Superposition of macroscopically distinct states in quantum many-body systems

We consider a coarse‐grained quasi joint probability density Ξ of two macroscopic observables. If a quantum many‐body state has a superposition of macroscopically distinct states, the structure of the superposition can be visualized by plotting Ξ for appropriate macroscopic observables. For example, the ground state of the XY model, that of the Heisenberg antiferromagnet, and a state in Grover's quantum search algorithm, which have superpositions of macroscopically distinct states, can be visualized. Like the Wigner distribution function, Ξ can take negative values. However, if the characteristic width W of the coarse‐graining is sufficiently large, Ξ becomes nonnegative. We study a sufficient magnitude of such W. We see that W = O(N) is not sufficient, but W = O(N) would be sufficient, where N is the size of the system.We consider a coarse‐grained quasi joint probability density Ξ of two macroscopic observables. If a quantum many‐body state has a superposition of macroscopically distinct states, the structure of the superposition can be visualized by plotting Ξ for appropriate macroscopic observables. For example, the ground state of the XY model, that of the Heisenberg antiferromagnet, and a state in Grover's quantum search algorithm, which have superpositions of macroscopically distinct states, can be visualized. Like the Wigner distribution function, Ξ can take negative values. However, if the characteristic width W of the coarse‐graining is sufficiently large, Ξ becomes nonnegative. We study a sufficient magnitude of such W. We see that W = O(N) is not sufficient, but W = O(N) would be sufficient, where N is the size of the system.

AIP conference proceedingsJan 1, 20070 citations

Macroscopic Quantum Superpositions in Many-Particle Systems

박채연

Jan 1, 20170 citations

Visualization of superposition of macroscopically distinct states

Tomoyuki Morimae, Akira Shimizu

We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more Hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the $XY$ model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes nonnegative (hence, becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.We propose a method of visualizing superpositions of macroscopically distinct states in many-body pure states. We introduce a visualization function, which is a coarse-grained quasi joint probability density for two or more Hermitian additive operators. If a state contains superpositions of macroscopically distinct states, one can visualize them by plotting the visualization function for appropriately taken operators. We also explain how to efficiently find appropriate operators for a given state. As examples, we visualize four states containing superpositions of macroscopically distinct states: the ground state of the $XY$ model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes nonnegative (hence, becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.

arXiv:quant-ph/0608196Physical Review ANov 22, 20069 citations

Macroscopic Superposition States in Isolated Quantum Systems

Roman V. Buniy, Stephen D. H. Hsu

arXiv:2011.11661Foundations of PhysicsJul 31, 20215 citations

Measuring the size of a quantum superposition of many-body states

Florian Marquardt, Benjamin Abel, Jan von Delft

We propose a measure for the ``size'' of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states, and we find the size of this superposition to be surprisingly small.We propose a measure for the ``size'' of a quantum superposition of two many-body states with (supposedly) macroscopically distinct properties by counting how many single-particle operations are needed to map one state onto the other. This definition gives sensible results for simple, analytically tractable cases and is consistent with a previous definition restricted to Greenberger-Horne-Zeilinger-like states. We apply our measure to the experimentally relevant, nontrivial example of a superconducting three-junction flux qubit put into a superposition of left- and right-circulating supercurrent states, and we find the size of this superposition to be surprisingly small.

arXiv:quant-ph/0609007Physical Review AJul 18, 200882 citations

XY

model, that of the Heisenberg antiferromagnet, a state in Shor's factoring algorithm, and a state in Grover's quantum search algorithm. Although the visualization function can take negative values, it becomes nonnegative (hence, becomes a coarse-grained joint probability density) if the characteristic width of the coarse-graining function used in the visualization function is sufficiently large.