Detecting non-decomposability of time evolution via extreme gain of correlations
arXiv:1804.09925 · doi:10.1103/PhysRevA.98.052321
Abstract
Non-commutativity is one of the most elementary non-classical features of quantum observables. Here we propose a method to detect non-commutativity of interaction Hamiltonians of two probe objects coupled via a mediator. If these objects are open to their local environments, our method reveals non-decomposability of temporal evolution into a sequence of interactions between each probe and the mediator. The Hamiltonians or Lindblad operators can remain unknown throughout the assessment, we only require knowledge of the dimension of the mediator. Furthermore, no operations on the mediator are necessary. Technically, under the assumption of decomposable evolution, we derive upper bounds on correlations between the probes and then demonstrate that these bounds can be violated with correlation dynamics generated by non-commuting Hamiltonians, e.g., Jaynes-Cummings coupling. An intuitive explanation is provided in terms of multiple exchanges of a virtual particle which lead to the excessive accumulation of correlations. A plethora of correlation quantifiers are helpful in our method, e.g., quantum entanglement, discord, mutual information, and even classical correlation. Finally, we discuss exemplary applications of the method in quantum information: the distribution of correlations and witnessing dimension of an object.
arXiv comment7 pages, 2 figures
References in corpus (28)
- Separability Criterion for Density Matrices
- A computable measure of entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Quantifying Entanglement
- Distillation of secret key and entanglement from quantum states
- Unified View of Quantum and Classical Correlations
- On the quantum, classical and total amount of correlations in a quantum state
- Local versus non-local information in quantum information theory: formalism and phenomena
- Limits for entanglement measures
- Testing the Hilbert space dimension
- Geometric quantum discord through the Schatten 1-norm
- The entanglement of purification
- The problem with the geometric discord
- Controlled entanglement of two field modes in a Cavity Quantum Electrodynamics experiment
- Quantum discord bounds the amount of distributed entanglement
- Are general quantum correlations monogamous?
- Quantum cost for sending entanglement
- Experimental estimation of the dimension of classical and quantum systems
- Separable states can be used to distribute entanglement
- Experimental Device-independent Tests of Classical and Quantum Dimensions
- Coherent spin-exchange via a quantum mediator
- Revealing non-classicality of inaccessible objects
- Experimental distribution of entanglement with separable carriers
- Experimental entanglement distribution by separable states
- Distributing Entanglement with Separable States
- Robust generation of entanglement between two cavities mediated by short interactions with an atom
- A single atom-based generation of Bell states of two cavities
- Replicating the benefits of closed timelike curves without breaking causality