Real quantum operations and state transformations
arXiv:2210.15820 · doi:10.1088/1367-2630/acf9c4
Abstract
Resource theory of imaginarity provides a useful framework to understand the role of complex numbers, which are essential in the formulation of quantum mechanics, in a mathematically rigorous way. In the first part of this article, we study the properties of ``real'' (quantum) operations both in single-party and bipartite settings. As a consequence, we provide necessary and sufficient conditions for state transformations under real operations and show the existence of ``real entanglement'' monotones. In the second part of this article, we focus on the problem of single copy state transformation via real quantum operations. When starting from pure initial states, we completely solve this problem by finding an analytical expression for the optimal fidelity of transformation, for a given probability of transformation and vice versa. Moreover, for state transformations involving arbitrary initial states and pure final states, we provide a semidefinite program to compute the optimal achievable fidelity, for a given probability of transformation.
arXiv comment9 pages. Close to published version
References in corpus (34)
- Quantum entanglement
- Entanglement of Formation of an Arbitrary State of Two Qubits
- Concentrating Partial Entanglement by Local Operations
- Quantifying Coherence
- QuTiP 2: A Python framework for the dynamics of open quantum systems
- Quantifying Entanglement
- Quantum Coherence as a Resource
- Quantum Resource Theories
- Conditions for a class of entanglement transformations
- Operational Resource Theory of Coherence
- The role of quantum information in thermodynamics --- a topical review
- Geometric measure of entanglement and applications to bipartite and multipartite quantum states
- The Resource Theory of Stabilizer Computation
- Quantum majorization and a complete set of entropic conditions for quantum thermodynamics
- The resource theory of quantum reference frames: manipulations and monotones
- Entanglement of pure states for a single copy
- Fidelity and Concurrence of conjugated states
- Quantum theory based on real numbers can be experimentally falsified
- Conditions for coherence transformations under incoherent operations
- An introductory review of the resource theory approach to thermodynamics
- Operational Resource Theory of Imaginarity
- Maximal Coherence and the Resource Theory of Purity
- Approximate transformations and robust manipulation of bipartite pure state entanglement
- Quantifying the Imaginarity of Quantum Mechanics
- Testing real quantum theory in an optical quantum network
- Ruling out real-valued standard formalism of quantum theory
- Resource theory of imaginarity: Quantification and state conversion
- No-Go Theorems for Quantum Resource Purification
- Linking a distance measure of entanglement to its convex roof
- Principles of Quantum Communication Theory: A Modern Approach
- Benchmarking one-shot distillation in general quantum resource theories
- Fundamental limitations on distillation of quantum channel resources
- Optimal local preparation of an arbitrary mixed state of two qubits. Closed expression for the single copy case
- Positive maps and entanglement in real Hilbert spaces
Cited by in corpus (17)
- Semidefinite programming relaxations for quantum correlations
- Resource Theory of Imaginarity: New Distributed Scenarios
- Imaginarity of Gaussian states
- Quantifying the imaginarity of quantum states via Tsallis relative entropy
- Pseudorandom unitaries are neither real nor sparse nor noise-robust
- Quantifying imaginarity in terms of pure-state imaginarity
- Coherence manipulation in asymmetry and thermodynamics
- Coherence and imaginarity of quantum states
- Geometric-Like imaginarity: quantification and state conversion
- Quantifying the imaginarity via different distance measures
- Real randomized measurements for analyzing properties of quantum states
- Imaginarity measures induced by real part states and the complementarity relations
- Detecting quantum resources in a semi-device independent framework
- Off-resonant preservation and generation of imaginarity in distributed scenarios
- Strict advantage of complex quantum theory in a communication task
- Experimental certification of the nonlocal advantages of quantum imaginarity
- Measure of set imaginarity