Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Gisin, M. Cibils (1992)
Quantum diffusions, quantum dissipation and spin relaxationJournal of Physics A, 25
S. Weinberg (1989)
Precision tests of quantum mechanics.Physical review letters, 62 5
C. Helstrom (1969)
Quantum detection and estimation theoryJournal of Statistical Physics, 1
Yilun Guan, D. Nguyen, Jingwei Xu, J. Gong (2013)
Reexamination of measurement-induced chaos in entanglement-purification protocolsPhysical Review A, 87
T. Kibble (1978)
Relativistic models of nonlinear quantum mechanicsCommunications in Mathematical Physics, 64
J. Rembieli'nski, P. Caban (2020)
Nonlinear extension of the quantum dynamical semigroupQuantum, 5
T. Brun, J. Harrington, M. Wilde (2008)
Localized closed timelike curves can perfectly distinguish quantum states.Physical review letters, 102 21
Andrew Childs, Joshua Young (2015)
Optimal state discrimination and unstructured search in nonlinear quantum mechanicsPhysical Review A, 93
D. Abrams, S. Physics, Mit, Dept. Engineering (1998)
NONLINEAR QUANTUM MECHANICS IMPLIES POLYNOMIAL-TIME SOLUTION FOR NP-COMPLETE AND P PROBLEMSPhysical Review Letters, 81
M. Wolf, J. Cirac (2006)
Dividing Quantum ChannelsCommunications in Mathematical Physics, 279
B. Mielnik (1980)
Mobility of nonlinear systemsJournal of Mathematical Physics, 21
K. Kowalski (2020)
Linear and integrable nonlinear evolution of the qutritQuantum Information Processing, 19
P. Hayden, C. King (2004)
Correcting quantum channels by measuring the environmentQuantum Inf. Comput., 5
J. Bollinger, D. Heinzen, W. Itano, S. Gilbert, D. Wineland (1989)
Test of the linearity of quantum mechanics by rf spectroscopy of the 9Be+ ground state.Physical review letters, 63 10
Anil Shaji, E. Sudarshan (2005)
Who's afraid of not completely positive maps?Physics Letters A, 341
In particular, they might not be trace preserving in the usual sense of tr(Λ(X)) = tr(X), because the trace preservation in Definition 4 is really a trace fixing condition
H. Carteret, Daniel Terno, K. Życzkowski (2008)
Dynamics beyond completely positive maps : some properties and applicationsPhysical Review A, 77
E. Davies (1984)
PROBABILISTIC AND STATISTICAL ASPECTS OF QUANTUM THEORY (North‐Holland Series in Statistics and Probability, 1)Bulletin of The London Mathematical Society, 16
Riccardo Porotti, Antoine Essig, B. Huard, F. Marquardt (2021)
Deep Reinforcement Learning for Quantum State Preparation with Weak Nonlinear MeasurementsQuantum, 6
P. Kalozoumis, D. Petrosyan (2021)
Self-Organized PT-Symmetry of Exciton-Polariton Condensate in a Double-Well PotentialApplied Sciences
E. Sudarshan, P. Mathews, Jayaseetha Rau (1961)
STOCHASTIC DYNAMICS OF QUANTUM-MECHANICAL SYSTEMSPhysical Review, 121
M. Muñoz-Arias, P. Poggi, P. Jessen, I. Deutsch (2019)
Simulating Nonlinear Dynamics of Collective Spins via Quantum Measurement and Feedback.Physical review letters, 124 11
Mahdi Kahou, D. Feder (2013)
Quantum search with interacting Bose-Einstein condensatesPhysical Review A, 88
E. Buks (2021)
The mean field approximation and disentanglement
T. Gao, E. Estrecho, K. Bliokh, T. Liew, M. Fraser, S. Brodbeck, M. Kamp, C. Schneider, S. Höfling, S. Höfling, Y. Yamamoto, F. Nori, Y. Kivshar, A. Truscott, R. Dall, E. Ostrovskaya (2015)
Observation of non-Hermitian degeneracies in a chaotic exciton-polariton billiardNature, 526
A. Chefles (2000)
Quantum state discriminationContemporary Physics, 41
C. Ho, S. Hsu (2014)
Locality and nonlinear quantum mechanicsInternational Journal of Modern Physics A, 30
M. Kuna, M. Czachor, S. Leble (1998)
Nonlinear von Neumann-type equations: Darboux invariance and spectraPhysics Letters A, 255
G. Lindblad (1976)
On the generators of quantum dynamical semigroupsCommunications in Mathematical Physics, 48
B. Linear positive φ and tr[ φ ( X )] (cid:54) = 1 for some X ∈ Her ≥ 0 1 ( H , C ). These can be called nonlinear in normalization only (NINO) channels
R. Alicki, J. Messer (1983)
Nonlinear quantum dynamical semigroups for many-body open systemsJournal of Statistical Physics, 32
Jason Dominy, Daniel Lidar (2015)
Beyond complete positivityQuantum Information Processing, 15
S. Aaronson (2005)
NP-complete Problems and Physical RealityElectron. Colloquium Comput. Complex., TR05
L. Di'osi (2016)
Nonlinear Schrödinger equation in foundations: summary of 4 catchesJournal of Physics: Conference Series, 701
T. Jordan (2010)
Fundamental significance of tests that quantum dynamics is linearPhysical Review A, 82
M. Czachor (1994)
Elements of nonlinear quantum mechanics (Part II): Triple bracket generalization of quantum mechanicsarXiv: High Energy Physics - Theory
M. Czachor (1995)
Nonlinear Schrödinger equation and two-level atoms.Physical review. A, Atomic, molecular, and optical physics, 53 3
T. Kiss, S. Vymětal, L. Tóth, L. Tóth, A. Gábris, I. Jex, G. Alber (2011)
Measurement-induced chaos with entangled states.Physical review letters, 107 10
Sebastian Deffner (2022)
Nonlinear speed-ups in ultracold quantum gasesEurophysics Letters, 140
Charles Bennett, D. Leung, Graeme Smith, J. Smolin (2009)
Can closed timelike curves or nonlinear quantum mechanics improve quantum state discrimination or help solve hard problems?Physical review letters, 103 17
We distinguish between infinitesimal generators G and Hamiltonians iG. Thus, unitary evolution results from Hermitian Hamiltonians but from anti-Hermitian generators
P. Pechukas (1994)
Reduced dynamics need not be completely positive.Physical review letters, 73 8
R. Nagel, H. Schaefer, Ulf Schlotlerbeck, U. Schlotterbeck, M. Wolff, M. Wolff (1986)
Aspects of Positivity in Functional AnalysisNorth-holland Mathematics Studies, 122
Mielnik B. (1980)
44J. Math. Phys., 21
arXiv : 0810 . 1970 . [ 103 ] A . Chefles
T. Kiss, I. Jex, G. Alber, S. Vymětal (2005)
Complex chaos in the conditional dynamics of qubitsPhysical Review A, 74
M. Czachor, M. Kuna (1997)
COMPLETE POSITIVITY OF NONLINEAR EVOLUTION : A CASE STUDYPhysical Review A, 58
H. Grabert (1982)
Nonlinear relaxation and fluctuations of damped quantum systemsZeitschrift für Physik B Condensed Matter, 49
G. Molfetta, Basile Herzog (2020)
Searching via Nonlinear Quantum Walk on the 2D-GridAlgorithms, 13
H.‐P. Breuer, F. Petruccione (2002)
The Theory of Open Quantum Systems
= 0 is not specified. However, this situation does not arise in the cases considered here
Abrams D. S. (1998)
3992Phys. Rev. Lett., 81
Let dX∕dt = Y(X) = a (X) a = a (r) a where each a : ℝ 3 → ℝ is a continuous function of r
S. Lloyd, J. Slotine (1999)
Quantum feedback with weak measurementsPhysical Review A, 62
K. Zloshchastiev, A. Sergi (2014)
Comparison and unification of non-Hermitian and Lindblad approaches with applications to open quantum optical systemsJournal of Modern Optics, 61
R. Xu, Yijing Yan (2002)
Theory of open quantum systemsJournal of Chemical Physics, 116
M. Czachor (1998)
Local modification of the Abrams-Lloyd nonlinear algorithmarXiv: Quantum Physics
N. Gisin (1981)
A simple nonlinear dissipative quantum evolution equationJournal of Physics A, 14
(2016)
arXiv : 2009 . 07800 . [ 16 ] S . Deffner
M. Czachor (1998)
Notes on nonlinear quantum algorithmsarXiv: Quantum Physics
N. Gisin (1989)
Stochastic quantum dynamics and relativityHelvetica Physica Acta, 62
J. Bae, L. Kwek (2015)
Quantum state discrimination and its applicationsJournal of Physics A: Mathematical and Theoretical, 48
K. Romero, P. Talkner, P. Hānggi (2003)
Is the dynamics of open quantum systems always linearPhysical Review A, 69
Pieter Lagrou (2019)
StatesEurope’s Postwar Periods 1989, 1945, 1918
E. Buks, Dvir Schwartz (2021)
Stability of the Grabert master equation
V. Man'ko, G. Marmo (1992)
GENERALIZED REDUCTION PROCEDURE AND NONLINEAR NONSTATIONARY DYNAMICAL SYSTEMSModern Physics Letters A, 07
O. K'alm'an, T. Kiss (2017)
Quantum state matching of qubits via measurement-induced nonlinear transformationsarXiv: Quantum Physics
A. Holevo, L. Ballentine (1982)
Probabilistic and Statistical Aspects of Quantum Theory
T. Jordan (2005)
Assumptions that imply quantum dynamics is linearPhysical Review A, 73
J. Rembieli'nski, P. Caban (2019)
Nonlinear evolution and signalingPhysical Review Research
Chupp, Hoare (1990)
Coherence in freely precessing 21Ne and a test of linearity of quantum mechanics.Physical review letters, 64 19
R. Levi, S. Masis, E. Buks (2020)
Instability in the Hartmann-Hahn double resonancearXiv: Quantum Physics
A. Gilyén, T. Kiss, I. Jex (2015)
Exponential Sensitivity and its Cost in Quantum PhysicsScientific Reports, 6
B. Mielnik (2001)
Nonlinear quantum mechanics: a conflict with the Ptolomean structure?Physics Letters A, 289
V. Gorini, A. Kossakowski, E. Sudarshan (1976)
Completely Positive Dynamical Semigroups of N Level SystemsJournal of Mathematical Physics, 17
Jason Dominy, A. Shabani, Daniel Lidar (2013)
A general framework for complete positivityQuantum Information Processing, 15
R. Walsworth, I. Silvera, E. Mattison, R. Vessot (1990)
Test of the linearity of quantum mechanics in an atomic system with a hydrogen maser.Physical review letters, 64 22
The existence of the representation (3) does not actually require to be positive
Florio Ciaglia, F. Cosmo, A. Figueroa, V. Man'ko, G. Marmo, Luca Schiavone, F. Ventriglia, P. Vitale (2019)
Nonlinear dynamics from linear quantum evolutionsAnnals of Physics
D. Bacon (2003)
Quantum computational complexity in the presence of closed timelike curvesPhysical Review A, 70
T. Jordan (2007)
Why quantum dynamics is lineararXiv: Quantum Physics, 196
Daniel Terno (1998)
Nonlinear operations in quantum-information theoryPhysical Review A, 59
Man-Duen Choi (1975)
Completely positive linear maps on complex matricesLinear Algebra and its Applications, 10
D. Meyer, T. Wong (2013)
Nonlinear quantum search using the Gross–Pitaevskii equationNew Journal of Physics, 15
K. Kraus (1983)
States, Effects, and Operations
(2009)
Dipojono, arXiv: 2009.06422
S. Weinberg (1988)
The First Three Minutes: A Modern View of the Origin of the Universe
C. Nonlinear positive φ and tr[ φ ( X )] = 1 for all X ∈ Her ≥ 0 1 ( H , C )
“Nonlinear Schr¨odinger equations and generalized Heisenberg uncertainty principle violating the principle of estimation independence,”
A. Bassi, Kasra Hejazi (2014)
No-faster-than-light-signaling implies linear evolution. A re-derivationEuropean Journal of Physics, 36
A. Scott, G. Milburn (2000)
Quantum nonlinear dynamics of continuously measured systemsPhysical Review A, 63
L. Erdős, B. Schlein (2008)
Quantum Dynamics with Mean Field Interactions: a New ApproachJournal of Statistical Physics, 134
Bechmann‐Pasquinucci H. (1998)
198Phys. Lett. A, 242
D. Kaplan, S. Rajendran (2021)
Causal framework for nonlinear quantum mechanicsPhysical Review D
M. Czachor, H. Doebner (2001)
Correlation experiments in nonlinear quantum mechanicsPhysics Letters A, 301
2C + 2G ab (r)r b = 2C + 2L ab r b + 2gN ab (r)r b , where 2C captures any r-independent part of a (r)
As discussed below, postselected measurement is formally in the NINO class
K. Kowalski, J. Rembielinski (2019)
Integrable nonlinear evolution of the qubitAnnals of Physics, 411
A. Winter (2005)
On environment-assisted capacities of quantum channelsarXiv: Quantum Physics
J. Polchinski, J. Polchinski (1991)
Weinberg's nonlinear quantum mechanics and the Einstein-Podolsky-Rosen paradox.Physical review letters, 66 4
Bernd Fernengel, B. Drossel (2019)
Bifurcations and chaos in nonlinear Lindblad equationsJournal of Physics A: Mathematical and Theoretical, 53
M. Gregoratti, R. Werner (2004)
On quantum error-correction by classical feedback in discrete timeJournal of Mathematical Physics, 45
D. Meyer, T. Wong (2013)
Quantum Search with General NonlinearitiesPhysical Review A, 89
N. Gisin, M. Rigo (1995)
Relevant and irrelevant nonlinear Schrodinger equationsJournal of Physics A, 28
K. Kraus (1971)
General state changes in quantum theoryAnnals of Physics, 64
A. Kent (2002)
Nonlinearity without superluminalityPhysical Review A, 72
P. Majumder, Venema Bj, S. Lamoreaux, B. Heckel, E. Fortson (1990)
Test of the linearity of quantum mechanics in optically pumped 201Hg.Physical review letters, 65 24
D. Brody, E. Graefe (2012)
Mixed-state evolution in the presence of gain and loss.Physical review letters, 109 23
(1996)
Separability criterion for density matrices
B. Drossel (2019)
What condensed matter physics and statistical physics teach us about the limits of unitary time evolutionQuantum Studies: Mathematics and Foundations, 7
S. Weinberg (1989)
Testing quantum mechanicsAnnals of Physics, 194
S. Barnett, S. Croke (2008)
Quantum state discriminationAdvances in Optics and Photonics, 1
Kaitlin Gili, Mykolas Sveistrys, C. Ballance (2022)
Introducing Non-Linearity into Quantum Generative ModelsArXiv, abs/2205.14506
Shu Xu, J. Schmiedmayer, B. Sanders (2022)
Nonlinear quantum gates for a Bose-Einstein condensatePhysical Review Research
Models of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension N=2$ N \! = \! 2$. For every normalizable linear or nonlinear positive map ϕ on bounded linear operators X, there is an associated normalized PTP channel ϕ(X)/tr[ϕ(X)]$ \phi (X) / {\rm tr}[\phi (X)]$. Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator.
Advanced Quantum Technologies – Wiley
Published: Jun 1, 2023
Keywords: nonlinear master equations; nonlinear quantum mechanics; quantum channels; quantum state discrimination
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.