2019

In this brief report, we prove that the robustness of coherence (ROC), in contrast with many popular quantitative measures of quantum coherence derived from the resource-theoretic framework of… Expand

Axiomatic and operational connections between the l 1 -norm of coherence and negativity

- Physics
- 2018

Quantum coherence plays a central role in various research areas. The ${l}_{1}$-norm of coherence is one of the most important coherence measures that are easily computable, but it is not easy to… Expand

Coherence manipulation with dephasing-covariant operations

- Mathematics, Physics
- 2019

It is shown that pure-state transformations under DIO are completely governed by majorization, establishing necessary and sufficient conditions for such transformations and adding to the list of operational paradigms where majorization plays a central role. Expand

Entropic Uncertainty Relations for Successive Measurements in the Presence of a Minimal Length

- Computer Science, Medicine
- Entropy
- 2018

The generalized uncertainty principle in scenarios of successive measurements of observables with continuous spectra is addressed, and uncertainty relations in terms of Shannon entropies of both the Rényi and Tsallis types are formulated. Expand

Zero uncertainty states in the presence of quantum memory

- Physics, Mathematics
- 2021

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The… Expand

Minimum uncertainty states in the presence of quantum memory

- Physics
- 2020

The uncertainty principle imposes a fundamental limit on predicting the measurement outcomes of incompatible observables even if complete classical information of the system state is known. The… Expand

Secure uniform random number extraction via incoherent strategies

- Mathematics, Physics
- ArXiv
- 2017

The maximum secure extraction rate is shown to be equal to the relative entropy of coherence, which clarifies the power of incoherent strategies in random number generation, and can be applied to guarantee the quality of random numbers generated by a quantum random number generator. Expand

#### References

SHOWING 1-10 OF 96 REFERENCES

Quantifying entanglement with witness operators

- Physics
- 2005

We present a unifying approach to the quantification of entanglement based on entanglement witnesses, which includes several already established entanglement measures such as the negativity, the… Expand

Operational one-to-one mapping between coherence and entanglement measures

- Physics
- 2017

We establish a general operational one-to-one mapping between coherence measures and entanglement measures: Any entanglement measure of bipartite pure states is the minimum of a suitable coherence… Expand

On quantum Rényi entropies: A new generalization and some properties

- Physics, Computer Science
- 2013

This work proposes a new quantum generalization of the family of Renyi entropies that contains the von Neumann entropy, min-entropy, collision entropy, and the max-entropies as special cases, thus encompassing most quantum entropie in use today. Expand

Quantum Coherence Quantifiers Based on Rényi α-Relative Entropy

- Physics
- 2017

The resource theories of quantum coherence attract a lot of attention in recent years. Especially, the monotonicity property plays a crucial role here. In this paper we investigate the monotonicity… Expand

Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2015

A class of quantum correlation measures are introduced as differences between total and classical correlations, in a shared quantum state, in terms of the sandwiched relative Rényi and Tsallis entropies, finding that the measures satisfy all the plausible axioms for quantum correlations. Expand

Max- Relative Entropy of Entanglement, alias Log Robustness

- Mathematics, Physics
- 2008

Properties of the max-relative entropy of entanglement, defined in Ref. 10, are investigated, and its significance as an upper bound to the one-shot rate for perfect entanglement dilution, under a… Expand

Min- and Max-Relative Entropies and a New Entanglement Monotone

- Mathematics, Physics
- IEEE Transactions on Information Theory
- 2009

The spectral divergence rates of the information spectrum approach are shown to be obtained from the smooth min- and max-relative entropies in the asymptotic limit. Expand

Measuring Quantum Coherence with Entanglement.

- Computer Science, Medicine
- Physical review letters
- 2015

This work demonstrates the usefulness of the approach by proving that the fidelity-based geometric measure of coherence is a full convex coherence monotone, and deriving a closed formula for it on arbitrary single-qubit states. Expand

Entanglement measures and purification procedures

- Physics
- 1998

We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative… Expand

Quantum-coherence quantifiers based on the Tsallis relative α entropies

- Physics
- 2016

The concept of coherence is one of cornerstones in physics. The development of quantum information science has lead to renewed interest in properly approaching the coherence at the quantum level.… Expand