International Journal of Quantum Information

A framework for categorizing entropic measures of non-classical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity obtained from measurements on the two systems. Three types of entropic quantities are used, and three different measurement strategies are applied to these quantities. Many of the resulting measures of non-classical correlations have been proposed previously. Properties of the various measures are explored, and results of evaluating the measures for two-qubit quantum states are presented.

A fundamental feature of quantum mechanics radically different from classical theory lies in the role and consequence of quantum measurements, which usually cause disturbance to quantum states. For a bipartite state, the minimum disturbance caused by local measurements has been used to define quantum correlations from a measurement perspective. In contrast to this minimum approach, we investigate the maximum disturbance of local measurements, and define the nonlocal effect of a bipartite state as the maximum discrepancy between the global and local disturbances caused by local quantum measurements. Some analytical results are obtained and the significance of the maximum nonlocal effect is briefly discussed.

In this paper, we first present a brief derivation of the dynamical decoupling condition by means of designing control Hamiltonians, which is used to preserve arbitrary quantum states in the case of interactions with environment. According to different time intervals between the adjacent pulses, two important dynamical decoupling schemes: periodic dynamical decoupling (PDD) and Uhrig dynamical decoupling (UDD) are analyzed. Based on the comparison between PDD and UDD, we propose our optimized dynamical decoupling scheme with different time intervals between adjacent pulses which follow a normal distribution. At last numerical simulations are carried out in a three-level atom in Ξ -configuration, we select the non-diagonal element of density matrix as a reference index to compare the performances of suppressing the decoherence of these three strategies, and the results indicate that dynamical decoupling strategy proposed has better performances than that of PDD and UDD have under some low range of the loss of the quantum coherence.

We construct a non-Markovian dynamical map that accounts for systems correlated to the environment. We refer to it as a canonical dynamical map, which forms an evolution family. The relationship between inverse maps and correlations with the environment is established. The mathematical properties of complete positivity is related to classical correlations, according to quantum discord, between the system and the environment. A generalized non-Markovian master equation is derived from the canonical dynamical map.

In quantum information processing, spin-3/2 electron or nuclear spin states are known as two-qubit states. For SI (S = 3/2, I = 1/2) spin system, there are eight three-qubit states. In this study, first, three-qubit CNOT logic gates are obtained. Then three-qubit entangled states are obtained by using the matrix representation of Hadamard and three-qubit CNOT logic gates. By considering single ³¹P@C₆₀ molecule as SI (S = 3/2, I = 1/2) spin system, three-qubit entangled states are also obtained using the magnetic resonance pulse sequences of Hadamard and CNOT logic gates.

A locking protocol between two parties is as follows: Alice gives an encrypted classical message to Bob which she does not want Bob to be able to read until she gives him the key. If Alice is using classical resources, and she wants to approach unconditional security, then the key and the message must have comparable sizes. But if Alice prepares a quantum state, the size of the key can be comparatively negligible. This effect is called quantum locking. Entanglement does not play a role in this quantum advantage. We show that, in this scenario, the quantum discord quantifies the advantage of the quantum protocol over the corresponding classical one for any classical-quantum state.

In this paper, we study the entanglement dynamics, its measure, and mean photon number of the field in the interaction between a quantized electromagnetic field and a 3-level atom surrounded by a nonlinear Kerr-like medium. Using the density matrix approach, we have calculated the time evolution of the entanglement and its magnitude at an arbitrary time, for different nonlinear coupling constant. Moreover, to show the effects of nonlinearity on the atom–field interaction and its relation with the entanglement the mean photon number of the field is also presented as a function of nonlinear coupling strength, χ. The results show that, envelope of entanglement fluctuation, their duration and amplitude strongly depend on the nonlinear coupling strength. Since the entanglement decreases with increasing nonlinearity, the mean number of photons reaches a constant value as a result of absorption increment by the surrounding medium.

We consider a multipartite system consisting of two noninteracting qubits each embedded in a single-mode leaky cavity, in turn connected to an external bosonic reservoir. Initially, we take the two qubits in an entangled state while the cavities and the reservoirs have zero photons. We investigate, in this six-partite quantum system, the transfer of quantum discord from the qubits to the cavities and reservoirs. We show that this transfer also occurs when the cavities are not entangled. Moreover, we discuss how quantum discord can be extracted from the cavities and transferred to distant systems by traveling leaking photons, using the input–output theory.

An efficient protocol for quantum secure dialogue by using single photons is proposed. Comparing with the previous protocols, in the proposed protocol, no classical message has been exchanged during the decoding of the secret messages, so the present scheme has not only overcome the drawback "information leakage" or "classical correlation" but also it possesses the characters of security and maximum efficiency. The other highlight of our protocol is that, in this method one party is able to first read the message received from the other party before sending another message back in reply.

We study quantum correlations in an isotropic Ising ring under the effects of a transverse magnetic field. After characterizing the behavior of two-spin quantum correlations, we extend our analysis to global properties of the ring, using a figure of merit for quantum correlations that shows enough sensitivity to reveal the drastic changes in the properties of the system at criticality. This opens up the possibility to relate statistical properties of quantum many-body systems to suitably tailored measures of quantum correlations that capture features going far beyond standard quantum entanglement.

In [Piani et al., PRL106 (2011) 220403], an activation protocol was introduced which maps the general non-classical (multipartite) correlations between given systems into bipartite entanglement between the systems and local ancillae by means of a potentially highly entangling interaction. Here, we study how this activation protocol can be used to entangle the starting systems themselves via entanglement swapping through a measurement on the ancillae. Furthermore, we bound the relative entropy of quantumness (a naturally arising measure of non-classicality in the scheme of Piani et al. above) for a special class of separable states, the so-called classical–quantum states. In particular, we fully characterize the classical–quantum two-qubit states that are maximally non-classical.

Using an exact approach, we study the dynamics of entanglement between two qubits coupled to independent reservoirs and between the two, initially disentangled, reservoirs. We also describe the transfer of bipartite entanglement from the two qubits to their respective reservoirs focussing on the case of two atoms inside two different leaky cavities with a specific attention to the role of the detuning. We present a scheme to prepare the cavity fields in a maximally entangled state, without direct interaction between the cavities, by exploiting the initial qubits entanglement. We discuss a deterministic protocol, working in the presence of cavity losses, for the generation of a W-state of one qubit and two cavity fields and we describe a probabilistic scheme to entangle one of the atoms with the reservoir (cavity field) of the other atom.

We address the interference of a pair of two-mode Gaussian states, interacting pairwise through a beam-splitter Hamiltonian. In the framework of a suitable phase-space analysis, the correlations generated through the interaction are studied by considering a quantity proportional to the variance of difference between the detected photocurrents of all the possible couples of modes. We use this quantity to demonstrate the invariance through the interaction and the correlations swapping also in the presence of nonideal photodetection.

We discuss a scheme for a full superdense coding of entangled photon states employing only linear optics elements. By using the mixed basis consisting of four states that are unambiguously distinguishable by a standard and polarizing beam splitters we can deterministically transfer four messages by manipulating just one of the two entangled photons. The sender achieves the determinism of the transfer either by giving up the control over 50% of sent messages (although known to her) or by discarding 33% of incoming photons.

For systems of identical Bosons, it is necessary to reformulate the notions of separability and entanglement in algebraic terms shifting the emphasis from the particle aspect of first quantization to the mode description typical of second quantization. Within this new framework, we show that, unlike for systems consisting of distinguishable qubits, negativity is an exhaustive bipartite entanglement witness for systems with fixed number of Bosons; further, we investigate the impact of dephasing noise in relation to the use of such many-body Bosonic systems in metrological applications.

Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspective. This is done by employing linear maps associated with generalized projective measurements. A generalized measurement corresponds to a quantum operation mapping a density matrix to another density matrix, preserving its positivity, hermiticity, and trace class. The positive operator valued measure (POVM) — employed earlier in the literature to optimize the measures of classical/quantum correlations — correspond to completely positive (CP) maps. The other class, the not completely positive (NCP) maps, are investigated here, in the context of measurements, for the first time. It is shown that such NCP projective maps provide a new clue to the understanding of quantumness of correlations in a general setting. Especially, the separability–classicality dichotomy gets resolved only when both the classes of projective maps (CP and NCP) are incorporated as optimizing measurements. An explicit example of a separable state — exhibiting nonzero quantum discord, when possible optimizing measurements are restricted to POVMs — is reexamined with this extended scheme incorporating NCP projective maps to elucidate the power of this approach.

We extend the geometric measure of quantum discord, introduced and computed for two-qubit states, to quantify non-classical correlations in composite Gaussian states of continuous variable systems. We lay the formalism for the evaluation of a Gaussian geometric discord in two-mode Gaussian states, and present explicit formulas for the class of two-mode squeezed thermal states. In such a case, under physical constraints of bounded mean energy, geometric discord is shown to admit upper and lower bounds for a fixed value of the conventional (entropic) quantum discord. We finally discuss alternative geometric approaches to quantify Gaussian quadrature correlations.

We discuss models of computing that are beyond classical. The primary motivation is to unearth the cause of non-classical advantages in computation. Completeness results from computational complexity theory lead to the identification of very disparate problems, and offer a kaleidoscopic view into the realm of quantum enhancements in computation. Emphasis is placed on the "power of one qubit" model, and the boundary between quantum and classical correlations as delineated by quantum discord. A recent result by Eastin on the role of this boundary in the efficient classical simulation of quantum computation is discussed. Perceived drawbacks in the interpretation of quantum discord as a relevant certificate of quantum enhancements are addressed.

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2D subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2D entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d.

The dynamics of a pair of coupled harmonic oscillators in separate or common thermal environments is studied, focusing on different indicators of quantumness, such as entanglement, twin oscillators correlations, and quantum discord. We compare their decay under the effect of dissipation and show, through a phase diagram, that entanglement is more likely to survive asymptotically than twin oscillators correlations.

Correlations are a very important tool in the study of multipartite systems, for both classical and quantum ones. The discussion about the quantum nature of correlations permeates Physics since Einstein, Podolski and Rosen published their famous article criticizing quantum mechanics. Here, we provide a short review about the quantum nature of correlations, discussing both its theoretical and experimental aspects. We focus on quantum discord and related measures. After discussing their fundamental aspects (theoretically and experimentally), we proceed by analysing the dynamical behavior of correlations under decoherence as well as some applications in different scenarios, such as quantum computation and relativity, passing through critical and biological systems.