Imaginarity of Gaussian states

Abstract

It has been a long-standing debate that why quantum mechanics uses complex numbers but not only real numbers. To address this topic, in recent years, the imaginarity theory has been developed in the way of quantum resource theory. However, the existing imaginarity theory mainly focuses on the quantum systems with finite dimensions. Gaussian states are widely used in many fields of quantum physics, but they are in the quantum systems with infinite dimensions. In this paper we establish a resource theory of imaginarity for bosonic Gaussian states. To do so, under the Fock basis, we determine the real Gaussian states and real Gaussian channels in terms of the means and covariance matrices of Gaussian states. Also, we provide two imaginary measures for Gaussian states based on the fidelity.

11 pages, 4 figures. Comments are welcome

References in corpus (6)

• Quantum information with Gaussian states
• Resource theory of imaginarity: Quantification and state conversion
• Cloning of Gaussian states by linear optics
• Bures distance as a measure of entanglement for symmetric two-mode Gaussian states
• Real quantum operations and state transformations
• Quantifying the phase of quantum states

Cited by in corpus (13)

• Quantifying the imaginarity of quantum states via Tsallis relative entropy
• Quantifying imaginarity in terms of pure-state imaginarity
• Coherence and imaginarity of quantum states
• Geometric-Like imaginarity: quantification and state conversion
• Expectation value dynamics within real Hilbert space quantum mechanics
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Quantifying the imaginarity via different distance measures
• One-shot manipulation of coherence in dynamic quantum resource theory
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Measure of set imaginarity
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• Experimental certification of the nonlocal advantages of quantum imaginarity
• Deformed angular momentum algebra within the real Hilbert space