Quantifying the Imaginarity of Quantum Mechanics

Abstract

The use of imaginary numbers in modelling quantum mechanical systems encompasses the wave-like nature of quantum states. Here we introduce a resource theoretic framework for imaginarity, where the free states are taken to be those with density matrices that are real with respect to a fixed basis. This theory is closely related to the resource theory of coherence, as it is basis dependent, and the imaginary numbers appear in the off-diagonal elements of the density matrix. Unlike coherence however, the set of physically realizable free operations is identical to both completely resource non-generating operations, and stochastically resource non-generating operations. Moreover, the resource theory of imaginarity does not have a self-adjoint resource destroying map. After introducing and characterizing the free operations, we provide several measures of imaginarity, and give necessary and sufficient conditions for pure state transformations via physically consistent free operations in the single shot regime.

12 pages, 3 figures, published version

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Cited by in corpus (67)

• Quantum Resource Theories
• Operational Resource Theory of Imaginarity
• Resource theory of imaginarity: Quantification and state conversion
• Hiding and masking quantum information in complex and real quantum mechanics
• Catalysis of entanglement and other quantum resources
• Probabilistic transformations of quantum resources
• Unitary-invariant witnesses of quantum imaginarity
• Imaginarity-free quantum multiparameter estimation
• Real quantum operations and state transformations
• Measures of imaginarity and quantum state order
• Resource Theory of Imaginarity: New Distributed Scenarios
• Fisher information universally identifies quantum resources
• Tight constraints on probabilistic convertibility of quantum states
• 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
• Arbitrary Amplification of Quantum Coherence in Asymptotic and Catalytic Transformation
• Quantum-state texture and gate identification
• Quantifying imaginarity in terms of pure-state imaginarity
• Coherence manipulation in asymmetry and thermodynamics
• Imaginarity of quantum channels: Refinement and Alternative
• Coherence and imaginarity of quantum states
• Geometric-Like imaginarity: quantification and state conversion
• Censorship of Quantum Resources in Quantum Networks
• Expectation value dynamics within real Hilbert space quantum mechanics
• Optimization free measures of quantum resources
• Anticoncentration and State Design of Doped Real Clifford Circuits and Tensor Networks
• Unitary symmetries in wormhole geometry and its thermodynamics
• Continuity of robustness measures in quantum resource theories
• Two imaginarity monotones induced by unified $(\alpha ,\beta )$-relative entropy
• Geometry of sets of Bargmann invariants
• Quantum Speed Limit for Change of Basis
• Unbreakable and breakable quantum censorship
• Quantifying the imaginarity via different distance measures
• Imaginarity measures induced by relative entropy
• Catalytic Transformation from Computationally Universal to Strictly Universal Measurement-Based Quantum Computation
• One-shot manipulation of coherence in dynamic quantum resource theory
• Quantum-imaginarity-based quantum speed limit
• Coherence and Imaginarity as Resources in Quantum Circuit Complexity
• Witness based nonlinear detection of quantum entanglement
• Real randomized measurements for analyzing properties of quantum states
• Choi-Defined Resource Theories
• Projective robustness for quantum channels and measurements and their operational significance
• Quantifying the phase of quantum states
• Coherence, superposition, and Löwdin symmetric orthogonalization
• Quantifying imaginarity of quantum operations
• Analyzing the free states of one quantum resource theory as resource states of another
• Imaginarity measures induced by real part states and the complementarity relations
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• Golden states in resource theory of superposition
• Off-resonant preservation and generation of imaginarity in distributed scenarios
• Completely positive completely positive maps (and a resource theory for non-negativity of quantum amplitudes)
• Coherence-induced deep thermalization transition in random permutation quantum dynamics
• Detecting quantum resources in a semi-device independent framework
• The detection power of real entanglement witnesses under local unitary equivalence
• Experimental Masking of Real Quantum States
• Stochastic approximate state conversion for entanglement and general quantum resource theories
• Quantum-state block texture and its quantification
• Imaginarity as a Resource within Quantum Coherence: Geometric Decomposition and Operational Conversion
• Entanglement concentration via measurement:- role of imaginarity
• Deformed angular momentum algebra within the real Hilbert space
• The operational foundations of PT-symmetric and quasi-Hermitian quantum theory
• Measure of set imaginarity
• Experimental certification of the nonlocal advantages of quantum imaginarity