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.

arXiv comment11 pages, 4 figures. Comments are welcome

References in corpus (39)

• Quantum entanglement
• Quantum information with continuous variables
• Gaussian Quantum Information
• Quantifying Coherence
• Quantifying Entanglement
• Quantum Coherence as a Resource
• Quantum Resource Theories
• The role of quantum information in thermodynamics --- a topical review
• Continuous variable quantum information: Gaussian states and beyond
• Quantum information with Gaussian states
• Quantum optics in the phase space - A tutorial on Gaussian states
• The resource theory of informational nonequilibrium in thermodynamics
• (Quantumness in the context of) Resource Theories
• Quantum fidelity for arbitrary Gaussian states
• Resource theory of quantum non-Gaussianity and Wigner negativity
• Reversible transformations from pure to mixed states, and the unique measure of information
• Quantum theory based on real numbers can be experimentally falsified
• An introductory review of the resource theory approach to thermodynamics
• Operational Resource Theory of Imaginarity
• Maximal Coherence and the Resource Theory of Purity
• Uhlmann fidelity between two-mode Gaussian states
• Fidelity for displaced squeezed states and the oscillator semigroup
• Quantifying the Imaginarity of Quantum Mechanics
• Quantifying coherence of Gaussian states
• Quantifying Coherence in Infinite Dimensional Systems
• Resource theory of imaginarity: Quantification and state conversion
• On nonlocality as a resource theory and nonlocality measures
• Resource theory of coherence based on positive-operator-valued measures
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Simulating realistic non-Gaussian state preparation
• Hiding and masking quantum information in complex and real quantum mechanics
• 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
• Distinguishing two single-mode Gaussian states by homodyne detection: An information-theoretic approach
• Operational quantification of continuous-variable quantum resources
• Multimode Bogoliubov transformation and Husimi's Q-function
• Generation of Coherence via Gaussian Measurements
• 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