Arbitrary Bipartite State Research Articles

Lower bound of entanglement of formation based on correlation matrix

The entanglement of formation (EOF), which quantifies the required minimally physical resources to prepare a quantum state, plays important roles in many quantum information processes. Due to the convex-roof definition, it is hard to find the explicit analytic formulae of EOF, except for some special quantum systems. The correlation matrix of a quantum state is closely related to entanglement property. In this paper, we use the Lagrange-multiplier approach to obtain an analytic lower bound of EOF for arbitrary dimensional bipartite states, which improves the previous conclusions. Numerical example shows that the bound is also valid for some PPT entangled states.

Generating entangled states from coherent states in circuit QED

Entangled states are self-evidently important to a wide range of applications in quantum communication and quantum information processing. We propose an efficient and convenient two-step protocol for generating Bell states and NOON states of two microwave resonators from merely coherent states. In particular, we derive an effective Hamiltonian for resonators coupled to a superconducting $\mathrm{\ensuremath{\Lambda}}$-type qutrit in the dispersive regime. By the excitation-number-dependent Stark shifts of the qutrit transition frequencies, we are able to individually control the amplitudes of specified Fock states of the resonators associated with relevant qutrit transition, using carefully tailored microwave drive signals. Thereby an arbitrary bipartite entangled state in Fock space can be generated by a typical evolution-and-measurement procedure. We analyze the undesired state transitions and the robustness of our protocol against the systematic errors from the microwave driving intensity and frequency, the quantum decoherence of all components, and the crosstalk of two resonators. In addition, we demonstrate that our protocol can be extended to a similar scenario with a $\mathrm{\ensuremath{\Xi}}$-type qutrit.

Experimental full-domain mapping of quantum correlation in Clauser-Horne-Shimony-Holt scenarios.

Quantum correlation between two parties serves as an important resource in the surging applications of quantum information. The Bell nonlocality and quantum steering have been proposed to describe non-classical correlations against local-hidden-variable and local-hidden-state theories, respectively. To characterize the two types of non-classical correlations, various nonlocality and steering inequalities have been established, and the amount of inequality violation serves as an important indicator for many entanglement-based tasks. Quantum state tomography has been employed for measuring quantum states, while the method requires intensive computation and does not directly verify either nonlocality or steering over the full domain independent of established theories. Here, we experimentally map the full-domain correlation with bipartite states for nonlocality and quantum steering in CHSH scenarios. The measurement of the maps automatically accounts for detection imperfections. Furthermore, we demonstrate the application of the correlation maps in the entanglement-based quantum key distribution protocol with arbitrary bipartite states. The correlation maps show direct measurements and simple interpretations that can answer fundamental questions about nonlocality and quantum steering as well as contribute to quantum information applications in a straightforward manner.

Visually capture quantum nonlocalities through quantum steering ellipsoid

Quantum steering ellipsoid (QSE) can faithfully characterize arbitrary bipartite state, and provide a new method to visually investigate and capture various quantum nonlocalities. Note that the dissipation of quantum nonlocalities can be accelerated by the coupling between the system and the decoherence channel, which induces great challenges in detecting quantum nonlocalities. Herein, considering the scenario in which the subsystem of a two-qubit system is coupled with a decoherence channel, the quantum discord (QD) and concurrence are visually characterized and detected by employing the QSE. The results reveal that the QSE y and z semiaxes are responsible for the traits of the QD and concurrence under the bit flip channel. The x and y semiaxes dominate and visualize the QD and concurrence under the phase damping channel. Of particular note is that one can realize the detections of the QD and concurrence via the shape of the QSE. To be clearer, the disappearance of the QD can be ascertained according to a needle-shaped QSE or a vanishing QSE in the Bloch sphere. In contrast, one can witness the concurrence if the total semiaxis length is greater than one. Beyond this, our results visually reveal that quantum entanglement is a stronger quantum nonlocality than the QD from the perspective of geometry, and thus deepens the understanding of the quantum nonlocality.

Chiral-dissipation-assisted generation of entanglement and asymmetric Gaussian steering in a driven cascaded quantum network

We study the dissipative dynamics and the formation of entangled states in a driven cascaded quantum network, where a cascaded double-cavity optomechanical system is coupled to a common unidirectional optical fiber. In terms of two coherent laser fields simultaneously driving the chiral coupling system, the entanglement can be effectively transferred from the light to two nanomechanical resonators (NMRs) through cavity modes based on the completely destructive interference of quantum noise. By adjusting the relative strength ratio of red- and blue-detuned pump lasers, it is found that the two NMRs can be driven into a mixed two-mode Gaussian entangled mechanical state rather than a non-Gaussian entangled dark state or a pure entangled dark state. If the frequency of the NMR is tuned to be much larger than the chiral coupled-cavity-chain damping rate, it is demonstrated that the chiral dissipative cascaded system can always realize one-way Einstein-Podolsky-Rosen (EPR) steering from one mechanical oscillator to the other, while the reverse one-way EPR steering is impossible to obtain, and the reason for achieving asymmetric Gaussian steering is analyzed. Furthermore, a simple one-way EPR steering criterion based on two-photon correlation can be achieved for an arbitrary bipartite Gaussian state under the standard form of EPR steering, and the effect of mechanical thermal noise on the steering is also discussed. Moreover, the present chiral system can be realized with currently available experimental technology; therefore, we hope that it can be very helpful for potential applications in quantum computation and quantum communication.

Quantification of quantumness in neutrino oscillations

Neutrino oscillation is an important physical phenomenon in elementary particle physics, and its nonclassical features can be revealed by the Leggett–Garg inequality. It shows that its quantum coherence can be sustained over astrophysical length scales. In this work, we investigate the measure of quantumness in experimentally observed neutrino oscillations via the nonlocal advantage of quantum coherence (NAQC), quantum steering, and Bell nonlocality. From various neutrino sources, ensembles of reactor and accelerator neutrinos are analyzed at distinct energies, such as Daya Bay (0.5 km and 1.6 km) and MINOS (735 km) collaborations. The NAQC of two-flavor neutrino oscillation is characterized experimentally compared to the theoretical prediction. It exhibits non-monotonously evolutive phenomenon with the increase of energy. Furthermore, it is found that the NAQC is a stronger quantum correlation than quantum steering and Bell nonlocality even in the order of km. Hence, for an arbitrary bipartite neutrino-flavor state with achieving a NAQC, it must be also a steerable and Bell nonlocal state. The results might offer an insight into the neutrino oscillation for the further applications on quantum information processing.

Measurability of D-concurrence

An effective approach to quantify entanglement of any bipartite systems is D-concurrence, which is important in quantum information science. In this paper, we present a direct method for experimental determination of the D-concurrence of an arbitrary bipartite pure state. To do this, we show that measurement of the D-concurrence of bipartite pure state can be conversed into the measurement performed on some observables so called generalized Gell-Mann operators. We first introduce the concept of D-concurrence for a bipartite system. Then we explain the method of measuring this entanglement measure for the pure state. Finally, for clarify of the subject, we give an example consisting of two parties A and B with dimensions 3.

Dynamics of initially correlated open quantum systems: Theory and applications

We show that the dynamics of any open quantum system that is initially correlated with its environment can be described by a set of (or less) completely positive maps, where d is the dimension of the system. Only one such map is required for the special case of no initial correlations. The same maps describe the dynamics of any system-environment state obtained from the initial state by a local operation on the system. The reduction of the system dynamics to a set of completely positive maps allows known numerical and analytic tools for uncorrelated initial states to be applied to the general case of initially correlated states, which we exemplify by solving the qubit dephasing model for such states, and provides a natural approach to quantum Markovianity for this case. We show that this set of completely positive maps can be experimentally characterised using only local operations on the system, via a generalisation of noise spectroscopy protocols. As further applications, we first consider the problem of retrodicting the dynamics of an open quantum system which is in an arbitrary state when it becomes accessible to the experimenter, and explore the conditions under which retrodiction is possible. We also introduce a related one-sided or limited-access tomography protocol for determining an arbitrary bipartite state, evolving under a sufficiently rich Hamiltonian, via local operations and measurements on just one component. We simulate this protocol for a physical model of particular relevance to nitrogen-vacancy centres, and in particular show how to reconstruct the density matrix of a set of three qubits, interacting via dipolar coupling and in the presence of local magnetic fields, by measuring and controlling only one of them.

Einstein-Podolsky-Rosen steering and entanglement based on two-photon correlation for bipartite Gaussian states

We propose and demonstrate a standard form of Einstein-Podolsky-Rosen (EPR) steering for an arbitrary bipartite Gaussian state under which a simple EPR steering criterion for two-photon correlation can be achieved. In terms of a beam splitter preparing three different steerable states, we further test that the simplified criterion is reliable and efficient when it is used to determine whether an arbitrary bipartite Gaussian state is steerable or not. Based on the same theoretical framework, the standard form and criterion of entanglement are reconstructed and discussed. Furthermore, it is found that EPR steering requires stronger two-photon correlation than entanglement, while its direction is strictly dependent on the mean photon number of two light modes. Moreover, the inherent asymmetric feature can be intuitively embodied in the corresponding criteria, and the essential difference and inherent relation between two standard forms is revealed. We hope the present results could be helpful for potential applications in quantum information processing.

Fidelity-based measurement-induced nonlocality over two-sided measurements

In this paper, we introduce fidelity-based measurement-induced nonlocality for bipartite quantum state to capture the nonlocal effects due to two-sided von Neumann projective measurements. We identify that all the properties of this quantity are reflected from that of One-sided measurement. We compute this quantity for arbitrary pure and mixed bipartite states. As an illustration, we have studied the nonlocality of Bell diagonal state.

Role of quantum coherence in the thermodynamics of energy transfer.

Recent research on the thermodynamic arrow of time, at the microscopic scale, has questioned the universality of its direction. Theoretical studies showed that quantum correlations can be used to revert the natural heat flow (from the hot body to the cold one), posing an apparent challenge to the second law of thermodynamics. Such an "anomalous" heat current was observed in a recent experiment (K. Micadei et al., arXiv:1711.03323), by employing two spin systems initially quantum correlated. Nevertheless, the precise relationship between this intriguing phenomenon and the initial conditions that allow it is not fully evident. Here, we address energy transfer in a wider perspective, identifying a nonclassical contribution that applies to the reversion of the heat flow as well as to more general forms of energy exchange. We derive three theorems that describe the energy transfer between two microscopic systems, for arbitrary initial bipartite states. Using these theorems, we obtain an analytical bound showing that certain type of quantum coherence can optimize such a process, outperforming incoherent states. This genuine quantum advantage is corroborated through a characterization of the energy transfer between two qubits. For this system, it is shown that a large enough amount of coherence is necessary and sufficient to revert the thermodynamic arrow of time. As a second crucial consequence of the presented theorems, we introduce a class of nonequilibrium states that only allow unidirectional energy flow. In this way, we broaden the set where the standard Clausius statement of the second law applies.

Double Dilation ≠ Double Mixing (extended abstract)

Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of 'doubled kets' (i.e. mixing), and by tracing out part of a 'doubled' two-system ket (i.e. dilation). Both constructions can be iterated, yielding new mathematical species that have already found applications outside physics. However, as we show in this paper, the iterated constructions no longer yield the same mathematical species. Hence, the constructions 'mixing' and 'dilation' themselves are by no means equivalent. Concretely, when applying the Choi-Jamiolkowski isomorphism to the second iteration, dilation produces arbitrary symmetric bipartite states, while mixing only yields the disentangled ones. All results are proven using diagrams, and hence they hold not only for quantum theory, but also for a much more general class of process theories.

A Necessary and Sufficient Criterion for the Separability of Quantum State

Quantum entanglement has been regarded as one of the key physical resources in quantum information sciences. However, the determination of whether a mixed state is entangled or not is generally a hard issue, even for the bipartite system. In this work we propose an operational necessary and sufficient criterion for the separability of an arbitrary bipartite mixed state, by virtue of the multiplicative Horn’s problem. The work follows the work initiated by Horodecki et al. and uses the Bloch vector representation introduced to the separability problem by J. De Vicente. In our criterion, a complete and finite set of inequalities to determine the separability of compound system is obtained, which may be viewed as trade-off relations between the quantumness of subsystems. We apply the obtained result to explicit examples, e.g. the separable decomposition of arbitrary dimension Werner state and isotropic state.

Evaluation of entanglement measures by a single observable

We present observable lower bounds for several bipartite entanglement measures including entanglement of formation, geometric measure of entanglement, concurrence, convex-roof extended negativity, and G-concurrence. The lower bounds facilitate estimates of these entanglement measures for arbitrary finite-dimensional bipartite states. Moreover, these lower bounds can be calculated analytically from the expectation value of a single observable. Based on our results, we use several real experimental measurement data to get lower bounds of entanglement measures for these experimentally realized states. In addition, we also study the relations between entanglement measures.

Generalized geometric measure of entanglement for multiparty mixed states

Computing entanglement of an arbitrary bipartite or multipartite mixed state is in general not an easy task as it usually involves complex optimization. Here we show that exploiting symmetries of certain mixed states, we can compute a genuine multiparty entanglement measure, the generalized geometric measure for these classes of mixed states. The chosen states have different ranks and consist of an arbitrary number of parties.

Entanglement-fluctuation relation for bipartite pure states

We identify subsystem fluctuations (variances) that measure entanglement in an arbitrary bipartite pure state. These fluctuations are of observables that generalize the notion of polarization to an arbitrary N-level subsystem. We express this polarization fluctuation in terms of subsystem purity and other entanglement measures. The derived fluctuation-entanglement relation is evaluated for the ground states of a one-dimensional free fermion gas and the Affleck-Kennedy-Lieb-Tasaki spin chain. Our results provide a framework for experimentally measuring entanglement using Stern-Gerlach-type state selectors.

Universal Steering Criteria.

We propose a general framework for constructing universal steering criteria that are applicable to arbitrary bipartite states and measurement settings of the steering party. The same framework is also useful for studying the joint measurement problem. Based on the data-processing inequality for an extended Rényi relative entropy, we then introduce a family of steering inequalities, which detect steering much more efficiently than those inequalities known before. As illustrations, we show unbounded violation of a steering inequality for assemblages constructed from mutually unbiased bases and establish an interesting connection between maximally steerable assemblages and complete sets of mutually unbiased bases. We also provide a single steering inequality that can detect all bipartite pure states of full Schmidt rank. In the course of study, we generalize a number of results intimately connected to data-processing inequalities, which are of independent interest.

Quantifying nonclassicality of correlations based on the concept of nondisruptive local state identification

A bipartite state is classical with respect to party $A$ if and only if party $A$ can perform nondisruptive local state identification (NDLID) by a projective measurement. Motivated by this we introduce a class of quantum correlation measures for an arbitrary bipartite state. The measures utilize the general Schatten $p$-norm to quantify the amount of departure from the necessary and sufficient condition of classicality of correlations provided by the concept of NDLID. We show that for the case of Hilbert-Schmidt norm, i.e. $p=2$, a closed formula is available for an arbitrary bipartite state. The reliability of the proposed measures is checked from the information theoretic perspective. Also, the monotonicity behavior of these measures under LOCC is exemplified. The results reveal that for the general pure bipartite states these measures have an upper bound which is an entanglement monotone in its own right. This enables us to introduce a new measure of entanglement, for a general bipartite state, by convex roof construction. Some examples and comparison with other quantum correlation measures are also provided.

Quantum Nonlocality of Arbitrary Dimensional Bipartite States.

We study the nonlocality of arbitrary dimensional bipartite quantum states. By computing the maximal violation of a set of multi-setting Bell inequalities, an analytical and computable lower bound has been derived for general two-qubit states. This bound gives the necessary condition that a two-qubit state admits no local hidden variable models. The lower bound is shown to be better than that from the CHSH inequality in judging the nonlocality of some quantum states. The results are generalized to the case of high dimensional quantum states, and a sufficient condition for detecting the non-locality has been presented.

Tensor networks and graphical calculus for open quantum systems

We describe a graphical calculus for completely positive maps and in doing so review the theory of open quantum systems and other fundamental primitives of quantum information theory using the language of tensor networks. In particular we demonstrate the construction of tensor networks to pictographically represent the Liouville-superoperator, Choi-matrix, process-matrix, Kraus, and system-environment representations for the evolution of quantum states, review how these representations interrelate, and illustrate how graphical manipulations of the tensor networks may be used to concisely transform between them. To further demonstrate the utility of the presented graphical calculus we include several examples where we provide arguably simpler graphical proofs of several useful quantities in quantum information theory including the composition and contraction of multipartite channels, a condition for whether an arbitrary bipartite state may be used for ancilla assisted process tomography, and the derivation of expressions for the average gate fidelity and entanglement fidelity of a channel in terms of each of the different representations of the channel.