Learning quantum states of continuous variable systems
Quantum state tomography, aimed at deriving a classical description of an unknown state from measurement data, is a fundamental task in quantum physics. In this work, we analyse the ultimate achievable performance of tomography of continuous-variable systems, such as bosonic and quantum optical syst...
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Main Authors | , , , , , , , |
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Format | Journal Article |
Language | English |
Published |
02.05.2024
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Subjects | |
Online Access | Get full text |
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Summary: | Quantum state tomography, aimed at deriving a classical description of an
unknown state from measurement data, is a fundamental task in quantum physics.
In this work, we analyse the ultimate achievable performance of tomography of
continuous-variable systems, such as bosonic and quantum optical systems. We
prove that tomography of these systems is extremely inefficient in terms of
time resources, much more so than tomography of finite-dimensional systems: not
only does the minimum number of state copies needed for tomography scale
exponentially with the number of modes, but it also exhibits a dramatic scaling
with the trace-distance error, even for low-energy states, in stark contrast
with the finite-dimensional case. On a more positive note, we prove that
tomography of Gaussian states is efficient. To accomplish this, we answer a
fundamental question for the field of continuous-variable quantum information:
if we know with a certain error the first and second moments of an unknown
Gaussian state, what is the resulting trace-distance error that we make on the
state? Lastly, we demonstrate that tomography of non-Gaussian states prepared
through Gaussian unitaries and a few local non-Gaussian evolutions is efficient
and experimentally feasible. |
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DOI: | 10.48550/arxiv.2405.01431 |