Controllability of open quantum systems with Kraus-map dynamics
Open accessAbstract
This paper presents a constructive proof of complete kinematic state controllability of finite-dimensional open quantum systems whose dynamics are represented by Kraus maps. For any pair of states (pure or mixed) on the Hilbert space of the system, we explicitly show how to construct a Kraus map that transforms one state into another. Moreover, we prove by construction the existence of a Kraus map that transforms all initial states into a predefined target state (such a process may be used, for example, in quantum information dilution). Thus, in sharp contrast to unitary control, Kraus-map dynamics allows for the design of controls which are robust to variations in the initial state of the system. The capabilities of non-unitary control for population transfer between pure states illustrated for an example of a two-level system by constructing a family of non-unitary Kraus maps to transform one pure state into another. The problem of dynamic state controllability of open quantum systems (i.e., controllability of state-to-state transformations, given a set of available dynamical resources such as coherent controls, incoherent interactions with the environment, and measurements) is also discussed.
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In most proposals or experimental realizations, OSAQSs allow for a wide control of parameters, which allows for simulation of open-system (Markovian) evolutions for wide families of open systems.
“Nevertheless, in most of the proposals [126-128] or experimental realizations they allow for a wide control of parameters, which in turn allows for simulation of open-system (Markovian) evolutions for wide families of open systems.”
From Can one trust quantum simulators? (2012) · cites this paper as [126]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Cites
Completely positive linear maps on complex matrices
Choi, M.-D. (1975) · Linear Algebra and its Applications · doi:10.1016/0024-3795(75)90075-0 · Cited by 2,659 · see citing works
Control of Chemical Reactions by Feedback-Optimized Phase-Shaped Femtosecond Laser Pulses
Assion, A., Baumert, T., Bergt, M., Brixner, T., Kiefer, B., Seyfried, V., Strehle, M. A., & Gerber, G. (1998) · Science · doi:10.1126/science.282.5390.919 · Cited by 1,632 · see citing works
States, Effects, and Operations Fundamental Notions of Quantum Theory
(1983) · Lecture Notes in Physics · doi:10.1007/3-540-12732-1 · Cited by 1,565 · see citing works
Whither the Future of Controlling Quantum Phenomena?
RABITZ, H. A., de Vivie‐Riedle, R., Motzkus, M., & Kompa, K. L. (2000) · Science · doi:10.1126/science.288.5467.824 · Cited by 1,150 · see citing works
Self-citationCoherent Control of Quantum Dynamics: The Dream Is Alive
Warren, W. S., RABITZ, H. A., & Dahleh, M. (1993) · Science · doi:10.1126/science.259.5101.1581 · Cited by 1,062 · see citing works
Self-citationSelective Bond Dissociation and Rearrangement with Optimally Tailored, Strong-Field Laser Pulses
Levis, R. J., Menkir, G. M., & RABITZ, H. A. (2001) · Science · doi:10.1126/science.1059133 · Cited by 909 · see citing works
Self-citationOptimal control of quantum-mechanical systems: Existence, numerical approximation, and applications
Peirce, A. P., Dahleh, M., & RABITZ, H. A. (1988) · Physical Review A · doi:10.1103/physreva.37.4950 · Cited by 897 · see citing works
Self-citationWineland, D. J., & Itano, W. M. (1979) · Physical Review A · doi:10.1103/physreva.20.1521 · Cited by 798 · see citing works
Quantum Reservoir Engineering with Laser Cooled Trapped Ions
Poyatos, J. F., Cirac, J. I., & Zoller, P. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.4728 · Cited by 756 · see citing works
Quantum control of energy flow in light harvesting
Herek, J. L., Wohlleben, W., Cogdell, R. J., Zeidler, D., & Motzkus, M. (2002) · Nature · doi:10.1038/417533a · Cited by 697 · see citing works
Decoherence of quantum superpositions through coupling to engineered reservoirs
Myatt, C. J., King, B. E., Turchette, Q. A., Sackett, C. A., Kielpinski, D., Itano, W. M., Monroe, C. R., & Wineland, D. J. (2000) · Nature · doi:10.1038/35002001 · Cited by 694 · see citing works
Fault-Tolerant Quantum Dynamical Decoupling
Khodjasteh, K., & Lidar, D. A. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.180501 · Cited by 575 · see citing works
Local Ordering in the Pseudogap State of the High- T c Superconductor Bi 2 Sr 2 CaCu 2 O 8+δ
Vershinin, M. D., Misra, S., Ono, S., et al. (2004) · Science · doi:10.1126/science.1093384 · Cited by 502 · see citing works
Quantum Computing Using Dissipation to Remain in a Decoherence-Free Subspace
Beige, A., Braun, D., Tregenna, B., & Knight, P. L. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.1762 · Cited by 493 · see citing works
Walmsley, I. A., & RABITZ, H. A. (2003) · Physics Today · doi:10.1063/1.1611352 · Cited by 418 · see citing works
Self-citationOn the controllability of quantum-mechanical systems
Huang, G. M., TARN, T. J., & Clark, J. W. (1983) · Journal of Mathematical Physics · doi:10.1063/1.525634 · Cited by 409 · see citing works
Lloyd, S. (2000) · Physical Review A · doi:10.1103/physreva.62.022108 · Cited by 384 · see citing works
Experimental Coherent Laser Control of Physicochemical Processes
Dantus, M. M., & Lozovoy, V. V. (2004) · Chemical Reviews · doi:10.1021/cr020668r · Cited by 372 · see citing works
Controllability of molecular systems
Ramakrishna, V., Salapaka, M. V., Dahleh, M., RABITZ, H. A., & Peirce, A. P. (1995) · Physical Review A · doi:10.1103/physreva.51.960 · Cited by 368 · see citing works
Self-citationDecoherence of matter waves by thermal emission of radiation
Hackermüller, L., Hornberger, K., Brezger, B., et al. (2004) · Nature · doi:10.1038/nature02276 · Cited by 337 · see citing works
Irreversible Thermodynamics for Quantum Systems Weakly Coupled to Thermal Reservoirs
Spohn, H. E., & Lebowitz, J. L. (1978) · Advances in chemical physics · doi:10.1002/9780470142578.ch2 · Cited by 328 · see citing works
Collisional Decoherence Observed in Matter Wave Interferometry
Hornberger, K., Uttenthaler, S., Brezger, B., Hackermüller, L., Arndt, M., & Zeilinger, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.160401 · Cited by 290 · see citing works
Complete controllability of quantum systems
Schirmer, S. G., Fu, H., & Solomon, A. I. (2001) · Physical Review A · doi:10.1103/physreva.63.063410 · Cited by 249 · see citing works
Notions of controllability for bilinear multilevel quantum systems
Albertini, F., & D’Alessandro, D. (2003) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2003.815027 · Cited by 213 · see citing works
Bang–bang control of fullerene qubits using ultrafast phase gates
Morton, J. J. L., Tyryshkin, A. M., Ardavan, A., Benjamin, S. C., Porfyrakis, K., Lyon, S. A., & Briggs, G. A. D. (2005) · Nature Physics · doi:10.1038/nphys192 · Cited by 208 · see citing works
Lloyd, S., & Viola, L. (2001) · Physical Review A · doi:10.1103/physreva.65.010101 · Cited by 197 · see citing works
Non-dispersive wave packets in periodically driven quantum systems
Buchleitner, A., Delande, D., & Zakrzewski, J. (2002) · Physics Reports · doi:10.1016/s0370-1573(02)00270-3 · Cited by 181 · see citing works
Random Decoupling Schemes for Quantum Dynamical Control and Error Suppression
Viola, L., & Knill, E. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.060502 · Cited by 180 · see citing works
Dynamics of initially entangled open quantum systems
Jordan, T. F., Shaji, A., & Sudarshan, E. C. G. (2004) · Physical Review A · doi:10.1103/physreva.70.052110 · Cited by 180 · see citing works
Diluting quantum information: An analysis of information transfer in system-reservoir interactions
Ziman, M., Štelmachovič, P., Bužek, V., Hillery, M. S., Scarani, V., & Gisin, N. (2002) · Physical Review A · doi:10.1103/physreva.65.042105 · Cited by 174 · see citing works
Quantum wavefunction controllability
Turinici, G., & RABITZ, H. A. (2001) · Chemical Physics · doi:10.1016/s0301-0104(01)00216-6 · Cited by 169 · see citing works
Self-citationControllability of quantum mechanical systems by root space decomposition of su(N)
Altafini, C. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1467611 · Cited by 165 · see citing works
Controllability properties for finite dimensional quantum Markovian master equations
Altafini, C. (2003) · Journal of Mathematical Physics · doi:10.1063/1.1571221 · Cited by 156 · see citing works
Loss of Spatial Coherence by a Single Spontaneous Emission
Pfau, T., Spalter, S. J., Kurtsiefer, C., et al. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.1223 · Cited by 150 · see citing works
Optimal control of uncertain quantum systems
Dahleh, M. D., Peirce, A. P., & RABITZ, H. A. (1990) · Physical Review A · doi:10.1103/physreva.42.1065 · Cited by 147 · see citing works
Self-citationState Selective Production of Molecules in Optical Lattices
Rom, T., Best, T., Mandel, O., Widera, A., Greiner, M., Hänsch, T. W., & Bloch, I. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.073002 · Cited by 139 · see citing works
Closing the Loop on Bond Selective Chemistry Using Tailored Strong Field Laser Pulses
Levis, R. J., & RABITZ, H. A. (2002) · The Journal of Physical Chemistry A · doi:10.1021/jp0134906 · Cited by 138 · see citing works
Self-citationQuantum control by von Neumann measurements
Pechen, A. N., Il’in, N., Shuang, F., et al. (2006) · Physical Review A · doi:10.1103/physreva.74.052102 · Cited by 119 · see citing works
Self-citationTeaching the environment to control quantum systems
Pechen, A. N., & RABITZ, H. A. (2006) · Physical Review A · doi:10.1103/physreva.73.062102 · Cited by 109 · see citing works
Self-citationCoherent control of open quantum dynamical systems
Altafini, C. (2004) · Physical Review A · doi:10.1103/physreva.70.062321 · Cited by 105 · see citing works
Pairwise Decoherence in Coupled Spin Qubit Networks
Morello, A., Stamp, P. C. E., & Tupitsyn, I. S. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.207206 · Cited by 100 · see citing works
Master Equation for a Quantum Particle in a Gas
Hornberger, K. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.060601 · Cited by 92 · see citing works
Control of decoherence in the generation of photon pairs from atomic ensembles
Felinto, D., Chou, C. W., de Riedmatten, H., Polyakov, S. V., & Kimble, H. J. (2005) · Physical Review A · doi:10.1103/physreva.72.053809 · Cited by 92 · see citing works
Landscape for optimal control of quantum-mechanical unitary transformations
RABITZ, H. A., Hsieh, M., & Rosenthal, C. M. (2005) · Physical Review A · doi:10.1103/physreva.72.052337 · Cited by 89 · see citing works
Self-citationComplete controllability of finite-level quantum systems
Fu, H., Schirmer, S. G., & Solomon, A. I. (2001) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/34/8/313 · Cited by 88 · see citing works
Degrees of controllability for quantum systems and application to atomic systems
Schirmer, S. G., Solomon, A. I., & Leahy, J. V. (2002) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/35/18/309 · Cited by 83 · see citing works
Wavefunction controllability for finite-dimensional bilinear quantum systems
Turinici, G., & RABITZ, H. A. (2003) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/36/10/316 · Cited by 82 · see citing works
Self-citationQuantum control of bound and continuum state dynamics
Shapiro, M., & Brumer, P. W. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.12.005 · Cited by 78 · see citing works
Optimal coherent control of dissipative N -level systems
Jirari, H., & Pötz, W. (2005) · Physical Review A · doi:10.1103/physreva.72.013409 · Cited by 78 · see citing works
Sklarz, S. E., Tannor, D. J., & Khaneja, N. (2004) · Physical Review A · doi:10.1103/physreva.69.053408 · Cited by 76 · see citing works
Quantum optimal control theory and dynamic coupling in the spin-boson model
Jirari, H., & Pötz, W. (2006) · Physical Review A · doi:10.1103/physreva.74.022306 · Cited by 76 · see citing works
Laser cooling of internal degrees of freedom of molecules by dynamically trapped states
Tannor, D. J., Kosloff, R., & Bartana, A. (1999) · Faraday Discussions · doi:10.1039/a902103e · Cited by 72 · see citing works
Quantum computer with mixed states and four-valued logic
Tarasov, V. E. (2002) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/35/25/305 · Cited by 65 · see citing works
Incoherent control and entanglement for two-dimensional coupled systems
Romano, R., & D’Alessandro, D. (2006) · Physical Review A · doi:10.1103/physreva.73.022323 · Cited by 62 · see citing works
Dynamical control of qubit coherence: Random versus deterministic schemes
Santos, L. F., & Viola, L. (2005) · Physical Review A · doi:10.1103/physreva.72.062303 · Cited by 59 · see citing works
Closed loop learning control to suppress the effects of quantum decoherence
Zhu, W., & RABITZ, H. A. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1559484 · Cited by 55 · see citing works
Self-citationDriving a known state by a discrete sequence of direct measurements
Roa, L., Delgado, A., de Guevara, M. L. L., & Klimov, A. B. (2006) · Physical Review A · doi:10.1103/physreva.73.012322 · Cited by 55 · see citing works
Optimal control landscapes for quantum observables
RABITZ, H. A., Hsieh, M., & Rosenthal, C. M. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2198837 · Cited by 54 · see citing works
Self-citationQuantum control and the Strocchi map
Mendes, R. V., & Man’ko, V. I. (2003) · Physical Review A · doi:10.1103/physreva.67.053404 · Cited by 54 · see citing works
Kraus representation in the presence of initial correlations
Hayashi, H., Kimura, G., & Ota, Y. (2003) · Physical Review A · doi:10.1103/physreva.67.062109 · Cited by 53 · see citing works
Smooth controllability of infinite-dimensional quantum-mechanical systems
Wu, R.-B., Tarn, T., & Li, C. (2006) · Physical Review A · doi:10.1103/physreva.73.012719 · Cited by 51 · see citing works
Self-citationObservation-assisted optimal control of quantum dynamics
Shuang, F., Pechen, A. N., Ho, T., et al. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2711806 · Cited by 48 · see citing works
Self-citationQuantum optimal control: Hessian analysis of the control landscape
Shen, Z., Hsieh, M., & RABITZ, H. A. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2198836 · Cited by 47 · see citing works
Self-citationDecoherence of molecular vibrational wave packets: Observable manifestations and control criteria
Brif, C., RABITZ, H. A., Wallentowitz, S., & Walmsley, I. A. (2001) · Physical Review A · doi:10.1103/physreva.63.063404 · Cited by 47 · see citing works
Self-citationKinematical bounds on optimization of observables for quantum systems
Girardeau, M. D., Schirmer, S. G., Leahy, J. V., et al. (1998) · Physical Review A · doi:10.1103/physreva.58.2684 · Cited by 46 · see citing works
Encoding a qubit into multilevel subspaces
Grace, M., Brif, C., RABITZ, H. A., Walmsley, I. A., Kosut, R. L., & Lidar, D. A. (2006) · New Journal of Physics · doi:10.1088/1367-2630/8/3/035 · Cited by 45 · see citing works
Self-citationCriteria for reachability of quantum states
Schirmer, S. G., Solomon, A. I., & Leahy, J. V. (2002) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/35/40/313 · Cited by 44 · see citing works
Clark, J. W., Lucarelli, D. G., & Tarn, T. (2003) · International Journal of Modern Physics B · doi:10.1142/s021797920302051x · Cited by 41 · see citing works
Optimal control of a single qubit by direct inversion
Wenin, M., & Pötz, W. (2006) · Physical Review A · doi:10.1103/physreva.74.022319 · Cited by 39 · see citing works
Single-Step Implementation of Universal Quantum Gates
Grigorenko, I. A., & Khveshchenko, D. V. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.110501 · Cited by 34 · see citing works
Theory of Decoherence due to Scattering Events and Lévy Processes
Vacchini, B. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.230402 · Cited by 34 · see citing works
Adler, S. L. (2006) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/39/45/015 · Cited by 33 · see citing works
Robust Two-Qubit Quantum Registers
Grigorenko, I. A., & Khveshchenko, D. V. (2005) · Physical Review Letters · doi:10.1103/physrevlett.94.040506 · Cited by 32 · see citing works
Laser cooling of internal molecular degrees of freedom for vibrationally hot molecules
Schirmer, S. G. (2000) · Physical Review A · doi:10.1103/physreva.63.013407 · Cited by 31 · see citing works
Quantum control of chemical reaction dynamics in a classical way
Umeda, H., & Fujimura, Y. (2000) · The Journal of Chemical Physics · doi:10.1063/1.1287837 · Cited by 27 · see citing works
Control of the quantum open system via quantum generalized measurement
Zhang, M., Dai, H., Zhu, X., Li, X.-W., & Hu, D. (2006) · Physical Review A · doi:10.1103/physreva.73.032101 · Cited by 26 · see citing works
Probabilistic quantum control via indirect measurement
Mandilara, A., & Clark, J. W. (2005) · Physical Review A · doi:10.1103/physreva.71.013406 · Cited by 23 · see citing works
Schirmer, S. G., & Leahy, J. V. (2001) · Physical Review A · doi:10.1103/physreva.63.025403 · Cited by 23 · see citing works
Two derivations of the master equation of quantum Brownian motion
Halliwell, J. J. (2007) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/40/12/s11 · Cited by 23 · see citing works
A STOCHASTIC GOLDEN RULE AND QUANTUM LANGEVIN EQUATION FOR THE LOW DENSITY LIMIT
Accardi, L., Pechen, A. N., & Volovich, I. V. (2003) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025703001304 · Cited by 18 · see citing works
Self-citationControllability of multi-partite quantum systems and selective excitation of quantum dots
Schirmer, S. G., Pullen, I. C. H., & Solomon, A. I. (2005) · Journal of Optics B Quantum and Semiclassical Optics · doi:10.1088/1464-4266/7/10/013 · Cited by 18 · see citing works
Impact of positivity and complete positivity on accessibility of Markovian dynamics
Romano, R. (2005) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/38/41/018 · Cited by 5 · see citing works
WHITE NOISE APPROACH TO THE LOW DENSITY LIMIT
Pechen, A. N. (2005) · doi:10.1142/9789812702104_0028 · Cited by 2 · see citing works
Self-citationOptimal Control of High-Fidelity Quantum Gates in the Presence of DecoherencePreprint
Grace, M., Brif, C., RABITZ, H. A., et al. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0611189 · Cited by 1 · see citing works
Self-citation
Flagged first, then by citations
Research works printed but not linked: 7
- Rice S A and Zhao M 2000 Optical Control of Molecular Dynamics (New York: Wiley)
- Shapiro M and Brumer P 2003 Principles of the Quantum Control of Molecular Processes (New York: Wiley)
- Rabitz H A, Hsieh M M and Rosenthal C M 2004 Science 303 1998 · DOI
- Schirmer S G and Solomon A I 2002 Proc. SIAM Conf. on Mathematical Theory of Systems and Networks (South Bend, IN)
- Nielsen M A and Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press)
- Alicki R and Lendi K 1987 Quantum Dynamical Semigroups and Applications (Berlin: Springer)
- Pechen A N 2005 Quantum Probab. White Noise Anal. 18 428 (Preprint quant-ph/0607134) · arXiv
Cited by
Sorted by citations
Can one trust quantum simulators?
Hauke, P., Cucchietti, F. M., Tagliacozzo, L., Deutsch, I., & Lewenstein, M. (2012) · Reports on Progress in Physics · doi:10.1088/0034-4885/75/8/082401 · Cited by 315 · see citing works
- Authors
- Wu, R., Pechen, A., Brif, C., & Rabitz, H.
- Affiliations
- Princeton University (US)
- Venue
- Journal of Physics A: Mathematical and Theoretical
- Publisher
- IOP Publishing
- Published
- 2007-05-08
- Volume
- 40
- Issue
- 21
- Pages
- 5681-5693
- ISSN
- 1751-8113 (ISSN-L)
- 1751-8121
- OpenAlex
- W2094428668
- Cited by
- 100
- References
- 84
- Citations by year
- 2026: 1 · 2025: 2 · 2024: 5 · 2023: 6 · 2022: 9 · 2021: 11 · 2020: 5 · 2019: 2 · 2018: 1 · 2017: 4 · 2016: 3 · 2015: 2 · 2014: 5 · 2013: 3 · 2012: 8
- FWCI
- 8.68
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of Physics A Mathematical and Theoretical (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- open quantum systems, population transfer, two-level system, measurement-based control
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
