skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: 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 » useful for deriving feedback protocols and determining their optimality properties in many other quantum systems subject to measurement and unitary operations.« less

Authors:
ORCiD logo [1];  [2];  [1]
  1. Berkeley Center for Quantum Information and Computation, CA (United States); Univ. of California, Berkeley, CA (United States)
  2. 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) (SC-22)
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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

A straightforward introduction to continuous quantum measurement
journal, September 2006


Remote Entanglement by Coherent Multiplication of Concurrent Quantum Signals
journal, October 2015


Quantum feedback control: how to use verification theorems and viscosity solutions to find optimal protocols
journal, November 2008


Analysis and synthesis of attractive quantum Markovian dynamics
journal, September 2009


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
  • DOI: 10.1038/nature12513

Theory of remote entanglement via quantum-limited phase-preserving amplification
journal, June 2016


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
  • DOI: 10.1098/rsta.2011.0485

Heralded entanglement between solid-state qubits separated by three metres
journal, April 2013


High-fidelity measurement and quantum feedback control in circuit QED
journal, December 2005


Locally Optimal Control of Quantum Systems with Strong Feedback
journal, December 2008


Comparing and Combining Measurement-Based and Driven-Dissipative Entanglement Stabilization
journal, March 2016


Rapid State Reduction of Quantum Systems Using Feedback Control
journal, January 2006


Reconsidering rapid qubit purification by feedback
journal, June 2006


Backaction-driven, robust, steady-state long-distance qubit entanglement over lossy channels
journal, September 2016


Optimality of qubit purification protocols in the presence of imperfections
journal, March 2013


Weak measurement and control of entanglement generation
journal, January 2008


Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
journal, January 1996


Optimality of Feedback Control Strategies for Qubit Purification
journal, April 2008


Measurement-induced long-distance entanglement of superconducting qubits using optomechanical transducers
journal, July 2016


Heralded Entanglement Between Widely Separated Atoms
journal, July 2012


Fidelity for Mixed Quantum States
journal, December 1994


Autonomously stabilized entanglement between two superconducting quantum bits
journal, November 2013


Introduction to quantum noise, measurement, and amplification
journal, April 2010


Deterministic generation of remote entanglement with active quantum feedback
journal, December 2015


Fidelity of mixed states of two qubits
journal, August 2002


Continuous joint measurement and entanglement of qubits in remote cavities
journal, September 2015


Determination of Maximal Gaussian Entanglement Achievable by Feedback-Controlled Dynamics
journal, June 2010


Observation of Measurement-Induced Entanglement and Quantum Trajectories of Remote Superconducting Qubits
journal, April 2014


Optimal feedback control of linear quantum systems in the presence of thermal noise
journal, April 2013


Entanglement of Formation of an Arbitrary State of Two Qubits
journal, March 1998


Linear quantum trajectories: Applications to continuous projection measurements
journal, April 1998


Surface codes: Towards practical large-scale quantum computation
journal, September 2012


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
  • DOI: 10.1038/ncomms2773

Stabilizing Entanglement via Symmetry-Selective Bath Engineering in Superconducting Qubits
journal, June 2016


Superconducting Circuits for Quantum Information: An Outlook
journal, March 2013


How to project qubits faster using quantum feedback
journal, March 2003


Rapid purification of quantum systems by measuring in a feedback-controlled unbiased basis
journal, August 2010


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
  • DOI: 10.1109/FOCS.2009.36

Optimal control of entanglement via quantum feedback
journal, January 2007