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Quantum Metrology with Quantum Time Flip

  • Gaurang Agrawal (20201049) Advisor: Prof. Aditi Sen De

Collaborator: Pritam Halder

Mid – Year Presentation

- Oct 2024

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Table of contents

01.

03.

02.

04.

Quantum Metrology

How do we estimate parameters?

Applications

Indefiniteness galore

Novel Quantum Operations

More operations more possibilities !

Preliminary Results and Future Ideas

Research time

- Oct 2024

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Quantum Metrology

01.

How do we estimate parameters?

- Oct 2024

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Classical Metrology

 

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  • Low variance

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  • Bounded by Cramer-Rao bound 🡪 inverse of Fisher Information
  • FI is additive.

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  • is N independent realizations of

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🡪

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  • FI can increase at most as O(n)

Amount of Extractable Information

Fisher Information

n

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  • Parameters are incorporated in quantum states and transformations

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  • Can quantum physics be utilized for better estimations of these parameters?

Ans: Yes!! Quantum Metrology

Quantum Metrology

1. Probe preparation

2. evolution of probe under the channel

3. measurement

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along with the classical task of choosing the estimator

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  • Entangled state, strategies and supermaps on transformations, entangled measurements

🡪 variance can fall faster than 1/n

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1

2

3

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Properties:

  1. Additivity
  2. Purification
  3. Saturability
  4. Convexity
  5. Metric
  6. Concavity under CPTP

Optimize over all measurements (POVMs) to maximize the Fisher Information 🡪 Quantum Fisher Information

Quantum Fisher Information

(Phys. Rev. Lett. 72, 3439), (arXiv:0804.2981)

arXiv:0804.2981

�

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In phase estimation problem

CRB 🡪 optimizing over estimators

QCRB 🡪 optimizing over measurements

Heisenberg Limit 🡪 optimizing over probe states

 

Untouched topics: multiparameter estimation, relation with information geometry etc.

Example: Phase Estimation

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Optimization over strategies?

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  • A less studied method : Use of supermaps to change transformations.

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  • 🡪 Super-Heisenberg metrology using quantum switch

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  • 🡪 Optimizing over strategies: advantages of certain maps and supermaps.

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Strategies

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References:

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  1. Braunstein, S. L., & Caves, C. M. (1994). Statistical distance and the geometry of quantum states. Phys. Rev. Lett., 72(22), 3439–3443. doi: 10.1103/PhysRevLett.72.3439
  2. Paris, M. G. A. (2008). Quantum estimation for quantum technology. arXiv, 0804.2981. Retrieved from https://arxiv.org/abs/0804.2981v3
  3. Rafał Demkowicz-Dobrzański home page. (2022, June 21). Retrieved from https://www.fuw.edu.pl/~demko/students.html
  4. Shettell, N. (2022). Quantum Information Techniques for Quantum Metrology. arXiv, 2201.01523. Retrieved from https://arxiv.org/abs/2201.01523v1
  5. Zhao, X., Yang, Y., & Chiribella, G. (2020). Quantum Metrology with Indefinite Causal Order. Phys. Rev. Lett., 124(19), 190503. doi: 10.1103/PhysRevLett.124.190503
  6. Liu, Q., Hu, Z., Yuan, H., & Yang, Y. (2023). Optimal Strategies of Quantum Metrology with a Strict Hierarchy. Phys. Rev. Lett., 130(7), 070803. doi: 10.1103/PhysRevLett.130.070803

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Novel Quantum Operations

02.

More operations more possibilities !

- Oct 2024

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Quantum Combs

  • What are the most general quantum transformations which send a bunch of channels to other channels 🡪 Quantum Supermaps

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Realization Theorem

[Requires definite causal order]

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Novel Supermaps

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Process Matrix

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Quantum Switch

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Quantum Operations with Indefinite Input-Output Direction

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References:

  1. Chiribella, G., D’Ariano, G. M., & Perinotti, P. (2008). Quantum Circuit Architecture. Phys. Rev. Lett., 101(6), 060401. doi: 10.1103/PhysRevLett.101.060401
  2. Chiribella, G., D’Ariano, G. M., & Perinotti, P. (2009). Theoretical framework for quantum networks. Phys. Rev. A, 80(2), 022339. doi: 10.1103/PhysRevA.80.022339
  3. Chiribella, G., D’Ariano, G. M., & Perinotti, P. (2008). Optimal Cloning of Unitary Transformation. Phys. Rev. Lett., 101(18), 180504. doi: 10.1103/PhysRevLett.101.180504
  4. Chiribella, G., D’Ariano, G. M., & Perinotti, P. (2008). Memory Effects in Quantum Channel Discrimination. Phys. Rev. Lett., 101(18), 180501. doi: 10.1103/PhysRevLett.101.180501
  5. Oreshkov, O., Costa, F., & Brukner, Č. (2012). Quantum correlations with no causal order. Nat. Commun., 3(1092), 1–8. doi: 10.1038/ncomms2076
  6. Araújo, M., Branciard, C., Costa, F., Feix, A., Giarmatzi, C., & Brukner, Č. (2015). Witnessing causal nonseparability. New J. Phys., 17(10), 102001. doi: 10.1088/1367-2630/17/10/102001
  7. Kissinger, A., & Uijlen, S. (2017). A categorical semantics for causal structure. arXiv, 1701.04732. Retrieved from https://arxiv.org/abs/1701.04732v6
  8. Chiribella, G., D’Ariano, G. M., Perinotti, P., & Valiron, B. (2013). Quantum computations without definite causal structure. Phys. Rev. A, 88(2), 022318. doi: 10.1103/PhysRevA.88.022318
  9. Chiribella, G., & Liu, Z. (2022). Quantum operations with indefinite time direction. Commun. Phys., 5(190), 1–8. doi: 10.1038/s42005-022-00967-3
  10. Liu, Z., Yang, M., & Chiribella, G. (2023). Quantum communication through devices with indefinite input-output direction. New J. Phys., 25(4), 043017. doi: 10.1088/1367-2630/acc8f2

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Applications

03.

Indefiniteness Galore

- Oct 2024

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Applications of Switch

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Need to do Semi-definite optimization

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References:

  1. Ebler, D., Salek, S., & Chiribella, G. (2018). Enhanced Communication with the Assistance of Indefinite Causal Order. Phys. Rev. Lett., 120(12), 120502. doi: 10.1103/PhysRevLett.120.120502Chiribella, G., D’Ariano, G. M., & Perinotti, P. (2009).
  2. Sazim, S., Sedlak, M., Singh, K., & Pati, A. K. (2021). Classical communication with indefinite causal order for N completely depolarizing channels. Phys. Rev. A, 103(6), 062610. doi: 10.1103/PhysRevA.103.062610
  3. Chiribella, G., Wilson, M., & Chau, H. F. (2021). Quantum and Classical Data Transmission through Completely Depolarizing Channels in a Superposition of Cyclic Orders. Phys. Rev. Lett., 127(19), 190502. doi: 10.1103/PhysRevLett.127.190502
  4. Wu, Z., Fullwood, J., Ma, Z., Zhou, S., Zhao, Q., & Chiribella, G. (2024). General Communication Enhancement via the Quantum Switch. arXiv preprint arXiv:2407.02726
  5. Zhao, X., Yang, Y., & Chiribella, G. (2020). Quantum Metrology with Indefinite Causal Order. Phys. Rev. Lett., 124(19), 190503. doi: 10.1103/PhysRevLett.124.190503
  6. Chapeau-Blondeau, F. (2021). Noisy quantum metrology with the assistance of indefinite causal order. Phys. Rev. A, 103(3), 032615. doi: 10.1103/PhysRevA.103.032615
  7. An, M., Ru, S., Wang, Y., Yang, Y., Wang, F., Zhang, P., & Li, F. (2024). Noisy quantum parameter estimation with indefinite causal order. Phys. Rev. A, 109(1), 012603. doi: 10.1103/PhysRevA.109.012603
  8. Liu, Q., Hu, Z., Yuan, H., & Yang, Y. (2023). Optimal Strategies of Quantum Metrology with a Strict Hierarchy. Phys. Rev. Lett., 130(7), 070803. doi: 10.1103/PhysRevLett.130.070803
  9. Liu, Z., Yang, M., & Chiribella, G. (2023). Quantum communication through devices with indefinite input-output direction. New J. Phys., 25(4), 043017. doi: 10.1088/1367-2630/acc8f2

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Preliminary Results and Future Ideas

04.

Research time

- Oct 2024

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Metrology Using Quantum Time Flip

  • Objective: Extract Fisher information using quantum time flip instead of switch

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  • Compare three strategies below

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  • Both are coherently controlled channels:

1

2

3

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Future Directions

  • Extend the results and derive analytically
  • Can we claim an advantage due to indefinite input output directions?

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Brief Introduction to SDP

  • Linear Programming
  • Semi-Definite Programming

Dual Problem

 

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References:

  1. Chapeau-Blondeau, F. (2021). Noisy quantum metrology with the assistance of indefinite causal order. Phys. Rev. A, 103(3), 032615. doi: 10.1103/PhysRevA.103.032615
  2. An, M., Ru, S., Wang, Y., Yang, Y., Wang, F., Zhang, P., & Li, F. (2024). Noisy quantum parameter estimation with indefinite causal order. Phys. Rev. A, 109(1), 012603. doi: 10.1103/PhysRevA.109.012603
  3. Abbott, A. A., Wechs, J., Horsman, D., Mhalla, M., & Branciard, C. (2020). Communication through coherent control of quantum channels. Quantum, 1810.09826v3. Retrieved from https://quantum-journal.org/papers/q-2020-09-24-333
  4. Mothe, R., Branciard, C., & Abbott, A. A. (2024). Reassessing the advantage of indefinite causal orders for quantum metrology. Phys. Rev. A, 109(6), 062435. doi: 10.1103/PhysRevA.109.062435
  5. Liu, Q., Hu, Z., Yuan, H., & Yang, Y. (2023). Optimal Strategies of Quantum Metrology with a Strict Hierarchy. Phys. Rev. Lett., 130(7), 070803. doi: 10.1103/PhysRevLett.130.070803
  6. Liu, Q., Hu, Z., Yuan, H., & Yang, Y. (2024). Fully-Optimized Quantum Metrology: Framework, Tools, and Applications. Adv. Quantum Technol., n/a(n/a), 2400094. doi: 10.1002/qute.202400094
  7. Skrzypczyk, P., & Cavalcanti, D. (2023). Semidefinite Programming in Quantum Information Science. IOP Publishing. doi: 10.1088/978-0-7503-3343-6
  8. Araújo, M., Branciard, C., Costa, F., Feix, A., Giarmatzi, C., & Brukner, Č. (2015). Witnessing causal nonseparability. New J. Phys., 17(10), 102001. doi: 10.1088/1367-2630/17/10/102001
  9. Oreshkov, O., & Giarmatzi, C. (2016). Causal and causally separable processes. New J. Phys., 18(9), 093020. doi: 10.1088/1367-2630/18/9/093020
  10. Chiribella, G., & Liu, Z. (2022). Quantum operations with indefinite time direction. Commun. Phys., 5(190), 1–8. doi: 10.1038/s42005-022-00967-3

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Thank You

- Oct 2024