A math problem developed 243 years ago can be solved only by using quantum entanglement, new research finds.
The mathematics problem is a bit like Sudoku on steroids. It's called Euler's officer problem, after Leonhard Euler, the mathematician who first proposed it in 1779. Here's the puzzle: You're commanding an army with six regiments. Each regiment contains six different officers of six different ranks. Can you arrange them in a 6-by-6 square without repeating a rank or regiment in any given row or column?
Euler couldn't find such an arrangement, and later computations proved that there was no solution. In fact, a paper published in 1960 in the Canadian Journal of Mathematics used the newfound power of computers to show that 6 was the one number over 2 where no such arrangement existed.
Now, though, researchers have found a new solution to Euler's problem. As Quanta Magazine's Daniel Garisto reported, a new study posted to the preprint database arXiv finds that you can arrange six regiments of six officers of six different ranks in a grid without repeating any rank or regiment more than once in any row or column if the officers are in a state of quantum entanglement.
The paper, which has been submitted for peer review at the journal Physical Review Letters, takes advantage of the fact that quantum objects can be in multiple possible states until they are measured. (Quantum entanglement was famously demonstrated by the Schrdinger's cat thought experiment, in which a cat is trapped in a box with radioactive poison; the cat is both dead and alive until you open the box.)
In Euler's classic problem, each officer has a static regiment and rank. They might be a first lieutenant in the Red Regiment, for example, or a captain in the Blue Regiment. (Colors are sometimes used in visualizing the grids, to make it easier to identify the regiments.)
But a quantum officer might occupy more than one regiment or rank at once. A single officer could be either a Red Regiment first lieutenant or a Blue Regiment captain; a Green Regiment major or Purple Regiment colonel. (Or, theoretically, any other combination.)
The key to solving Euler's problem with this identity switcheroo is that the officers on the grid can be in a state of quantum entanglement. In entanglement, the state of one object informs the state of another. If Officer No. 1 is, in fact, a Red Regiment first lieutenant, Officer No. 2 must be a major in the Green Regiment, and vice versa.
Using brute-force computer power, the authors of the new paper, led by Adam Burchardt, a postdoctoral researcher at Jagiellonian University in Poland, proved that filling the grid with quantum officers made the solution possible. Surprisingly, the entanglement has its own pattern, study co-author Suhail Rather, a physicist at the Indian Institute of Technology Madras, told Quanta Magazine. Officers are only entangled with officers of ranks one step below or above them, while regiments are also only entangled with adjacent regiments.
The results could have real impacts on quantum data storage, according to Quanta Magazine. Entangled states can be used in quantum computing to ensure that data is safe even in the case of an error a process called quantum error correction. By entangling 36 quantum officers in a state of interdependent relationships, the researchers found what is called an absolutely maximally entangled state. Such states can be important for resilient data storage in quantum computing.
You can read all about the impossible problem's solution in Quanta Magazine.
Originally published on Live Science.
Go here to read the rest:
- Wolfram Physics Project Seeks Theory Of Everything; Is It Revelation Or Overstatement? - Hackaday [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Elon Musk and Grimes Named Their Baby X A-12, Which Must Mean SomethingRight? - Esquire [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Free Will Astrology - Week of May 7 | Advice & Fun | Bend - The Source Weekly [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Free Will Astrology: May 6, 2020 - River Cities Reader [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Is string theory worth it? - Space.com [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Finding the right quantum materials - MIT News [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Quantum Tunneling Effects, Solving the Schrodinger Equation Bottleneck Recognized as Best Papers by The Journal of Chemical Physics - PRNewswire [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- What Is Quantum Mechanics? Quantum Physics Defined ... [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Quantum Physics Overview, Concepts, and History [Last Updated On: May 6th, 2020] [Originally Added On: May 6th, 2020]
- Tisca Chopra: This time has given me time to think about time - Daijiworld.com [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- Iron-Based Material has the Ability to Power Small Devices - AZoNano [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- How Einstein Failed to Find Flaws in the Copenhagen Interpretation - The Great Courses Daily News [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- Raytheon Technologies Reports First Quarter 2020 Results; Greg Hayes Quoted - ExecutiveBiz [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- Unified Field Theory: Einstein Failed, but What's the Future? - The Great Courses Daily News [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- Einstein Vs. the New Generation of Quantum Theorists - The Great Courses Daily News [Last Updated On: May 7th, 2020] [Originally Added On: May 7th, 2020]
- Why Self-Awareness and Communication Are Key for Self-Taught Players and Luthiers - Premier Guitar [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- Nine graduates head off to continue their higher educational pursuits - Nevada Today [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- 'The Theory of Everything' by Wolfram Gets Criticized by Physicists - Interesting Engineering [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- Cliff's Edge -- The Past Hypothesis - Adventist Review [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- Researchers Have Found a New Way to Convert Waste Heat Into Electricity to Power Small Devices - SciTechDaily [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- Quantum Computing Market New Technology Innovations, Advancements and Global Development Analysis 2020 to 2025 - Cole of Duty [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- Physicist Brian Greene on learning to focus on the here and now - KCRW [Last Updated On: May 10th, 2020] [Originally Added On: May 10th, 2020]
- OK, WTF Are Virtual Particles and Do They Actually Exist? - VICE [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Is the Big Bang in crisis? | Astronomy.com - Astronomy Magazine [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Raytheon Technologies Board of Directors to Take Voluntary Compensation Reduction - PRNewswire [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- What part of 'public' does PSC not get? - The Bozeman Daily Chronicle [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Exploring new tools in string theory - Space.com [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- The Era of Anomalies - Physics [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Registration Open for Inaugural IEEE International Conference on Quantum Computing and Engineering (QCE20) - thepress.net [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Exploring the quantum field, from the sun's core to the Big Bang - MIT News [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- The strange link between the human mind and quantum physics [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- quantum mechanics | Definition, Development, & Equations ... [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Quantum Physics Introduction Made Simple for Beginners [Last Updated On: May 15th, 2020] [Originally Added On: May 15th, 2020]
- Company Hopes to Have Carbon Nanotube COVID-19 Detector Available in June - SciTechDaily [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- The world is not as real as we think. - Patheos [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- Armin Strom Discusses Resonance With PhD Of Quantum Physics And Watch Collector In An Easy-To-Understand Way (Video) - Quill & Pad [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- Teaching the next generation of quantum scientists | Harvard John A. Paulson School of Engineering and Applied Sciences - Harvard School of... [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- Nasa discovers parallel universe where time runs backwards? Know the truth - Business Standard [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- Physicists Just Built The First Working Prototype Of A 'Quantum Radar' - ScienceAlert [Last Updated On: May 23rd, 2020] [Originally Added On: May 23rd, 2020]
- Next-Gen Laser Beams With Up to 10 Petawatts of Power Will Usher In New Era of Relativistic Plasmas Research - SciTechDaily [Last Updated On: May 26th, 2020] [Originally Added On: May 26th, 2020]
- What does the Tenet title mean? Quantum mechanics and Einsteins theory - Explica [Last Updated On: May 26th, 2020] [Originally Added On: May 26th, 2020]
- Looking up: UFO occupants and the legacy of language - Roswell Daily Record [Last Updated On: May 26th, 2020] [Originally Added On: May 26th, 2020]
- This is the light they have discovered and according to scientists it should not exist - Checkersaga [Last Updated On: June 2nd, 2020] [Originally Added On: June 2nd, 2020]
- MIT Student Probing Reality Through Physics, Philosophy and Writing - SciTechDaily [Last Updated On: June 2nd, 2020] [Originally Added On: June 2nd, 2020]
- David Baddiel: Kids have a better sense of humour than they used to' - The Guardian [Last Updated On: June 2nd, 2020] [Originally Added On: June 2nd, 2020]
- Some Information Regarding Medical Physics - - KUSI [Last Updated On: June 2nd, 2020] [Originally Added On: June 2nd, 2020]
- Francesca Vidotto: The Quantum Properties of Space-Time - JSTOR Daily [Last Updated On: June 2nd, 2020] [Originally Added On: June 2nd, 2020]
- These 8 Books Have the Power to Change Your Perspective on Life - Morocco World News [Last Updated On: June 8th, 2020] [Originally Added On: June 8th, 2020]
- Could Every Electron in the Universe Be the Same One? - Interesting Engineering [Last Updated On: June 8th, 2020] [Originally Added On: June 8th, 2020]
- Armijo: The absolute power of love | VailDaily.com - Vail Daily News [Last Updated On: June 8th, 2020] [Originally Added On: June 8th, 2020]
- Scientists predicted that the coronavirus death rate would fall over time, but instead it doubled. Here's why - Business Insider India [Last Updated On: June 13th, 2020] [Originally Added On: June 13th, 2020]
- Sussex Uni physicist creates the fifth state of matter whilst working from home - The Tab [Last Updated On: June 13th, 2020] [Originally Added On: June 13th, 2020]
- Beware of 'Theories of Everything' - Scientific American [Last Updated On: June 13th, 2020] [Originally Added On: June 13th, 2020]
- Duckworth on Education: The Feynman Technique - EMSWorld [Last Updated On: June 13th, 2020] [Originally Added On: June 13th, 2020]
- Scientists Discover Quantum Matter for the First Time in Space - Beebom [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- Physicists May Have Solved Long-Standing Mystery of Matter and Antimatter - SciTechDaily [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- Louis Broglie and the Idea of Wave-Particle Duality - Interesting Engineering [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- Letter reveals the quirky side of Albert Einstein - Chile News | Breaking News, Views, Analysis - The Santiago Times [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- Exploring the Quantum Field, From the Suns Core to the Big Bang at MIT - SciTechDaily [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- 10 of the best non-fiction science books to read right now - New Scientist [Last Updated On: June 14th, 2020] [Originally Added On: June 14th, 2020]
- Quantum material research connecting physicists in Hong Kong, Beijing and Shanghai facilitates discovery of better materials that benefit our society... [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- Flattening The Complexity Of Quantum Circuits - Asian Scientist Magazine [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- Borrowing from robotics, scientists automate mapping of quantum systems - News - The University of Sydney [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- Weird green glow spotted in atmosphere of Mars - Space.com [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- Why Gravity Is Not Like the Other Forces - Quanta Magazine [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- Cedar Hill grad pivots from science to law, determined to help others - The Dallas Morning News [Last Updated On: June 16th, 2020] [Originally Added On: June 16th, 2020]
- The stories a muon could tell - Symmetry magazine [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- In the atmosphere of Mars, a green glow offers scientists hints for future visits - NBCNews.com [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- Birdsong offers clues to the workings of short-term memory - AroundtheO [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- Restructuring cybersecurity with the power of quantum - TechRadar [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- Researchers Use Richard Feynman's Ideas to Develop a Working 'Theory of Everything' - Interesting Engineering [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- Nano-motor of just 16 atoms runs at the boundary of quantum physics - New Atlas [Last Updated On: June 18th, 2020] [Originally Added On: June 18th, 2020]
- 'Everything was centered around Sara, he was lost': Abhishek Kapoor on Sushant Singh Rajput after 'Kedarnath' - DNA India [Last Updated On: June 21st, 2020] [Originally Added On: June 21st, 2020]
- Physicists have proposed a new theory for Bose-Einstein condensates - Tech Explorist [Last Updated On: June 21st, 2020] [Originally Added On: June 21st, 2020]
- 8.13 and 8.14: Physics Junior Lab - MIT Technology Review [Last Updated On: June 21st, 2020] [Originally Added On: June 21st, 2020]
- The Period of the Universe's Clock - Physics [Last Updated On: June 21st, 2020] [Originally Added On: June 21st, 2020]
- If Wormholes Are Actually Going to Work, They'll Need to Look Weird - Yahoo! Voices [Last Updated On: June 25th, 2020] [Originally Added On: June 25th, 2020]
- At Long Last: An Answer to the Mystery Surrounding Matter and Antimatter - SciTechDaily [Last Updated On: June 25th, 2020] [Originally Added On: June 25th, 2020]
- Lost and found in French translation - The Guardian [Last Updated On: June 25th, 2020] [Originally Added On: June 25th, 2020]
- Do we need a 'Quantum Generation'? | TheHill - The Hill [Last Updated On: June 25th, 2020] [Originally Added On: June 25th, 2020]