Classification of four qubit states and their stabilisers under SLOCC operations

We classify four qubit states under SLOCC operations, that is, we classify the orbits of the group SL(2,C)^4 on the Hilbert space H_4 = (C^2)^{\otimes 4}. We approach the classification by realising this representation as a symmetric space of maximal rank. We first describe general methods for classifying the orbits of such a space. We then apply these methods to obtain the orbits in our special case, resulting in a complete and irredundant classification of SL(2,C)^4-orbits on H_4. It follows that an element of H_4 is conjugate to an element of precisely 87 classes of elements. Each of these classes either consists of one element or of a parametrised family of elements, and the elements in the same class all have equal stabiliser in SL(2,C)^4. We also present a complete and irredundant classification of elements and stabilisers up to the action of the semidirect product Sym_4\ltimes\SL(2,C)^4 where Sym_4 permutes the four tensor factors of H_4.

Robustness of two-qubit and three-qubit states in correlated quantum channels

We investigate how the correlated actions of quantum channels affect the robustness of entangled states. We consider the Bell-like state and random two-qubit pure states in the correlated depolarizing, bit flip, bit-phase flip, and phase flip channels. It is found that the robustness of two-qubit pure states can be noticeably enhanced due to the correlations between consecutive actions of these noisy channels, and the Bell-like state is always the most robust state. We also consider the robustness of three-qubit pure states in correlated noisy channels. For the correlated bit flip and phase flip channels, the result shows that although the most robust and most fragile states are locally unitary equivalent, they exhibit different robustness in different correlated channels, and the effect of channel correlations on them is also significantly different. However, for the correlated depolarizing and bit-phase flip channels, the robustness of two special three-qubit pure states is exactly the same. Moreover, compared with the random three-qubit pure states, they are neither the most robust states nor the most fragile states.

Dynamical second-order noise sweetspots in resonantly driven spin qubits

Quantum dot-based quantum computation employs extensively the exchange interaction between nearby electronic spins in order to manipulate and couple different qubits. The exchange interaction, however, couples the qubit states to charge noise, which reduces the fidelity of the quantum gates that employ it. The effect of charge noise can be mitigated by working at noise sweetspots in which the sensitivity to charge variations is reduced. In this work we study the response to charge noise of a double quantum dot based qubit in the presence of ac gates, with arbitrary driving amplitudes, applied either to the dot levels or to the tunneling barrier. Tuning with an ac driving allows to manipulate the sign and strength of the exchange interaction as well as its coupling to environmental electric noise. Moreover, we show the possibility of inducing a second-order sweetspot in the resonant spin-triplet qubit in which the dephasing time is significantly increased.

Controlling the dynamics of ultracold polar molecules in optical tweezers

Ultracold molecules trapped in optical tweezers show great promise for the implementation of quantum technologies and precision measurements. We study a prototypical scenario where two interacting polar molecules placed in separate traps are controlled using an external electric field. This, for instance, enables a quantum computing scheme in which the rotational structure is used to encode the qubit states. We estimate the typical operation timescales needed for state engineering to be in the range of few microseconds. We further underline the important role of the spatial structure of the two-body states, with the potential for significant gate speedup employing trap-induced resonances.

Current biased gradiometric flux qubit in a circuit-QED architecture

We propose a scheme for controlling the gradiometric flux qubit (GFQ) by applying an ac bias current in a circuit-QED architecture. The GFQ is insensitive to the magnetic flux fluctuations, which at the same time makes it challenging to manipulate the qubit states by an external magnetic field. In this study, we demonstrate that an ac bias current applied to the $\alpha$-junction of the GFQ can control the qubit states. Further, the present scheme is robust against the charge fluctuation as well as the magnetic flux fluctuations, promising a long coherence time for quantum gate operations. We introduce a circuit-QED architecture to perform the single and two-qubit operations with a sufficiently strong coupling strength.

Quantum Private Comparison of Arbitrary Single Qubit States Based on Swap Test

In this paper, by using swap test, a quantum private comparison (QPC) protocol of arbitrary single qubit states with a semi-honest third party is proposed. The semi-honest third party (TP) is required to help two participants perform the comparison. She can record intermediate results and do some calculations in the whole process of the protocol execution, but she cannot conspire with any participants. In the process of comparison, TP cannot get two participants' private information except the comparison results. According to the security analysis, the proposed protocol can resist both outsider attacks and participant attacks. Compared with the existing QPC protocols, the proposed one does not require any entanglement swapping technology, and it can compare two participants' qubits by performing swap test, which is easier to implement with current technology. Meanwhile, the proposed protocol can compare secret integers. It encodes secret integers into the amplitude of quantum state rather than transfer them as binary representations, and the encoded quantum state is compared by performing swap test. Additionally, the proposed QPC protocol is extended to the QPC of arbitrary single qubit states by using multi-qubit swap test.

Less entanglement exhibiting more nonlocality with noisy measurements

The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.

Quantum Contextual Advantage Depending on Nonzero Prior Probabilities in State Discrimination of Mixed Qubit States

Recently, Schmid and Spekkens studied the quantum contextuality in terms of state discrimination. By dealing with the minimum error discrimination of two quantum states with identical prior probabilities, they reported that quantum contextual advantage exists. Meanwhile, if one notes a striking observation that the selection of prior probability can affect the quantum properties of the system, it is necessary to verify whether the quantum contextual advantage depends on the prior probabilities of the given states. In this paper, we consider the minimum error discrimination of two states with arbitrary prior probabilities, in which both states are pure or mixed. We show that the quantum contextual advantage in state discrimination may depend on the prior probabilities of the given states. In particular, even though the quantum contextual advantage always exists in the state discrimination of two nonorthogonal pure states with nonzero prior probabilities, the quantum contextual advantage depends on prior probabilities in the state discrimination of two mixed states.

Experimental Certification of Quantum Entanglement Based on the Classical Complementary Correlations of Two-Qubit States

Quantum entanglement is one of the essential resources in quantum information processing. It is of importance to verify whether a quantum state is entangled. At present, a typical quantum certification focused on the classical correlations has attracted widespread attention. Here, we experimentally investigate the relation between quantum entanglement and the classical complementary correlations based on the mutual information, Pearson correlation coefficient and mutual predictability of two-qubit states. Our experimental results show the classical correlations for complementary properties have strong resolution capability to verify entanglement for two qubit pure states and Werner states. We find that the resolution capability has great performance improvement when the eigenstates of the measurement observables constitute a complete set of mutually unbiased bases. For Werner states in particular, the classical complementary correlations based on the Pearson correlation coefficient and mutual predictability can provide the ultimate bounds to certify entanglement.