What is the optimal way to prepare a Bell state using measurement and feedback?
Abstract
Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. In this work, we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77, 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will bemore »
- Authors:
-
- Berkeley Center for Quantum Information and Computation, CA (United States); Univ. of California, Berkeley, CA (United States)
- Berkeley Center for Quantum Information and Computation, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES)
- OSTI Identifier:
- 1575229
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Quantum Science and Technology
- Additional Journal Information:
- Journal Volume: 2; Journal Issue: 4; Journal ID: ISSN 2058-9565
- Publisher:
- IOPscience
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Martin, Leigh, Sayrafi, Mahrud, and Whaley, K. Birgitta. What is the optimal way to prepare a Bell state using measurement and feedback?. United States: N. p., 2017.
Web. doi:10.1088/2058-9565/aa804c.
Martin, Leigh, Sayrafi, Mahrud, & Whaley, K. Birgitta. What is the optimal way to prepare a Bell state using measurement and feedback?. United States. doi:10.1088/2058-9565/aa804c.
Martin, Leigh, Sayrafi, Mahrud, and Whaley, K. Birgitta. Tue .
"What is the optimal way to prepare a Bell state using measurement and feedback?". United States. doi:10.1088/2058-9565/aa804c. https://www.osti.gov/servlets/purl/1575229.
@article{osti_1575229,
title = {What is the optimal way to prepare a Bell state using measurement and feedback?},
author = {Martin, Leigh and Sayrafi, Mahrud and Whaley, K. Birgitta},
abstractNote = {Recent work has shown that the use of quantum feedback can significantly enhance both the speed and success rate of measurement-based remote entanglement generation, but it is generally unknown what feedback protocols are optimal for these tasks. In this work, we consider two common measurements that are capable of projecting into pairwise entangled states, namely half- and full-parity measurements of two qubits, and determine in each case a globally optimal protocol for generation of entanglement. For the half-parity measurement, we rederive a previously described protocol using more general methods and prove that it is globally optimal for several figures of merit, including maximal concurrence or fidelity and minimal time to reach a specified concurrence or fidelity. For the full-parity measurement, we derive a protocol for rapid entanglement generation related to that of (Hill, Ralph, Phys. Rev. A 77, 014305), and then map the dynamics of the concurrence of the state to the Bloch vector length of an effective qubit. This mapping allows us to prove several optimality results for feedback protocols with full-parity measurements. We further show that our full-parity protocol transfers entanglement optimally from one qubit to the other amongst all measurement-based schemes. The methods developed here will be useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.},
doi = {10.1088/2058-9565/aa804c},
journal = {Quantum Science and Technology},
number = 4,
volume = 2,
place = {United States},
year = {2017},
month = {8}
}
Web of Science
Works referenced in this record:
A straightforward introduction to continuous quantum measurement
journal, September 2006
- Jacobs, Kurt; Steck, Daniel A.
- Contemporary Physics, Vol. 47, Issue 5
Remote Entanglement by Coherent Multiplication of Concurrent Quantum Signals
journal, October 2015
- Roy, Ananda; Jiang, Liang; Stone, A. Douglas
- Physical Review Letters, Vol. 115, Issue 15
Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols
journal, November 2008
- Jacobs, Kurt; Shabani, Alireza
- Contemporary Physics, Vol. 49, Issue 6
Analysis and synthesis of attractive quantum Markovian dynamics
journal, September 2009
- Ticozzi, Francesco; Viola, Lorenza
- Automatica, Vol. 45, Issue 9
Deterministic entanglement of superconducting qubits by parity measurement and feedback
journal, October 2013
- Ristè, D.; Dukalski, M.; Watson, C. A.
- Nature, Vol. 502, Issue 7471
Theory of remote entanglement via quantum-limited phase-preserving amplification
journal, June 2016
- Silveri, Matti; Zalys-Geller, Evan; Hatridge, Michael
- Physical Review A, Vol. 93, Issue 6
Stabilizing entangled states with quasi-local quantum dynamical semigroups
journal, November 2012
- Ticozzi, Francesco; Viola, Lorenza
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 370, Issue 1979
Heralded entanglement between solid-state qubits separated by three metres
journal, April 2013
- Bernien, H.; Hensen, B.; Pfaff, W.
- Nature, Vol. 497, Issue 7447
High-fidelity measurement and quantum feedback control in circuit QED
journal, December 2005
- Sarovar, Mohan; Goan, Hsi-Sheng; Spiller, T. P.
- Physical Review A, Vol. 72, Issue 6
Locally Optimal Control of Quantum Systems with Strong Feedback
journal, December 2008
- Shabani, Alireza; Jacobs, Kurt
- Physical Review Letters, Vol. 101, Issue 23
Comparing and Combining Measurement-Based and Driven-Dissipative Entanglement Stabilization
journal, March 2016
- Liu, Y.; Shankar, S.; Ofek, N.
- Physical Review X, Vol. 6, Issue 1
Rapid State Reduction of Quantum Systems Using Feedback Control
journal, January 2006
- Combes, Joshua; Jacobs, Kurt
- Physical Review Letters, Vol. 96, Issue 1
Reconsidering rapid qubit purification by feedback
journal, June 2006
- Wiseman, H. M.; Ralph, J. F.
- New Journal of Physics, Vol. 8, Issue 6
Backaction-driven, robust, steady-state long-distance qubit entanglement over lossy channels
journal, September 2016
- Motzoi, Felix; Halperin, Eli; Wang, Xiaoting
- Physical Review A, Vol. 94, Issue 3
Optimality of qubit purification protocols in the presence of imperfections
journal, March 2013
- Li, Hanhan; Shabani, Alireza; Sarovar, Mohan
- Physical Review A, Vol. 87, Issue 3
Weak measurement and control of entanglement generation
journal, January 2008
- Hill, Charles; Ralph, Jason
- Physical Review A, Vol. 77, Issue 1
Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
journal, January 1996
- Bennett, Charles H.; Brassard, Gilles; Popescu, Sandu
- Physical Review Letters, Vol. 76, Issue 5
Optimality of Feedback Control Strategies for Qubit Purification
journal, April 2008
- Wiseman, Howard M.; Bouten, Luc
- Quantum Information Processing, Vol. 7, Issue 2-3
Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers
journal, July 2016
- Černotík, Ondřej; Hammerer, Klemens
- Physical Review A, Vol. 94, Issue 1
Heralded Entanglement Between Widely Separated Atoms
journal, July 2012
- Hofmann, Julian; Krug, Michael; Ortegel, Norbert
- Science, Vol. 337, Issue 6090
Fidelity for Mixed Quantum States
journal, December 1994
- Jozsa, Richard
- Journal of Modern Optics, Vol. 41, Issue 12
Autonomously stabilized entanglement between two superconducting quantum bits
journal, November 2013
- Shankar, S.; Hatridge, M.; Leghtas, Z.
- Nature, Vol. 504, Issue 7480
Introduction to quantum noise, measurement, and amplification
journal, April 2010
- Clerk, A. A.; Devoret, M. H.; Girvin, S. M.
- Reviews of Modern Physics, Vol. 82, Issue 2
Deterministic generation of remote entanglement with active quantum feedback
journal, December 2015
- Martin, Leigh; Motzoi, Felix; Li, Hanhan
- Physical Review A, Vol. 92, Issue 6
Fidelity of mixed states of two qubits
journal, August 2002
- Verstraete, Frank; Verschelde, Henri
- Physical Review A, Vol. 66, Issue 2
Continuous joint measurement and entanglement of qubits in remote cavities
journal, September 2015
- Motzoi, Felix; Whaley, K. Birgitta; Sarovar, Mohan
- Physical Review A, Vol. 92, Issue 3
Determination of Maximal Gaussian Entanglement Achievable by Feedback-Controlled Dynamics
journal, June 2010
- Serafini, Alessio; Mancini, Stefano
- Physical Review Letters, Vol. 104, Issue 22
Observation of Measurement-Induced Entanglement and Quantum Trajectories of Remote Superconducting Qubits
journal, April 2014
- Roch, N.; Schwartz, M. E.; Motzoi, F.
- Physical Review Letters, Vol. 112, Issue 17
Optimal feedback control of linear quantum systems in the presence of thermal noise
journal, April 2013
- Genoni, Marco G.; Mancini, Stefano; Serafini, Alessio
- Physical Review A, Vol. 87, Issue 4
Entanglement of Formation of an Arbitrary State of Two Qubits
journal, March 1998
- Wootters, William K.
- Physical Review Letters, Vol. 80, Issue 10
Linear quantum trajectories: Applications to continuous projection measurements
journal, April 1998
- Jacobs, K.; Knight, P. L.
- Physical Review A, Vol. 57, Issue 4
Surface codes: Towards practical large-scale quantum computation
journal, September 2012
- Fowler, Austin G.; Mariantoni, Matteo; Martinis, John M.
- Physical Review A, Vol. 86, Issue 3
Topological quantum computing with a very noisy network and local error rates approaching one percent
journal, April 2013
- Nickerson, Naomi H.; Li, Ying; Benjamin, Simon C.
- Nature Communications, Vol. 4, Issue 1
Stabilizing Entanglement via Symmetry-Selective Bath Engineering in Superconducting Qubits
journal, June 2016
- Kimchi-Schwartz, M. E.; Martin, L.; Flurin, E.
- Physical Review Letters, Vol. 116, Issue 24
Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013
- Devoret, M. H.; Schoelkopf, R. J.
- Science, Vol. 339, Issue 6124
How to project qubits faster using quantum feedback
journal, March 2003
- Jacobs, Kurt
- Physical Review A, Vol. 67, Issue 3
Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
journal, August 2010
- Combes, Joshua; Wiseman, Howard M.; Jacobs, Kurt
- Physical Review A, Vol. 82, Issue 2
Universal Blind Quantum Computation
conference, October 2009
- Broadbent, Anne; Fitzsimons, Joseph; Kashefi, Elham
- 2009 IEEE 50th Annual Symposium on Foundations of Computer Science (FOCS), 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Optimal control of entanglement via quantum feedback
journal, January 2007
- Mancini, Stefano; Wiseman, Howard M.
- Physical Review A, Vol. 75, Issue 1
Works referencing / citing this record:
Manipulation of Multi‐Level Quantum Systems via Unsharp Measurements and Feedback Operations
journal, September 2019
- Ran, Du; Shan, Wu‐Jiang; Shi, Zhi‐Cheng
- Annalen der Physik, Vol. 531, Issue 11
Error correction of quantum system dynamics via measurement–feedback control
journal, July 2019
- Ran, Du; Shi, Zhi-Cheng; Yang, Zhen-Biao
- Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 52, Issue 16
Generation and stabilization of Bell states via repeated projective measurements on a driven ancilla qubit
journal, May 2018
- Magazzù, L.; Jaramillo, J. D.; Talkner, P.
- Physica Scripta, Vol. 93, Issue 6