Behavior of quantum correlations under local noise

We characterize the behavior of quantum correlations under the influence of local noisy channels. Intuition suggests that such noise should be detrimental for quantumness. When considering qubit systems, we show for which channels this is indeed the case: The amount of quantum correlations can only decrease under the action of unital channels. However, nonunital channels (e.g., such as dissipation) can create quantum correlations for some initially classical states. Furthermore, for higher-dimensional systems even unital channels may increase the amount of quantum correlations. Thus, counterintuitively, local decoherence can generate quantum correlations.     

No-local-broadcasting theorem for multipartite quantum correlations

We prove that the correlations present in a multipartite quantum state have an operational quantum character even if the state is unentangled, as long as it does not simply encode a multipartite classical probability distribution. Said quantumness is revealed by the new task of local broadcasting, i.e., of locally sharing preestablished correlations, which is feasible if and only if correlations are stricly classical. Our operational approach leads to natural definitions of measures for quantumness of correlations. It also reproduces the standard no-broadcasting theorem as a special case.     

Non-zero total correlation means non-zero quantum correlation

We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with weak measurements. As an example, we present the assisted state-discrimination method.     

Quantum Discord in Nuclear Magnetic Resonance Systems at Room Temperature

We review the theoretical and the experimental researches aimed at quantifying or identifying quantum correlations in liquid-state nuclear magnetic resonance (NMR) systems at room temperature. We first overview, at the formal level, a method to determine the quantum discord and its classical counterpart in systems described by a deviation matrix. Next, we describe an experimental implementation of that method. Previous theoretical analysis of quantum discord decoherence had predicted the time dependence of the discord to change suddenly under the influence of phase noise. The experiment attests to the robustness of the effect, sufficient to confirm the theoretical prediction even under the additional influence of a thermal environment. Finally, we discuss an observable witness for the quantumness of correlations in two-qubit systems and its first NMR implementation. Should the nature, not the amount, of the correlation be under scrutiny, the witness offers the most attractive alternative.     

The classicality and quantumness of a quantum ensemble

In this Letter, we investigate the classicality and quantumness of a quantum ensemble. We define a quantity called ensemble classicality based on classical cloning strategy (ECCC) to characterize how classical a quantum ensemble is. An ensemble of commuting states has a unit ECCC, while a general ensemble can have a ECCC less than 1. We also study how quantum an ensemble is by defining a related quantity called quantumness. We find that the classicality of an ensemble is closely related to how perfectly the ensemble can be cloned, and that the quantumness of the ensemble used in a quantum key distribution (QKD) protocol is exactly the attainable lower bound of the error rate in the sifted key.     

Correlation properties of entangled multiphoton states and Bernstein’s paradox

A normally ordered characteristic function (NOCF) of Bose operators is calculated for a number of discrete-variable entangled states (Greenberger-Horne-Zeilinger (GHZ) and Werner (W) qubit states and a cluster state). It is shown that such NOCFs contain visual information on two types of correlations: pseudoclassical and quantum correlations. The latter manifest themselves in the interference terms of the NOCFs and lead to quantum paradoxes, whereas the pseudoclassical correlations of photons and their cumulants satisfy the relations for classical random variables. Three- and four-qubit states are analyzed in detail. An implementation of an analog of Bernstein’s paradox on discrete quantum variables is discussed. A measure of quantumness of an entangled state is introduced that is not related to the entropy approach. It is established that the maximum of the degree of quantumness substantiates the numerical values of the coefficients in multiqubit vector states derived from intuitive considerations.     

LMG model: Markovian evolution of classical and quantum correlations under decoherence

We have investigated the quantum phase transition in the ground state of collective Lipkin-Meshkov-Glick model (LMG model) subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. We discuss the behavior of quantum and classical pair wise correlations in the system, with the quantumness of correlations measured by quantum discord (QD), entanglement of formation (EOF), measurement-induced disturbance (MID) and the Clauser-Horne-Shimony-Holt-Bell function (CHSH-Bell function). The time evolution established by system-environment interactions is assumed to be Markovian in nature and the quantum channels studied include the amplitude damping (AD), phase damping (PD), bit-flip (BF), phase-flip (PF), and bit-phase-flip (BPF) channels. One can identify appropriate quantities associated with the dynamics of quantum correlations signifying quantum phase transition in the model. Surprisingly, the CHSH-Bell function is found to detect all the phase transitions, even when quantum and classical correlations are zero for the relevant ground state.     

A Measure of Quantum Correlation Based on von Neumann Entropy and Positive Operator-Valued Measurement

Quantum correlations in composite quantum systems are at the origin of the most peculiar features of quantum mechanics such as the violation of Bells inequalities and non-locality. In quantum information theory, they are viewed as quantum resources used by quantum algorithms and communication protocols to outperform their classical analogs. In this paper, we define a new measure of quantum correlation based on von Neumann entropy and positive operator-valued measurement,which has clear physical meaning and we can prove that it satisfying many good property for a measure of quantumness.     

On Quantum No-Broadcasting

We address the issue of one-side local broadcasting for correlations in a quantum bipartite state, and conjecture that the correlations can be broadcast if and only if they are classical–quantum, or equivalently, the quantum discord, as defined by Ollivier and Zurek (Phys Rev Lett 88:017901, 2002), vanishes. We prove this conjecture when the reduced state is maximally mixed and further provide various plausible arguments supporting this conjecture. Moreover, we demonstrate that the conjecture implies the following two elegant and fundamental no-broadcasting theorems: (1) The original no-broadcasting theorem by Barnum et al. (Phys Rev Lett 76:2818, 1996), which states that a family of quantum states can be broadcast if and only if the quantum states commute. (2) The no-local-broadcasting theorem for quantum correlations by Piani et al. (Phys Rev Lett 100:090502, 2008), which states that the correlations in a single bipartite state can be locally broadcast if and only if they are classical. The results provide an informational interpretation for classical–quantum states from an operational perspective and shed new lights on the intrinsic relation between non-commutativity and quantumness.     

Teaching a laser beam to go straight

In classical physics a beam of light propagates in a perfectly straight line and this means that we can measure small displacements with unlimited accuracy. However, this is not correct for real laser beams when we take the quantum properties of light into account. Spatial measurements will be limited by quantum noise, similar to the limitations for optical communication and sensing. Here we derive the spatial quantum noise limit and show how to measure it. Next we demonstrate that we can use specially prepared light with quantum correlations, so-called squeezed light, to improve spatial measurements to below this quantum limit. In this way we prepare a beam which goes in a straighter line than the output of any conventional laser.     

Making atom-atom correlations observable by feedback control

Application of continuous feedback control to the center of mass of a bosonic gas is shown to induce a breathing of the atomic cloud. The amplitude of the breathing depends on initial atom-atom correlations and can thus be directly used for characterizing the quantumness of the atom-atom correlations. Two levels of quantumness appear in the form of a single-atom quadrature squeezing and of a violation of the classical Schwarz inequality.     

Entanglement-Assisted Joint Monostatic-Bistatic Radars

With the help of entanglement, we can build quantum sensors with sensitivity better than that of classical sensors. In this paper we propose an entanglement assisted (EA) joint monostatic-bistatic quantum radar scheme, which significantly outperforms corresponding conventional radars. The proposed joint monostatic-bistatic quantum radar is composed of two radars, one having both wideband entangled source and EA detector, and the second one with only an EA detector. The optical phase conjugation (OPC) is applied on the transmitter side, while classical coherent detection schemes are applied in both receivers. The joint monostatic-bistatic integrated EA transmitter is proposed suitable for implementation in LiNbO₃ technology. The detection probability of the proposed EA joint target detection scheme outperforms significantly corresponding classical, coherent states-based quantum detection, and EA monostatic detection schemes. The proposed EA joint target detection scheme is evaluated by modelling the direct radar return and forward scattering channels as both lossy and noisy Bosonic channels, and assuming that the distribution of entanglement over idler channels is not perfect.     

Quantumness and Dequantumness Power of Quantum Channels

Focusing on the dynamics of quantumness in ensembles, we propose a framework to qualitatively and quantitatively characterize quantum channels from the perspective of the amount of quantumness in ensembles that a quantum channel can induce or reduce. Along this line, the quantumness power and dequantumness power are introduced. In particular, once a quantum dynamics described by time-varying quantum channels reduces the quantumness for any input ensembles all the time, we call it a completely dequantumness channel, whose relationship with Markovianity is analyzed through several examples.     

Probability representation and quantumness tests for qudits and two-mode light states

Using the tomographic-probability representation of spin states, the quantum behavior of qudits is examined. For a general j-qudit state, we propose an explicit formula for quantumness witness whose negative average value is incompatible with classical statistical model. The probability representations of quantum and classical (2j + 1)-level systems are compared within the framework of quantumness tests. In view of the Jordan–Schwinger map, the method is extended for checking the quantumness of two-mode light states.     

Decomposition Properties of Quantum Discord

The quantum discord was introduced by Ollivier,Zurek,Henderson,and Vedral as an indicator of the degree of quantumness of mixed states.In this paper,we provide a decomposition condition for quantum discord.Moreover,we show that under the condition,the quantum correlations between the quantum systems can be captured completely by the entanglement measure.Finally,we present examples of our conclusions.     

Computing with a single qubit faster than the computation quantum speed limit

The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations.     

Quantum walk under coherence non-generating channels

We investigate the probability distribution of the quantum walk under coherence non-generating channels. We definea model called generalized classical walk with memory. Under certain conditions, generalized classical random walk withmemory can degrade into classical random walk and classical random walk with memory. Based on its various spreadingspeed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring thequantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walkswith memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walkand classical random walk with memory by coherence non-generating channels. Also, we find that for another class ofcoherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of thecoin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore therelationship between coherence and quantum walk.     

All nonclassical correlations can be activated into distillable entanglement

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.     

Parameter estimation with mixed quantum states

We consider quantum enhanced measurements with initially mixed states. We show very generally that for any linear propagation of the initial state that depends smoothly on the parameter to be estimated, the sensitivity is bound by the maximal sensitivity that can be achieved for any of the pure states from which the initial density matrix is mixed. This provides a very general proof that purely classical correlations cannot improve the sensitivity of parameter estimation schemes in quantum enhanced measurement schemes.