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Switching Quantum Reference Frames for Quantum Measurement




Jianhao M. Yang

Qualcomm, San Diego, CA 92121, USA

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Physical observation is made relative to a reference frame. A reference frame is essentially a quantum system given the universal validity of quantum mechanics. Thus, a quantum system must be described relative to a quantum reference frame (QRF). Further requirements on QRF include using only relational observables and not assuming the existence of external reference frame. To address these requirements, two approaches are proposed in the literature. The first one is an operational approach (F. Giacomini, et al, Nat. Comm. 10:494, 2019) which focuses on the quantization of transformation between QRFs. The second approach attempts to derive the quantum transformation between QRFs from first principles (A. Vanrietvelde, et al, $textit{Quantum}$ 4:225, 2020). Such first principle approach describes physical systems as symmetry induced constrained Hamiltonian systems. The Dirac quantization of such systems before removing redundancy is interpreted as perspective-neutral description. Then, a systematic redundancy reduction procedure is introduced to derive description from perspective of a QRF. The first principle approach recovers some of the results from the operational approach, but not yet include an important part of a quantum theory – the measurement theory. This paper is intended to bridge the gap. We show that the von Neumann quantum measurement theory can be embedded into the perspective-neutral framework. This allows us to successfully recover the results found in the operational approach, with the advantage that the transformation operator can be derived from the first principle. In addition, the formulation presented here reveals several interesting conceptual insights. For instance, the projection operation in measurement needs to be performed after redundancy reduction, and the projection operator must be transformed accordingly when switching QRFs. These results represent one step forward in understanding how quantum measurement should be formulated when the reference frame is also a quantum system.

The paper is a step forward in the investigation of quantum measurement with quantum reference frames (QRF). Utilizing the recently published first-principle approach to the formulation of quantum mechanics when switching QRFs, the paper addresses the following issue of quantum measurement: How should the same measurement process be described from the points of view of different QRFs? How do the descriptions relate to one another? In the context of the first-principle approach, the answer is this: the unitary evolution of the measurement process can be embedded in a perspective-neutral framework, but the measurement projection is perspectival, and thus shall be implemented after the QRF is specified.

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What can you do in 48 hours?




Have you ever wondered what can be done in 48 hours? For instance, our heart beats around 200 000 times. One of the biggest supercomputers crunches petabytes (peta = 1015) of numbers to simulate an experiment that took Google’s quantum processor only 300 seconds to run. In 48 hours, one can also participate in the Sciathon with almost 500 young researchers from more than 80 countries! 

Two weeks ago I participated in a scientific marathon, the Sciathon. The structure of this event roughly resembled a hackathon. I am sure many readers are familiar with the idea of a hackathon from personal experience. For those unfamiliar — a hackathon is an intense collaborative event, usually organized over the weekend, during which people with different backgrounds work in groups to create prototypes of functioning software or hardware. For me, it was the very first time to have firsthand experience with a hackathon-like event!

The Sciathon was organized by the Lindau Nobel Laureate Meetings (more about the meetings with Nobel laureates, which happen annually in the lovely German town of Lindau, in another blogpost, I promise!) This year, unfortunately, the face-to-face meeting in Lindau was postponed until the summer of 2021. Instead, the Lindau Nobel Laureate Meetings alumni and this year’s would-be attendees had an opportunity to gather for the Sciathon, as well as the Online Science Days earlier this week, during which the best Sciathon projects were presented.

The participants of the Sciathon could choose to contribute new views, perspectives and solutions to three main topics: Lindau Guidelines, Communicating Climate Change and Capitalism After Corona. The first topic concerned an open, cooperative science community where data and knowledge are freely shared, the second — how scientists could show that the climate crisis is just as big a threat as the SARS-CoV-19 virus, and the last — how to remodel our current economic systems so that they are more robust to unexpected sudden crises. More detailed descriptions of each topic can be found on the official Sciathon webpage.

My group of ten eager scientists, mostly physicists, from master students to postdoctoral researchers, focused on the first topic. In particular, our goal was to develop a method of familiarizing high school students with the basics of quantum information and computation. We envisioned creating an online notebook, where an engaging story would be intertwined with interactive blocks of Python code utilizing the open-source quantum computing toolkit Qiskit. This hands-on approach would enable students to play with quantum systems described in the story-line by simply running the pre-programmed commands with a click of the mouse and then observe how “experiment” matches “the theory”. We decided to work with a system comprising one or two qubits and explain such fundamental concepts in quantum physics as superposition, entanglement and measurement. The last missing part was a captivating story.

The story we came up with involved two good friends from the lab, Miss Schrödinger and Miss Pauli, as well as their kittens, Alice and Bob. At first, Alice and Bob seemed to be ordinary cats, however whenever they sipped quantum milk, they would turn into quantum cats, or as quantum physicists would say — kets. Do I have to remind the reader that a quantum cat, unlike an ordinary one, could be both awake and asleep at the same time?

Miss Schrödinger was a proud cat owner who not only loved her cat, but also would take hundreds of pictures of Alice and eagerly upload them on social media. Much to Miss Schrödinger’s surprise, none of the pictures showed Alice partly awake and partly asleep — the ket would always collapse to the cat awake or the cat asleep! Every now and then, Miss Pauli would come to visit Miss Schrödinger and bring her own cat Bob. While the good friends were chit-chatting over a cup of afternoon tea, the cats sipped a bit of quantum milk and started to play with a ball of wool, resulting in a cute mess of two kittens tangled up in wool. Every time after coming back home, Miss Pauli would take a picture of Bob and share it with Miss Schrödinger, who would obviously also take a picture of Alice. After a while, the young scientists started to notice some strange correlations between the states of their cats… 

The adventures of Miss Schrödinger and her cat continue! For those interested, you can watch a short video about our project! 

Overall, I can say that I had a lot of fun participating in the Sciathon. It was an intense yet extremely gratifying event. In addition to the obvious difficulty of racing against the clock, our group also had to struggle with coordinating video calls between group members scattered across three almost equidistant time zones — Eastern Australian, Central European and Central US! During the Sciathon I had a chance to interact with other science enthusiasts from different backgrounds and work on something from outside my area of expertise. I would strongly encourage anyone to participate in hackathon-like events to break the daily routine, particularly monotonous during the lockdown, and unleash one’s creative spirit. Such events can also be viewed as an opportunity to communicate science and scientific progress to the public. Lastly, I would like to thank other members of my team — collaborating with you during the Sciathon was a blast!

During the Sciathon, we had many brainstorming sessions. You can see most of the members of my group in this video call (from left to right, top to bottom): Shuang, myself, Martin, Kyle, Hadewijch, Saskia, Michael and Bartłomiej. The team also included Ahmed and Watcharaphol.


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Optimal probes and error-correction schemes in multi-parameter quantum metrology




Wojciech Górecki1, Sisi Zhou2,3,4, Liang Jiang2,3,4, and Rafał Demkowicz-Dobrzański1

1Faculty of Physics, University of Warsaw, Pasteura 5, 02-093 Warsaw, Poland
2Departments of Applied Physics and Physics, Yale University, New Haven, Connecticut 06511, USA
3Yale Quantum Institute, Yale University, New Haven, Connecticut 06511, USA
4Pritzker School of Molecular Engineering, University of Chicago, Chicago, IL 60637, USA

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We derive a necessary and sufficient condition for the possibility of achieving the Heisenberg scaling in general adaptive multi-parameter estimation schemes in presence of Markovian noise. In situations where the Heisenberg scaling is achievable, we provide a semidefinite program to identify the optimal quantum error correcting (QEC) protocol that yields the best estimation precision. We overcome the technical challenges associated with potential incompatibility of the measurement optimally extracting information on different parameters by utilizing the Holevo Cramér-Rao (HCR) bound for pure states. We provide examples of significant advantages offered by our joint-QEC protocols, that sense all the parameters utilizing a single error-corrected subspace, over separate-QEC protocols where each parameter is effectively sensed in a separate subspace.

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Cited by

[1] Philippe Faist, Sepehr Nezami, Victor V. Albert, Grant Salton, Fernando Pastawski, Patrick Hayden, and John Preskill, “Continuous symmetries and approximate quantum error correction”, arXiv:1902.07714.

[2] Francesco Albarelli, Jamie F. Friel, and Animesh Datta, “Evaluating the Holevo Cramér-Rao Bound for Multiparameter Quantum Metrology”, Physical Review Letters 123 20, 200503 (2019).

[3] Francesco Albarelli, Mankei Tsang, and Animesh Datta, “Upper bounds on the Holevo Cramér-Rao bound for multiparameter quantum parametric and semiparametric estimation”, arXiv:1911.11036.

[4] F. Albarelli, M. Barbieri, M. G. Genoni, and I. Gianani, “A perspective on multiparameter quantum metrology: From theoretical tools to applications in quantum imaging”, Physics Letters A 384, 126311 (2020).

[5] Yingkai Ouyang, Nathan Shettell, and Damian Markham, “Robust quantum metrology with explicit symmetric states”, arXiv:1908.02378.

[6] Emanuele Polino, Mauro Valeri, Nicolò Spagnolo, and Fabio Sciarrino, “Photonic Quantum Metrology”, arXiv:2003.05821.

[7] Sisi Zhou and Liang Jiang, “Optimal approximate quantum error correction for quantum metrology”, Physical Review Research 2 1, 013235 (2020).

[8] Rafal Demkowicz-Dobrzanski, Wojciech Gorecki, and Madalin Guta, “Multi-parameter estimation beyond Quantum Fisher Information”, arXiv:2001.11742.

[9] Sisi Zhou and Liang Jiang, “The theory of entanglement-assisted metrology for quantum channels”, arXiv:2003.10559.

[10] Aleksander Kubica and Rafal Demkowicz-Dobrzanski, “Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem”, arXiv:2004.11893.

[11] Alexander Predko, Francesco Albarelli, and Alessio Serafini, “Time-local optimal control for parameter estimation in the Gaussian regime”, Physics Letters A 384, 126268 (2020).

[12] Le Bin Ho, Hideaki Hakoshima, Yuichiro Matsuzaki, Masayuki Matsuzaki, and Yasushi Kondo, “Multiparameter quantum estimation under dephasing noise”, arXiv:2004.00720.

The above citations are from SAO/NASA ADS (last updated successfully 2020-07-02 13:02:52). The list may be incomplete as not all publishers provide suitable and complete citation data.

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Efficient Quantum Walk Circuits for Metropolis-Hastings Algorithm




Jessica Lemieux1, Bettina Heim2, David Poulin1,3, Krysta Svore2, and Matthias Troyer2

1Département de Physique & Institut Quantique, Université de Sherbrooke, Québec, Canada
2Quantum Architecture and Computation Group, Microsoft Research, Redmond, WA 98052, USA
3Canadian Institute for Advanced Research, Toronto, Ontario, Canada M5G 1Z8

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We present a detailed circuit implementation of Szegedy’s quantization of the Metropolis-Hastings walk. This quantum walk is usually defined with respect to an oracle. We find that a direct implementation of this oracle requires costly arithmetic operations. We thus reformulate the quantum walk, circumventing its implementation altogether by closely following the classical Metropolis-Hastings walk. We also present heuristic quantum algorithms that use the quantum walk in the context of discrete optimization problems and numerically study their performances. Our numerical results indicate polynomial quantum speedups in heuristic settings.

► BibTeX data

► References

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Cited by

[1] Jessica Lemieux, Guillaume Duclos-Cianci, David Sénéchal, and David Poulin, “Resource estimate for quantum many-body ground state preparation on a quantum computer”, arXiv:2006.04650.

The above citations are from SAO/NASA ADS (last updated successfully 2020-06-29 12:29:48). The list may be incomplete as not all publishers provide suitable and complete citation data.

Could not fetch Crossref cited-by data during last attempt 2020-06-29 12:29:47: Could not fetch cited-by data for 10.22331/q-2020-06-29-287 from Crossref. This is normal if the DOI was registered recently.


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