Resource theory of imaginarity: Quantification and state conversion

Abstract

Complex numbers are widely used in both classical and quantum physics, and are indispensable components for describing quantum systems and their dynamical behavior. Recently, the resource theory of imaginarity has been introduced, allowing for a systematic study of complex numbers in quantum mechanics and quantum information theory. In this work we develop theoretical methods for the resource theory of imaginarity, motivated by recent progress within theories of entanglement and coherence. We investigate imaginarity quantification, focusing on the geometric imaginarity and the robustness of imaginarity, and apply these tools to the state conversion problem in imaginarity theory. Moreover, we analyze the complexity of real and general operations in optical experiments, focusing on the number of unfixed wave plates for their implementation. We also discuss the role of imaginarity for local state discrimination, proving that any pair of real orthogonal pure states can be discriminated via local real operations and classical communication. Our study reveals the significance of complex numbers in quantum physics, and proves that imaginarity is a resource in optical experiments.

arXiv comment13 pages, 2 figures. Accompanying article for arXiv:2007.14847

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Cited by in corpus (52)

• Operational Resource Theory of Imaginarity
• Experimental progress on quantum coherence: detection, quantification, and manipulation
• Catalysis of entanglement and other quantum resources
• Imaginarity-free quantum multiparameter estimation
• Unitary-invariant witnesses of quantum imaginarity
• Real quantum operations and state transformations
• Measures of imaginarity and quantum state order
• Resource Theory of Imaginarity: New Distributed Scenarios
• Imaginarity of Gaussian states
• Quantifying the imaginarity of quantum states via Tsallis relative entropy
• Is there a finite complete set of monotones in any quantum resource theory?
• Resource theory of causal connection
• Nonlocal Advantages of Quantum Imaginarity
• Pseudorandom unitaries are neither real nor sparse nor noise-robust
• Experimental entanglement characterization of two-rebit states
• Quantifying imaginarity in terms of pure-state imaginarity
• Coherence manipulation in asymmetry and thermodynamics
• Catalysis always degrades external quantum correlations
• Coherence and imaginarity of quantum states
• Geometric-Like imaginarity: quantification and state conversion
• Geometry of sets of Bargmann invariants
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Quantifying the imaginarity via different distance measures
• Quantum-imaginarity-based quantum speed limit
• One-shot manipulation of coherence in dynamic quantum resource theory
• Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation
• Quantum Speed Limit for Change of Basis
• Quantifying the phase of quantum states
• Real randomized measurements for analyzing properties of quantum states
• Choi-Defined Resource Theories
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Imaginarity measures induced by real part states and the complementarity relations
• Analyzing the free states of one quantum resource theory as resource states of another
• Quantifying imaginarity of quantum operations
• Methods of constructing superposition measures
• Detecting quantum resources in a semi-device independent framework
• The detection power of real entanglement witnesses under local unitary equivalence
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Non-locality of conjugation symmetry: characterization and examples in quantum network sensing
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Entropic and operational characterizations of dynamic quantum resources
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)
• Measure of set imaginarity
• Entanglement concentration via measurement:- role of imaginarity
• Experimental certification of the nonlocal advantages of quantum imaginarity
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• Statistics of Entanglement Transformation with Hierarchies among Catalysts
• Quantum-state block texture and its quantification