Quantifying Quantumness of Channels Without Entanglement

Abstract

Quantum channels breaking entanglement, incompatibility, or nonlocality are defined as such because they are not useful for entanglement-based, one-sided device-independent, or device-independent quantum information processing, respectively. Here, we show that such breaking channels are related to complementary tests of macrorealism i.e., temporal separability, channel unsteerability, temporal unsteerability, and the temporal Bell inequality. To demonstrate this we first define a steerability-breaking channel, which is conceptually similar to entanglement and nonlocality-breaking channels and prove that it is identical to an incompatibility-breaking channel. A hierarchy of quantum non-breaking channels is derived, akin to the existing hierarchy relations for temporal and spatial quantum correlations. We then introduce the concept of channels that break temporal correlations, explain how they are related to the standard breaking channels, and prove the following results: (1) A robustness-based measure for non-entanglement-breaking channels can be probed by temporal nonseparability. (2) A non-steerability-breaking channel can be quantified by channel steering. (3) Temporal steerability and non-macrorealism can be used for, respectively, distinguishing unital steerability-breaking channels and nonlocality-breaking channels for a maximally entangled state. Finally, a two-dimensional depolarizing channel is experimentally implemented as a proof-of-principle example to demonstrate the hierarchy relation of non-breaking channels using temporal quantum correlations

Comments welcome

References in corpus (20)

• Entanglement detection
• Device-independent security of quantum cryptography against collective attacks
• Steering, Entanglement, Nonlocality, and the EPR Paradox
• Realization of a multi-node quantum network of remote solid-state qubits
• Einstein-Podolsky-Rosen steering provides the advantage in entanglement-assisted subchannel discrimination with one-way measurements
• Joint measurability of generalized measurements implies classicality
• All entangled states are useful for channel discrimination
• Quantum random number generation on a mobile phone
• Verifying the quantumness of a channel with an untrusted device
• Quantum Entanglement in Time
• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Temporal Steering in Four Dimensions with applications to coupled qubits and magnetoreception
• Fisher information universally identifies quantum resources
• Qutrit witness from the Grothendieck constant of order four
• Channel Steering
• Loophole free interferometric test of macrorealism using heralded single photons
• A network-ready random-access qubits memory
• Temporal correlations in the simplest measurement sequences
• Mesoscopic and macroscopic quantum correlations in photonic, atomic and optomechanical systems
• Hierarchy and robustness of multilevel two-time temporal quantum correlations

Cited by in corpus (29)

• Complete classification of steerability under local filters and its relation with measurement incompatibility
• Steering-enhanced quantum metrology using superpositions of noisy phase shifts
• Leggett-Garg Macrorealism and temporal correlations
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Experimental hierarchy of two-qubit quantum correlations without state tomography
• Deep learning the hierarchy of steering measurement settings of qubit-pair states
• Unlimited One-Way Steering
• Maxwell's two-demon engine under pure dephasing noise
• Verification of Continuous-Variable Quantum Memories
• Improvement in quantum communication using quantum switch
• Thermodynamic Approach to Quantifying Incompatible Instruments
• Resource Marginal Problems
• Experimental hierarchy of the nonclassicality of single-qubit states via potentials for entanglement, steering, and Bell nonlocality
• Unveiling quantum steering by quantum-classical uncertainty complementarity
• Operational Interpretation of the Choi Rank Through k-State Exclusion
• Interplay of nonlocality and incompatibility breaking qubit channels
• Observation of Full Hierarchy of Temporal Quantum Correlations with a Superconducting Qubit
• Entanglement-breaking channels are a quantum memory resource
• Fidelity of entanglement and quantum entropies: unveiling their relationship in quantum states and channels
• Revealing the Boundary between Quantum Mechanics and Classical Model by EPR-Steering Inequality
• Certifying the dimensionality of any quantum channel with minimal assumptions
• Leggett-Garg inequalities for multitime processes
• Weight-based measure of quantum memory as a universal and operational benchmark
• Complete characterisation of state conversions by work extraction
• General quantum resources providing advantages in work-extraction tasks
• Theory-Independent Context Incompatibility: Quantification and Experimental Demonstration
• Operational Coherent Measurements with Steering and Randomness
• On the characterization of partially entanglement breaking and annihilating channels
• Some Entanglement Survives Most Measurements