Two-qubit States Research Articles

Stronger EPR-steering criterion based on inferred Schrödinger–Robertson uncertainty relation

Steering is one of the three in-equivalent forms of nonlocal correlations intermediate between Bell nonlocality and entanglement. Schrödinger–Robertson uncertainty relation (SRUR), has been widely used to detect entanglement and steering. However, the steering criterion in earlier works, based on SRUR, did not involve complete inferred-variance uncertainty relation. In this paper, by considering the local hidden state model and Reid’s formalism, we derive a complete inferred-variance EPR-steering criterion based on SRUR in the bipartite scenario. Furthermore, we check the effectiveness of our steering criterion with discrete variable bipartite two-qubit and two-qutrit isotropic states.

Quantum Fisher information in moving reference frame

In the field of quantum metrology, an important application is quantum parameter estimation. As the fundamental theory of quantum parameter estimation, quantum Cramér-Rao inequality shows that the variance of parameter estimation is determined by the inverse of quantum Fisher information. Higher quantum Fisher information corresponds to a lower variance, thereby improving the precision of parameter estimation. Quantum Fisher information has been extensively investigated in many aspects of non-relativistic quantum mechanics, including entanglement structure detection, quantum teleportation, quantum phase transition, quantum chaos, and quantum computation. However, there are few researches considering the influence of relativistic effect on quantum Fisher information, and therefore, we attempt to investigate this topic in this work. The relativistic transformation of particle states is employed, and the quantum Fisher information about amplitude parameter <inline-formula><tex-math id="M3">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M3.png"/></alternatives></inline-formula> and phase parameter <inline-formula><tex-math id="M4">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M4.png"/></alternatives></inline-formula> are investigated in moving reference frame. In this work, the parameters to be estimated are encoded into the spin degree of freedom, and the pure single-qubit state and the pure two-qubit state are both considered. The quantum Fisher information about <inline-formula><tex-math id="M5">\begin{document}$ \theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M5.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M6">\begin{document}$\varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M6.png"/></alternatives></inline-formula> of single-qubit state and two-qubit state in moving reference frame are numerically calculated, respectively. It can be observed that the quantum Fisher information is associated with rapidity, amplitude parameter, and the ratio of the width to the particle mass <inline-formula><tex-math id="M7">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M7.png"/></alternatives></inline-formula>. The quantum Fisher information of the estimated parameters decreases with rapidity increasing for both single-qubit state and two-qubit state. As rapidity approaches infinity, i.e. increases to the speed of light, the quantum Fisher information reaches to a constant which decreases as the ratio <inline-formula><tex-math id="M8">\begin{document}${{{\sigma _r}} \mathord{\left/ {\vphantom {{{\sigma _r}} m}} \right. } m}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M8.png"/></alternatives></inline-formula> increases. More importantly, for the phase parameter <inline-formula><tex-math id="M9">\begin{document}$ \varphi $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M9.png"/></alternatives></inline-formula>, it is observed that the quantum Fisher information of two-qubit state reduces more significantly than that of single-qubit state. While, for the amplitude parameter <inline-formula><tex-math id="M10">\begin{document}$\theta $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231394_M10.png"/></alternatives></inline-formula>, the quantum Fisher information of two-qubit state is greater than that of single-qubit state. These results are useful and valuable for improving the precision of parameter estimation under the influence of relativistic effect.

Parameterized entanglement measures based on Rényi-<i>α</i> entropy

Parameterized entanglement measures have demonstrated their superiority compared with kinds of unparameterized entanglement measures. Entanglement concurrence has been widely used to describe entanglement in quantum experiments. As an entanglement measure it is related to specific quantum Rényi-<i>α</i> entropy. In the work, we propose a parameterized bipartite entanglement measure based on the general Rényi-<i>α</i> entropy, which is named <i>α</i>-logarithmic concurrence. This measure, different from existing parameterized measures, is defined first for pure states, then extended to the mixed states. Furthermore, we verify three necessary conditions for <i>α</i>-logarithmic concurrence to satisfy the entanglement measures. We show that this measure is easy to calculate for pure states. However, for mixed states, analytical calculations are only suitable for special two-qubit states or special higher-dimensional mixed states. Therefore, we devote our efforts to developing the analytical lower bound of the-logarithmic concurrence for general bipartite states. Surprisingly, this lower bound is a function on positive partial transposition criterion and realignment criterion of this mixed state. This shows the connection among the three entanglement measures. The interesting feature is that the lower bound depends on the entropy parameter associated with the detailed state. This allows us to choose appropriate parameter <i>α</i> such that <inline-formula><tex-math id="M3">\begin{document}$ G_\alpha({\boldsymbol{\rho}})\gg0$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M3.png"/></alternatives></inline-formula> for experimental entanglement detection of specific state <i>ρ</i>. Moreover, we calculate expressions of the <i>α</i>-logarithmic concurrence for isotropic states, and give a the analytic expressions for isotropic states with <inline-formula><tex-math id="M4">\begin{document}$ d = 2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="4-20231503_M4.png"/></alternatives></inline-formula>. Finally, the monogamy of the <i>α</i>-logarithmic concurrence is also discussed. We set up a mathematical formulation for the monogamous property in terms of <i>α</i>-logarithmic concurrence. Here we set up the functional relation between concurrence and <i>α</i>-logarithmic concurrence in two qubit systems. Then we obtain some useful properties of this function, and by combining the Coffman–Kundu–Wootters (CKW) inequality, we establish the monogamy inequality about <i>α</i>-logarithmic concurrence. We finally prove that the monogamy inequality holds true for <i>α</i>-logarithmic concurrence.

Optimal teleportation fidelity and its deviation in noisy scenarios

In this work, we study quantum teleportation, a fundamental protocol of quantum physics. In particular, we present a mathematical methodology to study the combined effects of noisy resource state and noisy classical communication on teleportation fidelity and its deviation. We describe a teleportation protocol where an arbitrary two-qubit state in canonical form is used as a resource. Thereafter, to teleport an unknown qubit, Alice measures her qubits in Bell basis and conveys the measurement outcome to Bob via noisy classical channel(s). We derive the exact formulae of optimal teleportation fidelity and corresponding fidelity deviation where the resource state and the classical communication, both can be noisy. To provide the proof of optimality, we provide a systematic method. We further find conditions for non-classical fidelity and dispersion-free teleportation for our teleportation protocol. In this way, we identify noisy environments where it is possible to achieve dispersion-free teleportation without compromising non-classical fidelity. We also demonstrate scenarios where the increase of entanglement in the resource state, may degrade the quality of teleportation — a counter-intuitive instance. Finally, we discuss about the minimum classical communication cost required to achieve non-classical fidelity for our protocol. Here we mainly focus on a possible way to optimize the classical communication cost.

Nonlocality of two-qubit states of a nuclear spin-3/2

Nonlocality of two-qubit states of a nuclear spin-3/2

Transformation of Bell states using linear optics

Bell states form a complete set of four maximally polarization entangled two-qubit quantum state. Being a key ingredient of many quantum applications such as entanglement based quantum key distribution protocols, superdense coding, quantum teleportation, entanglement swapping etc, Bell states have to be prepared and measured. Spontaneous parametric down-conversion (SPDC) is the easiest way of preparing Bell states and a desired Bell state can be prepared from any entangled photon pair through single-qubit logic gates. In this paper, we present the generation of complete set of Bell states, only by applying unitary transformations of half-wave plate (HWP) on the initial Bell state. The initial Bell state is prepared using a combination of a nonlinear crystal and a beam-splitter (BS) and the rest of the Bell states are created by applying single-qubit logic gates on the entangled photon pairs using HWPs. Our results can be useful in many quantum applications, especially in superdense coding where control over basis of maximally entangled state is required.

Programmable heralded linear optical generation of two-qubit states

Programmable heralded linear optical generation of two-qubit states

Improving the capacity of quantum dense coding via non-Hermitian operation

We propose a novel method to enhance the capacity of quantum dense coding under amplitude damping noise using non-Hermitian operations. With the assistance of non-Hermitian operations, we show that the capacity of quantum dense coding can always be larger than 1 for any two-qubit states. In particular, the non-Hermitian operation can improve quantum dense coding more efficiently in the case of strong decoherence strength than those with small decoherence strength. Our results shed new light on the protection of quantum dense coding in a quantum environment.

Distribution dynamics of fisher and Wigner–Yanase information correlations of two qubits coupled to an open superconducting cavity

In this paper, we explore distribution dynamics of two-qubit Fisher and skew information correlations of a dissipative microwave cavity field interacting with two charged superconducting qubits. Besides the negativity function, non-classical correlations beyond entanglement are studied using local quantum Fisher information (LQFI) and local quantum uncertainty (LQU). We find that the two-qubit non-classical correlations are sensitive to qubit–qubit distribution angle, two-qubit dissipation parameter, and initial coherent state intensity. The phenomena of frozen quantum correlations, sudden death or birth, as well as revival dynamical maps are feasible in the current two-qubit state when exposed to a microwave cavity. The non-classical correlations and entanglement have been found damped under the two-qubit dissipation appearance in the field. For the increasing strength of coherence intensity of the field, the two-qubit non-classical correlations functions remain to emerge quickly and oscillate with higher frequency, although with the least amplitudes. Interestingly, unlike the non-classical correlations, negativity does not emerge against higher coherence strengths of the cavity and remains completely zero. Finally, for the least dissipation and higher coherence strength, one can readily generate non-classical two-qubit states employing a microwave cavity.

Neural Network Approach to the Simulation of Entangled States with One Bit of Communication

Bell's theorem states that Local Hidden Variables (LHVs) cannot fully explain the statistics of measurements on some entangled quantum states. It is natural to ask how much supplementary classical communication would be needed to simulate them. We study two long-standing open questions in this field with neural network simulations and other tools. First, we present evidence that all projective measurements on partially entangled pure two-qubit states require only one bit of communication. We quantify the statistical distance between the exact quantum behaviour and the product of the trained network, or of a semianalytical model inspired by it. Second, while it is known on general grounds (and obvious) that one bit of communication cannot eventually reproduce all bipartite quantum correlation, explicit examples have proved evasive. Our search failed to find one for several bipartite Bell scenarios with up to 5 inputs and 4 outputs, highlighting the power of one bit of communication in reproducing quantum correlations.

Sharing quantum nonlocality in the noisy scenario

It was showed in [Phys. Rev. Lett. 125 090401 (2020)] that there exist unbounded number of independent Bobs who can share quantum nonlocality with a single Alice by performing sequentially measurements on the Bob’s half of the maximally entangled pure two-qubit state. However, from practical perspectives, errors in entanglement generation and noises in quantum measurements will result in the decay of nonlocality in the scenario. In this paper, we analyze the persistency and termination of sharing nonlocality in the noisy scenario. We first obtain the two sufficient conditions under which there exist n independent Bobs who can share nonlocality with a single Alice under noisy measurements and the noisy initial two qubit entangled state. Analyzing the two conditions, we find that the influences on persistency under different kinds of noises can cancel each other out. Furthermore, we describe the change patterns of the maximal nonlocality-sharing number under the influence of different noises. Finally, we extend our investigation to the case of arbitrary finite-dimensional systems.

Quantum teleportation and phase quantum estimation in a two-qubit state influenced by dipole and symmetric cross interactions

In this paper, we address the problem of quantum teleportation in single and two-qubit scenarios based on the Heisenberg XYZ two-qubit chain model under the influence of atomic dipole and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEWA) interactions. Using the concepts of fidelity threshold and average fidelity in classical and quantum, we reveal the effectiveness of the current channel to remain in the quantum limits. In addition, we investigate the quantum estimation of the encoded phase in single and two-qubit scenarios at the teleportation destination. By using different variables of the system, the average fidelity of the quantum teleportation and the quantum estimation of the encoded phase in one and two teleported qubit(s) can be improved.

Experimental discrimination of two-qubit orthogonal states via local operations and classical communication

Experimental discrimination of two-qubit orthogonal states via local operations and classical communication

Dynamics of two-qubit Heisenberg XY state: external magnetic field and intrinsic decoherence effects

Dynamics of two-qubit Heisenberg XY state: external magnetic field and intrinsic decoherence effects

Bidirectional field-steering and atomic steering induced by a magnon mode in a qubit-photon system

This paper investigates the cavity–magnon steering and qubit–qubit steering of a hybrid quantum system consisting of a single-mode magnon, a two-qubit state, and a single-mode cavity field in the presence of their damping rates. The temporal wave vector of the system is obtained for the initial maximally entangled two-qubit state and initial vacuum state of the magnon and cavity modes. Additionally, the mathematical inequalities for obtaining the cavity–magnon steering and qubit–qubit steering are introduced. The findings reveal that steering between the magnon and cavity is asymmetric, while steering between the two qubits is symmetric in our system. Increasing the atom–field coupling improves steering from magnon to field, while reducing steering between the two qubits. Moreover, increasing magnon–field coupling enhances and elevates the lower bounds of qubit–qubit steering. Further, adding the damping rates causes deterioration of the cavity–magnon steering and qubit–qubit steering. However, the steering persistence is slightly greater when damping originates from the cavity field rather than the magnon modes based on the coupling parameters.

The quantum communication efficiency of the fractional anti-Jaynes–Cummings model

The efficiency of the fractional state that is generated between a single atom and field by using anti-Jaynes–Cummings model (AJCM) is discussed. The fractional degree and the interaction parameters may be used as controllers to increase the efficiency of the fractional state in the context of quantum communication. It has been shown that, the quantum correlation, capacity, and the ability of the fractional state, increase suddenly/gradually at small/large fractional degree, respectively. At small fractional orders, the constant behavior for all these phenomena is displayed at a short interaction time. The fractional quantum state that is generated by the anti-Jaynes–Cummings model is more efficient than that generated by the well-known Jaynes–Cummings model (JCM), where it can be used to teleport an unknown two-qubit state with larger fidelity.

Asymmetric bidirectional quantum qubit teleportation scheme via six-qubit Bell-cluster state

Using a six-qubit Bell-cluster state, we proposed an asymmetric bidirectional quantum teleportation scheme. Two participants Anne and Benson are both the sender and receiver. Only applying Bell-state measurement, single- and two-qubit unitary operations as well as classical communication, Anne can transmit an arbitrary two-qubit unknown state to Benson, meanwhile Benson can also send an arbitrary single-qubit unknown state to Anne. Analysis shows that our scheme is feasible with the present experiment technologies.

Noise induced dynamics of two-qubit entangled Bell’s states

The stability of different types two-qubit entangled states was analyzed by a direct calculations of the time dependent probability to find the system in its initial state in the presence of Gaussian noise. The entangled states time evolution was studied in the presence of both classical and quantum noise. It was demonstrated that one pair of Bell’s states is robust to the Gaussian fluctuations, while the another one decays. The decay law of unstable entangled states is determined by the noise correlation function. The developed general formalism was applied for analysis the dynamics of entangled states in the presence of fluctuations produced by the electron–phonon interaction. It was revealed that unstable entangled states interacting with phonon bath can demonstrate the crossover between short time exponential decay law and long time power law decay. Obtained results can be effectively exploited for quantum computation, in which it is essential to be able to retrieve information about the initial quantum state even in the presence of interaction with the environment.

Entanglement witness measurement of time-bin two-qubit states using fiber-based Franson interferometers

Entanglement, that is, quantum correlations that do not have a classical counterpart, is a precondition to establishing communication protocols beyond the existing classical protocols, such as quantum key distribution, that achieves a higher level of security without computational assumptions. In this work, we present a proof of demonstration of detecting various entangled states, prepared by time-bin encoding with photons that are natural resources for long-distance quantum communication. We generate a maximally entangled state in time-bin qubits and verify the state in two ways. We first consider measurements that realize entanglement witnesses for the verification of entanglement. We then perform a quantum state tomography for the full characterization. Experimental resources are also discussed.

Sufficient conditions for quantum advantage in random access code protocols with two-qubit states

Sufficient conditions for quantum advantage in random access code protocols with two-qubit states