Extremal quantum correlations: Experimental study with two-qubit states (original) (raw)
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Physical Review A, 2011
Measurements of Quantum Systems disturb their states. To quantify this non-classical characteristic, Zurek and Ollivier [1] introduced the quantum discord, a quantum correlation which can be nonzero even when entanglement in the system is zero. Discord has aroused great interest as a resource that is more robust against the effects of decoherence and offers exponential speed up of certain computational algorithms. Here, we study general two-level bipartite systems and give general results on the relationship between discord, entanglement, and linear entropy, and identify the states for which discord takes a maximal value for a given entropy or entanglement, thus placing strong bounds on entanglement-discord and entropy-discord relations. We find out that although discord and entanglement are identical for pure states, they differ when generalized to mixed states as a result of the difference in the method of generalization.
Physical Review A, 2013
We address the experimental determination of entropic quantum discord for systems made of a pair of polarization qubits. We compare results from full and partial tomography and found that the two determinations are statistically compatible, with partial tomography leading to a smaller value of discord for depolarized states. Despite the fact that our states are well described, in terms of fidelity, by families of depolarized or phase-damped states, their entropic discord may be largely different from that predicted for these classes of states, such that no reliable estimation procedure beyond tomography may be effectively implemented. Our results, together with the lack of an analytic formula for the entropic discord of a generic two-qubit state, demonstrate that the estimation of quantum discord is an intrinsically noisy procedure. Besides, we question the use of fidelity as a figure of merit to assess quantum correlations.
Linking Quantum Discord to Entanglement in a Measurement
Physical Review Letters, 2011
We show that a von Neumann measurement on a part of a composite quantum system unavoidably creates distillable entanglement between the measurement apparatus and the system if the state has nonzero quantum discord. The minimal distillable entanglement is equal to the one way information deficit. The quantum discord is shown to be equal to the minimal partial distillable entanglement, that is the part of entanglement which is lost, when we ignore the subsystem which is not measured. We then show that any entanglement measure corresponds to some measure of quantum correlations. This powerful correspondence also yields necessary properties for quantum correlations. We generalize the results to multipartite measurements on a part of the system and on the total system. PACS numbers: 03.65.Ta, 03.67.Mn
Optimal estimation of entanglement and discord in two-qubit states
Scientific Reports
Recently, the fast development of quantum technologies led to the need for tools allowing the characterization of quantum resources. In particular, the ability to estimate non-classical aspects, e.g. entanglement and quantum discord, in two-qubit systems, is relevant to optimise the performance of quantum information processes. Here we present an experiment in which the amount of entanglement and discord are measured exploiting different estimators. Among them, some will prove to be optimal, i.e., able to reach the ultimate precision bound allowed by quantum mechanics. These estimation techniques have been tested with a specific family of states ranging from nearly pure Bell states to completely mixed states. This work represents a significant step towards the development of reliable metrological tools for quantum technologies.
Quantum discord from system–environment correlations
Physica Scripta, 2014
In an initially uncorrelated mixed separable bi-partite system, quantum correlations can emerge under the action of a local measurement or local noise [1]. We analyze this counter-intuitive phenomenon using quantum discord as a quantifier. We then relate changes in quantum discord to system-environment correlations between the system in a mixed state and some purifying environmental mode using the Koashi-Winter inequality. On this basis, we suggest an interpretation of discord as a byproduct of transferring entanglement and correlations around the different subsystems of a global pure state.
Experimental Entanglement Activation from Discord in a Programmable Quantum Measurement
Physical Review Letters, 2014
To acquire knowledge about nature we need to observe its constituents. In quantum mechanics, observing is not a passive act. Consider a system of two quantum particles A and B: if a measurement apparatus M is used to make an observation on particle B, then the overall state of the system AB will typically be altered. When this happens no matter which local measurement is performed, the two objects A and B are revealed to possess peculiar correlations known as quantum discord. Here we demonstrate that the very act of local observation gives rise to an "activation protocol" which converts discord into distillable entanglement, a stronger and more useful form of quantum correlations, between the apparatus M and the composite system AB. In order to experimentally implement such activation protocol, we adopt a flexible two-photon setup to realize a three-qubit system (A, B, M) with programmable degrees of initial correlations, measurement interaction, and characterization processes. Our experiment demonstrates the fundamental mechanism underpinning the ubiquitous act of observing the quantum world, and unlocks the potential of discord for entanglement generation, a primitive for quantum technology.
Faithful nonclassicality indicators and extremal quantum correlations in two-qubit states
Journal of Physics A: Mathematical and Theoretical, 2011
Abstract. The state disturbance induced by locally measuring a quantum system yields a signature of nonclassical correlations beyond entanglement. Here, we present a detailed study of such correlations for two-qubit mixed states. To overcome the asymmetry of quantum discord and the unfaithfulness of measurement-induced disturbance (severely overestimating quantum correlations), we propose an ameliorated measurement-induced disturbance as nonclassicality indicator, optimized over joint local measurements, and we ...
Physical Review A, 2013
We show that the phenomenon of frozen discord, exhibited by specific classes of two-qubit states under local nondissipative decoherent evolutions, is a common feature of all known bona fide measures of general quantum correlations. All those measures, despite inducing typically inequivalent orderings on the set of nonclassically correlated states, return a constant value in the considered settings. Every communication protocol which relies on quantum correlations as resource will run with a performance completely unaffected by noise in the specified dynamical conditions. We provide a geometric interpretation of this phenomenon. PACS numbers: 03.65.Ta, 03.65.Yz, 03.67.Mn
Quantifying Quantum Entanglement in Two-Qubit Mixed State from Connected Correlator
Cornell University - arXiv, 2022
The connected correlation function contributes to Classical and Quantum Entanglement simultaneously. The separable state contains the non-zero connected correlation. It shows the difficulty of quantifying Quantum Entanglement. We propose a connected correlation matrix for quantifying Quantum Entanglement in the two-qubit mixed state. Our study begins from the three-qubit state. We partial trace over one qubit to obtain the mixed state. Therefore, one can characterize Quantum Entanglement in the two-qubit mixed state from the three-qubit entanglement measures. We show that the maximum violation of Bell's inequality lose one entanglement degree. When considering the connected correlation, the result contains all necessary entanglement measures. Hence we eliminate the non-connected sector. We classify the mixed states and then demonstrate that separable states have the lowest correlation in each classified class. The entanglement measure also monotonically increases for the correlation measure. Hence we successfully quantify Quantum Entanglement. We also compare the result to the logarithmic negativity. The negativity is increasing for the correlation measure but is not monotonic. In the end, we discuss whether the quantification reflects the degree of non-locality. We assume that the observable is a vector with the locality but violates the freedom of choice. The probability distribution of the local hidden variable needs to depend on a measurement setting. Hence the interpretation of Quantum Entanglement from the locality is possible.