Coherence and entanglement measures based on Rényi relative entropies

  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},
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

Figures from this paper

Coherence measures based on coherence eigenvalue and their applications
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
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
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
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 ofExpand
Axiomatic and operational connections between the l 1 -norm of coherence and negativity
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 toExpand
Coherence manipulation with dephasing-covariant operations
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
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
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. TheExpand
Minimum uncertainty states in the presence of quantum memory
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. TheExpand
Secure uniform random number extraction via incoherent strategies
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


Quantifying entanglement with witness operators
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, theExpand
Operational one-to-one mapping between coherence and entanglement measures
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 coherenceExpand
On quantum Rényi entropies: A new generalization and some properties
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
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 monotonicityExpand
Quantum correlation with sandwiched relative entropies: Advantageous as order parameter in quantum phase transitions.
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
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 aExpand
Min- and Max-Relative Entropies and a New Entanglement Monotone
  • N. Datta
  • 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.
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
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 relativeExpand
Quantum-coherence quantifiers based on the Tsallis relative α entropies
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