Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2109.06190 · Physical review. D/Physical review. D.

Geometric phases distinguish entangled states in wormhole quantum mechanics

Flavio S. Nogueira, Souvik Banerjee, Moritz Dorband, René Meyer, Jeroen van den Brink, Johanna Erdmenger B

Published Apr 19, 2022• 20 citations
arXivHTMLPDF

Abstract

We establish a relation between entanglement in simple quantum mechanical qubit systems and in wormhole physics as considered in the context of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence. We show that in both cases, states with the same entanglement structure, indistinguishable by any local measurement, nevertheless are characterized by a different Berry phase. This feature is experimentally accessible in coupled qubit systems where states with different Berry phase are related by unitary transformations. In the wormhole case, these transformations are identified with a time evolution of one of the two throats.

DOI
10.1103/physrevd.105.l081903

Related papers

A thermofield-double model of Uhlmann’s anholonomy

Péter Lévay, Csaba Velich

A bstract Recently it has been shown that certain aspects of changing states in holography can be studied by considering the Berry Phase properties of simple entangled qubit systems. In this context the term wormhole quantum mechanics has been coined. In particular an interesting interplay between entanglement and Berry Phase was found. Here we present a mixed state generalization of this connection illustrated for a simple parametrized family of entangled quantum systems in the thermofield double state. Our state is purifying two subsystems dubbed the left and the right ones and evolves in a purely geometric manner based on a parallel transport condition due to Uhlmann. We show that different interpretations of this evolution relative to observers either coupled to the left or to the right exist. When the evolution on say the left manifests itself via local operations of non-unitary optimal measurements then on the right the evolutionary steps are organized into a sequence of unitary operations of a holonomic quantum computation. For closed curves featuring geodesic segments with respect to the Bures metric we calculate the anholonomy of Uhlmann’s connection which turns out to be related to the one of higher dimensional instantons. The initial and final states are having the same entanglement but different Uhlman’s Phase. We show that by conducting an interference experiment one can observe the physical effects of the resulting anholonomic quantum computation. The consequences of our findings in the holographic context are discussed.

Journal of High Energy Physics•Mar 24, 2026•0 citations

Geometric Phases in Open Quantum Systems: Analysis and Applications

Ludmila Viotti

This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and environmentally-induced dissipative effects, and the concept known as geometric phases. The first mention of such an object in the context of quantum mechanics goes back to the seminal work by Berry. He demonstrated that the phase acquired by an eigenstate of a time-dependent Hamiltonian in an adiabatic cycle consists of two distinct contributions: one termed 'geometric' and the other known as the dynamical phase. Since Berry's work, the notion of geometric phase has been extended far beyond the original context, encompassing definitions applicable to arbitrary unitary evolutions. These geometric phases naturally arise in the geometric description of Hilbert space, where they manifest as holonomies and possess significance in the fundamental understanding of quantum mechanics and its mathematical framework, and in explaining various physical phenomena, including the Fractional Hall Effect. Moreover, from a modern perspective, geometric phases hold promise for practical applications, such as constructing geometric gates for quantum information processing and storage. However, in practice, a pure state of a quantum system is an idealized concept, and every experimental or real-world implementation must account for the presence of an environment that interacts with the observed system. This interaction necessitates a description in terms of mixed states and non-unitary evolutions. The definition of a geometric phase applicable in such scenarios remains an open problem, giving rise to multiple proposed solutions. Consequently, characterizing these geometric phases encompase motivations from fundamental aspects of quantum mechanics to technological applications.

arXiv:2307.03825•Jul 7, 2023•0 citations

C\ast-geometric phase for mixed states: entanglement, decoherence and spin system

José Lages, David Viennot

We study a kind of geometric phases for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C\ast-module structure. We show that the system presents from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.

•Nov 29, 2017•0 citations

C*-geometric phase for mixed states: entanglement, decoherence and the spin system

David Viennot, José Lages

We study a kind of geometric phase for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C *-module structure. We show that the system presents, from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.

arXiv:1207.7340•Journal of Physics A Mathematical and Theoretical•Aug 22, 2012•3 citations

Phase dynamics of entangled qubits

P. Milman

We make a geometric study of the phases acquired by a general, pure bipartite two-level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\ensuremath{\pi}$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n\ensuremath{\pi}$ global phase. They can be identified as dynamical, geometrical, and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory, and the results obtained are shown to be in connection to those on mixed state phases.

arXiv:quant-ph/0608114•Physical Review A•Jun 30, 2006•40 citations

Mixed State Geometric Phases, Entangled Systems, and Local Unitary Transformations

Marie Ericsson, Arun Kumar Pati, Erik Sjöqvist +2 more

The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.

arXiv:quant-ph/0206063•Physical Review Letters•Aug 28, 2003•69 citations
We establish a relation between entanglement in simple quantum mechanical qubit systems and in wormhole physics as considered in the context of the AdS/CFT\mathrm{AdS}/\mathrm{CFT}AdS/CFT correspondence. We show that in both cases, states with the same entanglement structure, indistinguishable by any local measurement, nevertheless are characterized by a different Berry phase. This feature is experimentally accessible in coupled qubit systems where states with different Berry phase are related by unitary transformations. In the wormhole case, these transformations are identified with a time evolution of one of the two throats.
A bstract Recently it has been shown that certain aspects of changing states in holography can be studied by considering the Berry Phase properties of simple entangled qubit systems. In this context the term wormhole quantum mechanics has been coined. In particular an interesting interplay between entanglement and Berry Phase was found. Here we present a mixed state generalization of this connection illustrated for a simple parametrized family of entangled quantum systems in the thermofield double state. Our state is purifying two subsystems dubbed the left and the right ones and evolves in a purely geometric manner based on a parallel transport condition due to Uhlmann. We show that different interpretations of this evolution relative to observers either coupled to the left or to the right exist. When the evolution on say the left manifests itself via local operations of non-unitary optimal measurements then on the right the evolutionary steps are organized into a sequence of unitary operations of a holonomic quantum computation. For closed curves featuring geodesic segments with respect to the Bures metric we calculate the anholonomy of Uhlmann’s connection which turns out to be related to the one of higher dimensional instantons. The initial and final states are having the same entanglement but different Uhlman’s Phase. We show that by conducting an interference experiment one can observe the physical effects of the resulting anholonomic quantum computation. The consequences of our findings in the holographic context are discussed.
This thesis consists of several studies performed over different few-dof quantum systems exposed to the effect of an uncontrolled environment. The primary focus of the work is to explore the relation between decoherence and environmentally-induced dissipative effects, and the concept known as geometric phases. The first mention of such an object in the context of quantum mechanics goes back to the seminal work by Berry. He demonstrated that the phase acquired by an eigenstate of a time-dependent Hamiltonian in an adiabatic cycle consists of two distinct contributions: one termed 'geometric' and the other known as the dynamical phase. Since Berry's work, the notion of geometric phase has been extended far beyond the original context, encompassing definitions applicable to arbitrary unitary evolutions. These geometric phases naturally arise in the geometric description of Hilbert space, where they manifest as holonomies and possess significance in the fundamental understanding of quantum mechanics and its mathematical framework, and in explaining various physical phenomena, including the Fractional Hall Effect. Moreover, from a modern perspective, geometric phases hold promise for practical applications, such as constructing geometric gates for quantum information processing and storage. However, in practice, a pure state of a quantum system is an idealized concept, and every experimental or real-world implementation must account for the presence of an environment that interacts with the observed system. This interaction necessitates a description in terms of mixed states and non-unitary evolutions. The definition of a geometric phase applicable in such scenarios remains an open problem, giving rise to multiple proposed solutions. Consequently, characterizing these geometric phases encompase motivations from fundamental aspects of quantum mechanics to technological applications.
We study a kind of geometric phases for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C\ast-module structure. We show that the system presents from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.
We study a kind of geometric phase for entangled quantum systems, and particularly a spin driven by a magnetic field and entangled with another spin. The new kind of geometric phase is based on an analogy between open quantum systems and dissipative quantum systems which uses a C *-module structure. We show that the system presents, from the viewpoint of their geometric phases, two behaviours. The first one is identical to the behaviour of an isolated spin driven by a magnetic field, as the problem originally treated by Berry. The second one is specific to the decoherence process. The gauge structures induced by these geometric phases are then similar to a magnetic monopole gauge structure for the first case, and can be viewed as a kind of instanton gauge structure for the second case. We study the role of these geometric phases in the evolution of a mixed state, particularly by focusing on the evolution of the density matrix coherence. We investigate also the relation between the geometric phase of the mixed state of one of the entangled systems and the geometric phase of the bipartite system.
We make a geometric study of the phases acquired by a general, pure bipartite two-level system after a cyclic unitary evolution. The geometric representation of the two particle Hilbert space makes use of Hopf fibrations. It allows for a simple description of the dynamics of the entangled state's phase during the whole evolution. The global phase after a cyclic evolution is always an entire multiple of $\ensuremath{\pi}$ for all bipartite states, a result that does not depend on the degree of entanglement. There are three different types of phases combining themselves so as to result in the $n\ensuremath{\pi}$ global phase. They can be identified as dynamical, geometrical, and topological. Each one of them can be easily identified using the presented geometric description. The interplay between them depends on the initial state and on its trajectory, and the results obtained are shown to be in connection to those on mixed state phases.
The geometric phase for a pure quantal state undergoing an arbitrary evolution is a "memory" of the geometry of the path in the projective Hilbert space of the system. We find that Uhlmann's geometric phase for a mixed quantal state undergoing unitary evolution depends not only on the geometry of the path of the system alone but also on a constrained bilocal unitary evolution of the purified entangled state. We analyze this in general, illustrate it for the qubit case, and propose an experiment to test this effect. We also show that the mixed state geometric phase proposed recently in the context of interferometry requires unilocal transformations and is therefore essentially a property of the system alone.