# Quantum information science: tools and applications for fundamental physics

### Abstract

Computer science has led to a new paradigm in physics, where one understands the laws of nature in terms of the manipulation of information. Computer science also has tools which can be used to analyse how efficient these manipulations are. In the last two decades, this has led to fundamental breakthroughs in our understanding of quantum mechanics, and we now know that quantum computers can be much faster than classical computers, and that quantum particles can be used to transmit information privately, in a way that is impossible in the classical world. The proposed research will apply tools from computer science to other areas of physics, in a way which aims to deepen our understanding of fundamental laws. The mathematical tools from information theory which we will use are very general since any theory can be thought of as evolution and manipulation of information, and so they can be applied to many different areas of physics.

One example where these tools can be applied, is in the field of thermodynamics. The laws of thermodynamics govern much of the world around us - they tell us that a hot cup of tea in a cold room will cool down rather than heat up; they tell us that unless we are vigilant, our houses will become untidy rather than spontaneously tidy;. But the laws of thermodynamics only apply to large objects, when many particles are involved. Can the laws of thermodynamics be applied to small systems, such as the kind of microscopic motors currently been fabricated in labs? Or perhaps even quantum systems? Tools from information theory can be used to do so, and this research aims to construct laws of thermodynamics for quantum systems. What's more, it appears that nature imposes fundamental limitations on microscopic devices and heat engines. A quantum heat engines will sometimes fail. We cannot extract energy optimally from a quantum system. This means that the present laws of thermodynamics are fundamentally incorrect if applied to small systems, and many of the standard laws need to be modified. Another example is that our current laws of thermodynamics tell us that thermodynamical processes can be made reversible: a fridge is just a heat pump in reverse. But at the nano-scale, reversibility breaks down. The results if this research have wide applications in small systems, from nano-scale devices, to biological motors, to quantum technologies such as quantum computers, and to nano-robots drinking molecular amounts of tea.

These same mathematical tools are very general and can be applied in other contexts, for example, to better understand black holes. This is perhaps not so surprising, since one of the key properties of black holes is that they behave like thermodynamical objects with a temperature and entropy. In fact, the black hole information problem, posed by Hawking, is precisely about the way information behaves. We can also apply techniques from information theory to better understand fundamental features of quantum theory, and we can ask questions such as why quantum theory has to be the way it is. For example, recently, we've used tools from computer science to examine links between Heisenberg's uncertainty principle (which says that you can never know a particle's position and momentum at the same time), and quantum non-locality (the strong correlations which occur when you measure entangled particles). These two fundamental features had been considered separate and distinct concepts. But using tools from computer science, one sees that they are inextricably linked. It is the uncertainty principle which determines exactly the strength of quantum nonlocality.

One example where these tools can be applied, is in the field of thermodynamics. The laws of thermodynamics govern much of the world around us - they tell us that a hot cup of tea in a cold room will cool down rather than heat up; they tell us that unless we are vigilant, our houses will become untidy rather than spontaneously tidy;. But the laws of thermodynamics only apply to large objects, when many particles are involved. Can the laws of thermodynamics be applied to small systems, such as the kind of microscopic motors currently been fabricated in labs? Or perhaps even quantum systems? Tools from information theory can be used to do so, and this research aims to construct laws of thermodynamics for quantum systems. What's more, it appears that nature imposes fundamental limitations on microscopic devices and heat engines. A quantum heat engines will sometimes fail. We cannot extract energy optimally from a quantum system. This means that the present laws of thermodynamics are fundamentally incorrect if applied to small systems, and many of the standard laws need to be modified. Another example is that our current laws of thermodynamics tell us that thermodynamical processes can be made reversible: a fridge is just a heat pump in reverse. But at the nano-scale, reversibility breaks down. The results if this research have wide applications in small systems, from nano-scale devices, to biological motors, to quantum technologies such as quantum computers, and to nano-robots drinking molecular amounts of tea.

These same mathematical tools are very general and can be applied in other contexts, for example, to better understand black holes. This is perhaps not so surprising, since one of the key properties of black holes is that they behave like thermodynamical objects with a temperature and entropy. In fact, the black hole information problem, posed by Hawking, is precisely about the way information behaves. We can also apply techniques from information theory to better understand fundamental features of quantum theory, and we can ask questions such as why quantum theory has to be the way it is. For example, recently, we've used tools from computer science to examine links between Heisenberg's uncertainty principle (which says that you can never know a particle's position and momentum at the same time), and quantum non-locality (the strong correlations which occur when you measure entangled particles). These two fundamental features had been considered separate and distinct concepts. But using tools from computer science, one sees that they are inextricably linked. It is the uncertainty principle which determines exactly the strength of quantum nonlocality.

### Planned Impact

Research into the fundamentals of theoretical physics has the potential to radically reshape our world, both from a technological perspective, and through challenging our foundational assumptions. Much of the research based on quantum information theory is driven by the view that it will revolutionize technology and the way information is processed. One only needs to look at Claude Shannon and Alan Turing's seminal work on classical information theory and computing, to see the far reaching impact that quantum information theory and quantum computation is likely to have. Much of their initial work was abstract and theoretical when first formulated, but now underpins the information revolution -- driving everything from the internet, to mobile technologies, to super-computers at research institutions. In the future, we expect the sending, receiving, and processing of quantum information to become key drivers of technological change. The proposed research contributes to the advancement of quantum technologies and devices, including quantum computers, cryptographic systems, and micro-machines, bringing these technologies closer to reality.

It will also advance other areas of knowledge, including condensed matter physics, nano-technology, statistical mechanics, and thermodynamics. The latter is of particular importance: the potential to miniaturise devices to the nanoscale and into the quantum regime brings with it the potential to overcome many upcoming socio-economic challenges. In the case of thermodynamical devices, we are already at the stage where quantum effects are becoming increasingly important in micro-heat engines which have been constructed in the lab. The present research impacts such devices, including nanomachines such as Brownian rotors which have been constructed at the nano scale, and suffer from efficiency limitations which the PI recently demonstrated and which the present research hopes to explore further. It is widely believed that micro-machines and nanodevices will significantly reshape future technology, and the present research aims to improve their efficiency, and construct protocols and methods for their operation. The research can also be applied to understand the statistical mechanical properties of strongly correlated systems, which has application in spin-glasses, and substances with long range interactions, something which can advance material science, and has applications in condensed matter systems -- again, with potential technological applications.

The current research also aims to improve our understanding of quantum mechanics at the fundamental level. The potential impact for this part of the project is clearly long term, and more difficult to predict, as is often the case for more high risk theoretical work. At the same time, the potential for exciting breakthroughs (and hence, significant impact) is perhaps greatest.

Finally, the development of mathematical tools and building blocks of information theory, is likely to find application in a wide variety of applied mathematical research areas. The impact on industry or technology is likely to be long term and difficult to predict, but such mathematical tools tend to have very broad utility.

It will also advance other areas of knowledge, including condensed matter physics, nano-technology, statistical mechanics, and thermodynamics. The latter is of particular importance: the potential to miniaturise devices to the nanoscale and into the quantum regime brings with it the potential to overcome many upcoming socio-economic challenges. In the case of thermodynamical devices, we are already at the stage where quantum effects are becoming increasingly important in micro-heat engines which have been constructed in the lab. The present research impacts such devices, including nanomachines such as Brownian rotors which have been constructed at the nano scale, and suffer from efficiency limitations which the PI recently demonstrated and which the present research hopes to explore further. It is widely believed that micro-machines and nanodevices will significantly reshape future technology, and the present research aims to improve their efficiency, and construct protocols and methods for their operation. The research can also be applied to understand the statistical mechanical properties of strongly correlated systems, which has application in spin-glasses, and substances with long range interactions, something which can advance material science, and has applications in condensed matter systems -- again, with potential technological applications.

The current research also aims to improve our understanding of quantum mechanics at the fundamental level. The potential impact for this part of the project is clearly long term, and more difficult to predict, as is often the case for more high risk theoretical work. At the same time, the potential for exciting breakthroughs (and hence, significant impact) is perhaps greatest.

Finally, the development of mathematical tools and building blocks of information theory, is likely to find application in a wide variety of applied mathematical research areas. The impact on industry or technology is likely to be long term and difficult to predict, but such mathematical tools tend to have very broad utility.

### Organisations

- University College London, United Kingdom (Fellow, Lead Research Organisation)
- Princeton University, United States (Collaboration)
- California Institute of Technology, United States (Collaboration)
- Massachusetts Institute of Technology (Collaboration)
- Stanford University, United States (Collaboration)
- Simons Foundation (Collaboration)
- University of Gdansk, Poland (Project Partner)

## People |
## ORCID iD |

Jonathan Oppenheim (Principal Investigator / Fellow) |

Bandyopadhyay S
(2014)

*Publisher's Note: Conclusive exclusion of quantum states [Phys. Rev. A89, 022336 (2014)]*in Physical Review A
Bandyopadhyay S
(2014)

*Conclusive exclusion of quantum states*in Physical Review A
Brandão F
(2015)

*The second laws of quantum thermodynamics.*in Proceedings of the National Academy of Sciences of the United States of America
Brandão FG
(2015)

*Quantum Conditional Mutual Information, Reconstructed States, and State Redistribution.*in Physical review letters
Brandão FG
(2013)

*Resource theory of quantum states out of thermal equilibrium.*in Physical review letters
Cwiklinski P
(2015)

*Limitations on the Evolution of Quantum Coherences: Towards Fully Quantum Second Laws of Thermodynamics.*in Physical review letters
Faist P
(2015)

*The minimal work cost of information processing.*in Nature communications
Faist P
(2015)

*Gibbs-preserving maps outperform thermal operations in the quantum regime*in New Journal of Physics
Korzekwa K
(2016)

*The extraction of work from quantum coherence*in New Journal of Physics
Müller M
(2014)

*Hiding Information in Theories Beyond Quantum Mechanics, and It's Application to the Black Hole Information Problem*in Foundations of PhysicsDescription | It from Qubit |

Organisation | California Institute of Technology |

Country | United States of America |

Sector | Academic/University |

PI Contribution | Drafting of proposal and details of collaboration |

Collaborator Contribution | ibid |

Impact | schools, conferences, workshops, postdocs, forums |

Start Year | 2015 |

Description | It from Qubit |

Organisation | Massachusetts Institute of Technology (MIT) |

Country | United States of America |

Sector | Academic/University |

PI Contribution | Drafting of proposal and details of collaboration |

Collaborator Contribution | ibid |

Impact | schools, conferences, workshops, postdocs, forums |

Start Year | 2015 |

Description | It from Qubit |

Organisation | Princeton University |

Country | United States of America |

Sector | Academic/University |

PI Contribution | Drafting of proposal and details of collaboration |

Collaborator Contribution | ibid |

Impact | schools, conferences, workshops, postdocs, forums |

Start Year | 2015 |

Description | It from Qubit |

Organisation | Simons Foundation |

Country | United States of America |

Sector | Charity/Non Profit |

PI Contribution | Drafting of proposal and details of collaboration |

Collaborator Contribution | ibid |

Impact | schools, conferences, workshops, postdocs, forums |

Start Year | 2015 |

Description | It from Qubit |

Organisation | Stanford University |

Country | United States of America |

Sector | Academic/University |

PI Contribution | Drafting of proposal and details of collaboration |

Collaborator Contribution | ibid |

Impact | schools, conferences, workshops, postdocs, forums |

Start Year | 2015 |

Description | Cafe Scientifique |

Form Of Engagement Activity | A talk or presentation |

Part Of Official Scheme? | No |

Geographic Reach | Local |

Primary Audience | Public/other audiences |

Results and Impact | Cafe Scientifique |

Year(s) Of Engagement Activity | 2016 |

URL | https://www.facebook.com/events/1007914265913598/ |