![Page 1: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/1.jpg)
Absolute irreversibility and continuous quantum measurement: a fluctuation theorem perspective
Sreenath K. Manikandan
Manikandan, Sreenath K., Cyril Elouard, and AndrewN. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 2: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/2.jpg)
Quantum measurement:
Reversal of motion (time reversal)
Quantum mechanics:
Classical mechanics:
Sakurai, Jun John, and Eugene D. Commins. "Modern quantum mechanics, revised edition." (1995): 93-95.
![Page 3: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/3.jpg)
X
Z
X
Z
X
Z
Example: Continuous weak measurement of
Reversibility at each step:
Readout
![Page 4: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/4.jpg)
A quantum trajectory
A quantum trajectory is the sequence:
The sequence is realized with probability density:
![Page 5: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/5.jpg)
The quantum measurement reversal
We considered general measurements, and obtained the inverse measurement operator:
For the reversed sequence of readouts,
we have the backward trajectory:
Manikandan, S.K. & Jordan, A.N. Quantum Stud.: Math. Found. (2019). https://doi.org/10.1007/s40509-019-00182-w
![Page 6: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/6.jpg)
Time-symmetry of equations
Dressel, Justin, et al. "Arrow of time for continuous quantum measurement." Physical review letters 119.22 (2017): 220507.
➢ Dynamical equations time reversal invariant…!!
![Page 7: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/7.jpg)
The quantum measurement arrow of time
Using Bayes theorem,
Assume uniform priors
The arrow of time measure:
Dressel, Justin, et al. "Arrow of time for continuous quantum measurement." Physical review letters 119.22 (2017): 220507.
![Page 8: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/8.jpg)
Manikandan, Sreenath K., and Andrew N. Jordan. "Time reversal symmetry of generalized quantum measurements with past and future boundary conditions." arXivpreprint arXiv:1801.04364 (2018).
![Page 9: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/9.jpg)
Example: Continuous weak measurement of
• The arrow of time:
• Here
Measurement duration increases
X
Z
X
Z
Image from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 10: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/10.jpg)
Probability distribution of the arrow of time
Image from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 11: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/11.jpg)
Canonical distribution with inverse temperature
Thermodynamics of small systems (free expansion)
Murashita, Yûto, Ken Funo, and Masahito Ueda. "Nonequilibrium equalities in absolutely irreversible processes." Physical Review E 90.4 (2014): 042110.
![Page 12: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/12.jpg)
Thermodynamic arrow of time
Murashita, Yûto, Ken Funo, and Masahito Ueda. "Nonequilibrium equalities in absolutely irreversible processes." Physical Review E 90.4 (2014): 042110.
![Page 13: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/13.jpg)
X
Backward process
Use this approach in the quantummeasurement problem!
![Page 14: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/14.jpg)
Absolute irreversibility
Strictly positive average arrow of time!
Measurement duration increases
The average in three distributions can be explained using trajectories which do not go back. We find that is not the completestory.
![Page 15: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/15.jpg)
❑ A complementary description is contained in❑ Reflects the many to one mapping aspect of the quantum measurement problem.
Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 16: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/16.jpg)
Simulated experiments
The quantum state collapse becomes more and more absolutely irreversible with the measurement duration
Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 17: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/17.jpg)
Simulated experiments
The quantum state collapse becomes more and more absolutely irreversible with increasing measurement strength.
Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.
![Page 18: Sreenath K. Manikandan - qtd2019.aalto.fi · Results from: Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117. Conclusions & forward](https://reader034.vdocuments.mx/reader034/viewer/2022042805/5f62ec41c9bbca5eca0f6424/html5/thumbnails/18.jpg)
Conclusions & forward
❑We discussed the idea of measurement reversal and introduced the notion of a statistical arrowof time for arbitrary weak measurements on a qubit.
❑We found that the quantum measurement dynamics is absolutely irreversible, similar to the freeexpansion of a single particle gas.
❑This absolute irreversibility is deeply connected to information acquisition in quantummeasurements, and to the many-to-one mapping aspect of the quantum measurement problem.
❑Experimental verification on superconducting qubits: Harrington, P. M., et al. "Characterizing astatistical arrow of time in quantum measurement dynamics." arXiv preprintarXiv:1811.07708 (2018).
❑Quantum measurement process is inherently probabilistic, which disturbs the system beingmeasured similar to the uncontrollable fluctuations created by a thermal bath. Our microscopicreversibility approach to the measurement problem open new directions for probing the resourcenature of quantum coherence and correlations, similar to energy in the thermodynamic sense.
Thank you for your time.
Manikandan, Sreenath K., Cyril Elouard, and Andrew N. Jordan. Physical Review A 99.2 (2019): 022117.