Geometry of quantum correlations in space-time

Zhao, Zhikuan; Pisarczyk, Robert; Thompson, Jayne; Gu, Mile; Vedral, Vlatko; Fitzsimons, Joseph F.

doi:10.1103/physreva.98.052312

Cited by 38 publications

(50 citation statements)

References 24 publications

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“…Thus it is an invalid spatial covariance matrix. This illustrates how the covariance statistics for spatial and temporal matrices are different, just as Pauli correlations in spatial and temporal cases are different [25,34], which makes the study of temporal statistics particularly interesting.…”

Section: Similarity and Difference Of Temporal And Spatial Correlationsmentioning

confidence: 97%

“…The pseudo-density matrix formulation [16,[25][26][27][28][29]] is a finite-dimensional quantum-mechanical formalism which aims to treat space and time on an equal footing via unifying spatial and temporal correlations. Among all indefinite causal structures, only the pseudo-density matrix assumes a single Hilbert space for each spacetime event while all the others use double Hilbert spaces, e.g.…”

Section: Revisedmentioning

confidence: 99%

“…Then we conclude that the temporal covariance matrix is equal to the spatial covariance matrix under the partial transpose and the high temperature approximation. This can be understood as a continuous-variable analogue on temporal and spatial correlations of bipartite pseudo-density matrices for the qubit case [25]. Note that taking the partial trace of a two-qubit maximally entangled state…”

Section: Similarity and Difference Of Temporal And Spatial Correlationsmentioning

confidence: 99%

“…That is the basic principle for the formalism. In [25], they showed a symmetry between spatial correlations and temporal correlations in bipartite pseudo-density matrix; that is, the sets of all possible bipartite spatial correlations and certain temporal correlations flip into each other from the á ñ -á ñ XX ZZ plane. This shows a relationship as well as difference of spatial and temporal correlations.…”

Section: A Few Comments On Pseudo-density Matrix Formulationmentioning

confidence: 99%

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Different instances of time as different quantum modes: quantum states across space-time for continuous variables

2020

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Space-time is one of the most essential, yet most mysterious concepts in physics. In quantum mechanics it is common to understand time as a marker of instances of evolution and define states around all the space but at one time; while in general relativity space-time is taken as a combinator, curved around mass. Here we present a unified approach on both space and time in quantum theory, and build quantum states across spacetime instead of only on spatial slices. We no longer distinguish measurements on the same system at different times with measurements on different systems at one time and construct spacetime states upon these measurement statistics. As a first step towards nonrelativistic quantum field theory, we consider how to approach this in the continuous-variable multimode regime. We propose six possible definitions for spacetime states in continuous variables, based on four different measurement processes: quadratures, displaced parity operators, position measurements and weak measurements. The basic idea is to treat different instances of time as different quantum modes. They are motivated by the pseudo-density matrix formulation among indefinite causal structures and the path integral formalism. We show that these definitions lead to desirable properties, and raise the differences and similarities between spatial and temporal correlations. An experimental proposal for tomography is presented, construing the operational meaning of the spacetime states. REVISEDThe pseudo-density matrix formulation [16,[25][26][27][28][29]] is a finite-dimensional quantum-mechanical formalism which aims to treat space and time on an equal footing via unifying spatial and temporal correlations. Among all indefinite causal structures, only the pseudo-density matrix assumes a single Hilbert space for each spacetime event while all the others use double Hilbert spaces, e.g. for inputs and outputs in process matrices. As a price to pay, pseudo-density matrices may not be positive semi-definite. In general, this formulation defines an event via making a measurement for a single qubit at one time and is built upon correlations from measurement results of different events on arbitrary qubits at arbitrary times. By making a tensor product of different event Hilbert 8 Note that a continuous-variable version of process matrices defined e.g. in [10], posing a challenge for treating field theory scenarios with such formulations.

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Section: Similarity and Difference Of Temporal And Spatial Correlationsmentioning

confidence: 97%

Section: Revisedmentioning

confidence: 99%

Section: Similarity and Difference Of Temporal And Spatial Correlationsmentioning

confidence: 99%

Section: A Few Comments On Pseudo-density Matrix Formulationmentioning

confidence: 99%

See 2 more Smart Citations

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

2020

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“…[5]). This triggered research on the question which temporal correlations can be realized within quantum mechanics [6][7][8][9][10]. For the spatial scenario, i.e.…”

Section: Introductionmentioning

confidence: 99%

Genuine temporal correlations can certify the quantum dimension

et al. 2020

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Temporal correlations in quantum mechanics are the origin of several non-classical phenomena, but they depend on the dimension of the underlying quantum system. This allows one to use such correlations for the certification of a minimal Hilbert space dimension. Here we provide a theoretical proposal and an experimental implementation of a device-independent dimension test, using temporal correlations observed on a single trapped 171 Yb + ion. Our test goes beyond the prepare-and-measure scheme of previous approaches, demonstrating the advantage of genuine temporal correlations.

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General covariance for quantum states over time

Fullwood

2024

Lett Math Phys

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Geometry of quantum correlations in space-time

Cited by 38 publications

References 24 publications

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Different instances of time as different quantum modes: quantum states across space-time for continuous variables

Genuine temporal correlations can certify the quantum dimension

General covariance for quantum states over time

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