Entanglement as the Symmetric Portion of Correlated Coherence.

We show that the symmetric portion of correlated coherence is always a valid quantifier of entanglement, and that this property is independent of the particular choice of coherence measure. This leads to an infinitely large class of coherence based entanglement monotones, which is always computable for pure states if the coherence measure is also computable. It is already known that every entanglement measure can be constructed as a coherence measure. The results presented here show that the converse is also true. The constructions that are presented can also be extended to include more general notions of nonclassical correlations, leading to quantifiers that are related to quantum discord, thus providing an avenue for unifying all such notions of quantum correlations under a single framework.

[1]  S. Qin,et al.  Relating quantum coherence and correlations with entropy-based measures , 2017, Scientific Reports.

[2]  K. C. Tan,et al.  Coherence, asymmetry, and quantum macroscopicity , 2017, 1704.06469.

[3]  T. Paterek,et al.  Separable states improve protocols with finite randomness , 2014 .

[4]  V. Vedral,et al.  Quantum processes which do not use coherence , 2015, 1512.02085.

[5]  Charles H. Bennett,et al.  Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. , 1992, Physical review letters.

[6]  Gerardo Adesso,et al.  Measuring Quantum Coherence with Entanglement. , 2015, Physical review letters.

[7]  Chiara Macchiavello,et al.  Generation and detection of bound entanglement , 2004 .

[8]  M. Plenio,et al.  Colloquium: quantum coherence as a resource , 2016, 1609.02439.

[9]  A. Winter,et al.  Operational Resource Theory of Coherence. , 2015, Physical review letters.

[10]  Florian Mintert,et al.  A quantitative theory of coherent delocalization , 2013, 1310.6962.

[11]  M. N. Bera,et al.  Entanglement and Coherence in Quantum State Merging. , 2016, Physical review letters.

[12]  Vlatko Vedral,et al.  General framework for quantum macroscopicity in terms of coherence , 2015, 1505.03792.

[13]  Michael M. Wolf,et al.  Bell inequalities and entanglement , 2001, Quantum Inf. Comput..

[14]  Kok Chuan Tan,et al.  Unified view of quantum correlations and quantum coherence , 2016, 1603.01958.

[15]  Eric Chitambar,et al.  Relating the Resource Theories of Entanglement and Quantum Coherence. , 2015, Physical review letters.

[16]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[17]  W. Wootters.  Entanglement of Formation of an Arbitrary State of Two Qubits , 1997, quant-ph/9709029.

[18]  Mark Hillery,et al.  Coherence as a resource in decision problems: The Deutsch-Jozsa algorithm and a variation , 2015, 1512.01874.

[19]  Ekert,et al.  Quantum cryptography based on Bell's theorem. , 1991, Physical review letters.

[20]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information: Frontmatter , 2010 .

[21]  M Paternostro,et al.  Quantum discord bounds the amount of distributed entanglement. , 2012, Physical review letters.

[22]  Davide Girolami,et al.  Converting Coherence to Quantum Correlations. , 2015, Physical review letters.

[23]  Albert Einstein,et al.  Can Quantum-Mechanical Description of Physical Reality Be Considered Complete? , 1935 .

[24]  Yannick Ole Lipp,et al.  Quantum discord as resource for remote state preparation , 2012, Nature Physics.

[25]  W. Zurek,et al.  Quantum discord: a measure of the quantumness of correlations. , 2001, Physical review letters.

[26]  M. Horodecki,et al.  Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature? , 1998, quant-ph/9801069.

[27]  Jianwei Xu,et al.  Quantifying coherence of Gaussian states , 2015, 1510.02916.

[28]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[29]  V. Vedral,et al.  Classical, quantum and total correlations , 2001, quant-ph/0105028.

[30]  Heng Fan,et al.  Quantifying coherence in infinite-dimensional systems , 2015, 1505.05270.

[31]  Guang-Can Guo,et al.  Directly Measuring the Degree of Quantum Coherence using Interference Fringes. , 2017, Physical review letters.

[32]  K. C. Tan,et al.  Disturbance-based measure of macroscopic coherence , 2016, 1608.01122.

[33]  Kok Chuan Tan,et al.  Quantifying the Coherence between Coherent States. , 2017, Physical review letters.

[34]  Robert W. Spekkens,et al.  Quantum speed limits, coherence, and asymmetry , 2015, 1510.06474.

[35]  M. Plenio,et al.  Quantifying coherence. , 2013, Physical review letters.

[36]  M. B. Plenio,et al.  Coherent control of quantum systems as a resource theory , 2015, 1512.07486.

[37]  K. C. Tan,et al.  Coherence, quantum Fisher information, superradiance, and entanglement as interconvertible resources , 2017, 1711.07185.

[38]  P. Parrilo,et al.  Distinguishing separable and entangled states. , 2001, Physical review letters.

[39]  M. Piani,et al.  Genuine correlated coherence , 2018, Journal of Physics A: Mathematical and Theoretical.

[40]  Animesh Datta,et al.  Quantum discord and the power of one qubit. , 2007, Physical review letters.