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arXiv:1201.1212 · Physical Review A

Witnessing the quantumness of a single system: From anticommutators to interference and discord

Rosario Fazio, Kavan Kishore Modi, Saverio Pascazio, Vlatko Vedral, Kazuya Yuasa

Published May 23, 2013• 11 citations
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Abstract

We introduce a method to witness the quantumness of a system. The method relies on the fact that the anticommutator of two classical states is always positive. By contrast, we show that there is always a nonpositive anticommutator due to any two quantum states. We notice that interference depends on the trace of the anticommutator of two states, and it is therefore operationally more suitable to detect quantumness by looking at anticommutators of states rather than their commutators.

DOI
10.1103/physreva.87.052132

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We introduce a method to witness the quantumness of a system. The method relies on the fact that the anticommutator of two classical states is always positive. By contrast, we show that there is always a nonpositive anticommutator due to any two quantum states. We notice that interference depends on the trace of the anticommutator of two states, and it is therefore operationally more suitable to detect quantumness by looking at anticommutators of states rather than their commutators.
Quantum correlations in composite and separable quantum systems are characterized by non-vanishing quantum discord. We demonstrate the necessary and sufficient conditions for existence of hermitian witness operators for quantum discord, bypassing the problem of non-convexity of the set of all classical states. We propose an example of a linear witness which can detect quantum correlations in large classes of separable bipartite systems. Decomposition of the witness in terms of a small number of locally measurable operators as shown here, paves the way for experimental detection of quantum correlations beyond entanglement.
Like entanglement, quantum discord quantifies the quantum correlations. Unlike entanglement, whose detection is extremely difficult, the quantum discord of an arbitrary bipartite state allows itself to be detected perfectly by a single observable, the quantum discord witness. In particular, we report a single observable whose expectation value provides a necessary and sufficient condition for the vanishing quantum discord of an arbitrary bipartite unknown state with four copies. A quantum circuit is designed to measure the quantum discord witness by using only local qubit-measurements.
We identify and characterize all the local quantum channels that preserves the set of classical states, i.e., does not create any quantum correlations. At first we show that the quantum correlations cannot be created from without if and only if the local quantum channel preserves the commutativity, i.e., the images of any two commuting states also commute. And then we provide an operational necessary and sufficient criterion for a known quantum channel to preserve the commutativity as well as a single observable to witness an arbitrary unknown commutativity-preserving channel. All the distance-based measures for quantum correlations, e.g., the geometric measure, are non-increasing while the quantum discord defined by von Neumann measurements can be increasing or decreasing under local commutativity-preserving channels.
Quantum mechanics predicts the existence of correlations between composite systems that, although puzzling to our physical intuition, enable technologies not accessible in a classical world. Notwithstanding, there is still no efficient general method to theoretically quantify and experimentally detect entanglement of many qubits. Here we propose to detect entanglement by measuring the statistical response of a quantum system to an arbitrary nonlocal parametric evolution. We witness entanglement without relying on the tomographic reconstruction of the quantum state, or the realization of witness operators. The protocol requires two collective settings for any number of parties and is robust against noise and decoherence occurring after the implementation of the parametric transformation. To illustrate its user friendliness we demonstrate multipartite entanglement in different experiments with ions and photons by analyzing published data on fidelity visibilities and variances of collective observables.