Information-based approach towards a unified resource theory

Resource theories play an important role in quantum information theory, as they identify resourceful states and channels that are potentially useful for the accomplishment of tasks that would be otherwise unreachable. The elementary structure of such theories, which is based on the definition of free states and free operations, successfully accommodates different nonclassical aspects, such as quantum coherence and entanglement, but it is still not clear whether and how far such formal framework can be extended. In this work, by taking information as the most primitive quantum resource and defining resource-destroying operations, we develop a unifying approach that proves able to encompass several nonclassical aspects, including the newly developed concepts of quantum irreality and realism-based nonlocality.

[1]  R. M. Angelo,et al.  Weak quantum discord , 2018, Quantum Inf. Process..

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

[3]  A. L. O. Bilobran,et al.  A measure of physical reality , 2014, 1411.7811.

[4]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[5]  M. Horodecki,et al.  Quantum entanglement , 2007, quant-ph/0702225.

[6]  C ARPUAT.  Bayes Rule , 2009, Encyclopedia of Biometrics.

[7]  Xiaoguang Wang,et al.  The upper bound and continuity of quantum discord , 2011 .

[8]  M. Horodecki,et al.  QUANTUMNESS IN THE CONTEXT OF) RESOURCE THEORIES , 2012, 1209.2162.

[9]  Gerardo Adesso,et al.  Operational Advantage of Quantum Resources in Subchannel Discrimination. , 2018, Physical review letters.

[10]  Alexandre C. Orthey,et al.  Nonlocality, quantum correlations, and violations of classical realism in the dynamics of two noninteracting quantum walkers , 2019, Physical Review A.

[11]  Gerardo Adesso,et al.  Generic Bound Coherence under Strictly Incoherent Operations. , 2018, Physical review letters.

[12]  F. Brandão,et al.  Reversible Framework for Quantum Resource Theories. , 2015, Physical review letters.

[13]  S. Luo.  Using measurement-induced disturbance to characterize correlations as classical or quantum , 2008 .

[14]  V. S. Gomes,et al.  Nonanomalous realism-based measure of nonlocality , 2017 .

[15]  Paul Skrzypczyk,et al.  The role of quantum information in thermodynamics—a topical review , 2015, 1505.07835.

[16]  G. Adesso,et al.  Assisted Distillation of Quantum Coherence. , 2015, Physical review letters.

[17]  MAXWELL’S DEMONS,et al.  Quantum Discord and Maxwell's Demons , 2002 .

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

[19]  Stefano Pironio,et al.  Random numbers certified by Bell’s theorem , 2009, Nature.

[20]  Stefano Pirandola,et al.  Quantum discord as a resource for quantum cryptography , 2013, Scientific Reports.

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

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

[23]  R. M. Angelo,et al.  Quantifying continuous-variable realism , 2019, Physical Review A.

[24]  Ryuji Takagi,et al.  General Resource Theories in Quantum Mechanics and Beyond: Operational Characterization via Discrimination Tasks , 2019, Physical Review X.

[25]  Seth Lloyd,et al.  Resource Destroying Maps. , 2016, Physical review letters.

[26]  Yongming Li,et al.  Necessary and sufficient condition for achieving the upper bound of quantum discord , 2011, ArXiv.

[27]  G. Gour,et al.  Quantum resource theories , 2018, Reviews of Modern Physics.

[28]  R. M. Angelo,et al.  Nonanomalous measure of realism-based nonlocality , 2017, 1709.04783.

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

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

[31]  Maciej Lewenstein,et al.  Towards Resource Theory of Coherence in Distributed Scenarios , 2015, 1509.07456.

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

[33]  Animesh Datta,et al.  QUANTUM DISCORD AS A RESOURCE IN QUANTUM COMMUNICATION , 2012, 1204.6042.

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

[35]  Ludovico Lami,et al.  Completing the Grand Tour of Asymptotic Quantum Coherence Manipulation , 2019, IEEE Transactions on Information Theory.

[36]  M. S. Sarandy,et al.  Global quantum discord in multipartite systems , 2011, 1105.2548.

[37]  Robert W. Spekkens,et al.  A mathematical theory of resources , 2014, Inf. Comput..

[38]  P. R. Dieguez,et al.  Information-reality complementarity: The role of measurements and quantum reference frames , 2017, 1711.07739.

[39]  R. Angelo,et al.  Bayes' rule, generalized discord, and nonextensive thermodynamics , 2012, 1207.3337.

[40]  T. Paterek,et al.  Unified view of quantum and classical correlations. , 2009, Physical review letters.

[41]  G. Tóth,et al.  Quantum metrology from a quantum information science perspective , 2014, 1405.4878.

[42]  M. Horodecki,et al.  Reversible transformations from pure to mixed states and the unique measure of information , 2002, quant-ph/0212019.

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

[44]  D. Bruß,et al.  Maximal coherence and the resource theory of purity , 2016, New Journal of Physics.

[45]  R. M. Angelo,et al.  Resilience of realism-based nonlocality to local disturbance , 2018, Physical Review A.

[46]  H. Bechmann-Pasquinucci,et al.  Quantum cryptography , 2001, quant-ph/0101098.

[47]  Nicole Yunger Halpern,et al.  The resource theory of informational nonequilibrium in thermodynamics , 2013, 1309.6586.

[48]  M. Horodecki,et al.  Local versus nonlocal information in quantum-information theory: Formalism and phenomena , 2004, quant-ph/0410090.