# Noncausal Page-Wootters circuits

@article{Baumann2021NoncausalPC, title={Noncausal Page-Wootters circuits}, author={Veronika Baumann and Marius Krumm and Philippe Allard Gu{\'e}rin and vCaslav Brukner}, journal={Physical Review Research}, year={2021} }

Veronika Baumann, 2, 3, ∗ Marius Krumm, 2, ∗ Philippe Allard Guérin, 2, 4 and Časlav Brukner 2 Faculty of Physics, University of Vienna, Boltzmanngasse 5, 1090 Vienna, Austria Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria Faculty of Informatics, Università della Svizzera italiana, Via G. Buffi 13, CH-6900 Lugano, Switzerland Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, Ontario, N2L…

## 7 Citations

### Quantum Supermaps are Characterized by Locality

- Computer Science
- 2022

We prove that the sequential and parallel composition rules for quantum channels are all that need to be referenced to axiomatise quantum supermaps from ﬁrst principles. To do so we provide a simple…

### Non-inertial quantum clock frames lead to non-Hermitian dynamics

- PhysicsCommunications Physics
- 2022

The operational approach to time is a cornerstone of relativistic theories, as evidenced by the notion of proper time. In standard quantum mechanics, however, time is an external parameter. Recently,…

### $SU(\infty)$-QGR: Emergence of Gravity in an Infinitely Divisible Quantum Universe

- Physics
- 2023

SUp8q-QGR is a foundationally quantum approach to gravity. It assumes that Hilbert spaces of the Universe as a whole and its subsystems represent the symmetry group SUp8q. The Universe is divided to…

### Flow of time during energy measurements and the resulting time-energy uncertainty relations

- PhysicsQuantum
- 2022

Uncertainty relations play a crucial role in quantum mechanics. Well-defined methods exist for the derivation of such uncertainties for pairs of observables. Other approaches also allow the…

### A model of Non-Relativistic Quantum Spacetime

- Physics
- 2022

We consider a global quantum system (the “Universe”) satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a…

### A model of quantum spacetime

- Physics
- 2022

We consider a global quantum system (the “Universe”) satisfying a double constraint, both on total energy and total momentum. Generalizing the Page and Wootters quantum clock formalism, we provide a…

### Internal quantum reference frames for finite Abelian groups

- MathematicsJournal of Mathematical Physics
- 2022

Employing internal quantum systems as reference frames is a crucial concept in quantum gravity, gauge theories, and quantum foundations whenever external relata are unavailable. In this work, we give…

## References

SHOWING 1-10 OF 60 REFERENCES

### Quantum networks: General theory and applications

- Computer Science
- 2011

This work presents a general mathematical framework to deal with Quantum Networks, i.e. networks resulting from the interconnection of elementary quantum circuits, that allows one to efficiently represent any given Quantum Network in terms of a single positive operator.

### Clocks in Feynman's computer and Kitaev's local Hamiltonian: Bias, gaps, idling, and pulse tuning

- PhysicsPhysical Review A
- 2018

We present a collection of results about the clock in Feynman's computer construction and Kitaev's Local Hamiltonian problem. First, by analyzing the spectra of quantum walks on a line with varying…

### Theoretical framework for quantum networks

- Physics, Computer Science
- 2009

We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, such…

### Experimental superposition of orders of quantum gates

- PhysicsNature Communications
- 2015

This work experimentally demonstrates the creation of the required superposition of gate orders by using additional degrees of freedom of the photons encoding qubits, which could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer.

### Indefinite Causal Order in a Quantum Switch.

- Physics, PhilosophyPhysical review letters
- 2018

A photonic quantum switch is realized, where two operations A and B act in a quantum superposition of their two possible orders, on the transverse spatial mode of the photons; polarization coherently controls their order.

### Causal Structures and the Classification of Higher Order Quantum Computations

- Computer Science
- 2017

A formal language is provided to form all possible types of transformations, and it is used to prove general structure theorems for transformations in the hierarchy, and a mathematical characterisation of the set of maps from combs to combs is provided, hinting at a route for the completeCharacterisation of maps in the Hierarchy.

### Experimental Quantum Switching for Exponentially Superior Quantum Communication Complexity.

- Computer Science, PhysicsPhysical review letters
- 2019

The results elucidate the crucial role of the coherence of communication direction in achieving the exponential separation for the one-way processing task, and open a new path for experimentally exploring the fundamentals and applications of advanced features of indefinite causal structures.

### Consequences of preserving reversibility in quantum superchannels

- PhysicsQuantum
- 2021

This paper provides a mathematical characterization for pure superchannels with two slots (also known as bipartite pure processes), which are superch channels preserving the reversibility of quantum operations, and shows that the reversible preserving condition restricts all pure super channels withTwo slots to be either a causally ordered quantum circuit only consisting of unitary operations or a coherent superposition of two pure causally order circuits.

### Increasing communication capacity via superposition of order

- Computer Science
- 2020

This work shows that by combining a depolarising channel with another channel in an indefinite causal order---that is, when there is superposition of the order that these two channels were applied---it becomes possible to transmit significant information.

### Quantum-Mechanical Computers

- Art
- 1995

E very two years for the past 50, computers have become twice as fast while their components have become half as big. Circuits now contain wires and transistors that measure only one hundredth of a…