Two-qubit States Research Articles

Strong entanglement criteria for mixed states, based on uncertainty relations

We propose an entanglement criterion, specially designed for mixed states, based on uncertainty relation and the Wigner–Yanase skew information. The variances in this uncertainty relation do not involve any classical mixing uncertainty, and is therefore purely of quantum mechanical nature. We show that a large class of mixed entangled states can be characterized by our criterion. We demonstrate its utility for several generalized mixed entangled state including two-qubit and two-qutrit Werner states and it turns out, for the states discussed in this paper, to be stronger than any other known criterion in identifying the correct domain of relevant parameters for entanglement. The relevant uncertainty relation reduces to the Schrodinger–Robertson inequality for pure states.

Quantifying concurrence of two-qubit quantum states on a quantum computer

Quantifying concurrence of two-qubit quantum states on a quantum computer

Suppressing Decoherence in Quantum State Transfer with Unitary Operations.

Decoherence is the fundamental obstacle limiting the performance of quantum information processing devices. The problem of transmitting a quantum state (known or unknown) from one place to another is of great interest in this context. In this work, by following the recent theoretical proposal, we study an application of quantum state-dependent pre- and post-processing unitary operations for protecting the given (multi-qubit) quantum state against the effect of decoherence acting on all qubits. We observe the increase in the fidelity of the output quantum state both in a quantum emulation experiment, where all protecting unitaries are perfect, and in a real experiment with a cloud-accessible quantum processor, where protecting unitaries themselves are affected by the noise. We expect the considered approach to be useful for analyzing capabilities of quantum information processing devices in transmitting known quantum states. We also demonstrate the applicability of the developed approach for suppressing decoherence in the process of distributing a two-qubit state over remote physical qubits of a quantum processor.

Probabilistic resumable quantum teleportation for an arbitrary two-qubit entangled state with different quantum channels

We propose two probabilistic resumable quantum teleportation schemes for an arbitrary two-qubit entangled state with different quantum channels. The characteristic of our schemes is that the initial state in the sender’s hand can be recovered instead of being destroyed when teleportation fails, so we can improve the success probabilities by repeating the teleportation process more times. The analysis results show that the number of repetitions required for successful teleportation depends on the entanglement strength of the quantum channels, and even weak entanglement enables a high probability of success.

Protectability of IBMQ Qubits by Dynamical Decoupling Technique

We study the current effectiveness of the dynamical decoupling technique on a publicly accessible IBM quantum computer (IBMQ). This technique, also known as bang-bang decoupling or dynamical symmetrization, consists of applying sequences of pulses for protecting a qubit from decoherence by symmetrizing the qubit–environment interactions. Works in the field have studied sequences with different symmetries and carried out tests on IBMQ devices typically considering single-qubit states. We show that the simplest universal sequences can be interesting for preserving two-qubit states on the IBMQ device. For this, we considered a collection of single-qubit and two-qubit states. The results indicate that a simple dynamical decoupling approach using available IBMQ pulses is not enough for protecting a general single-qubit state without further care. Nevertheless, the technique is beneficial for the Bell states. This encouraged us to study logical qubit encodings such as |0⟩L≡|01⟩,|1⟩L≡|10⟩, where a quantum state has the form |ψab⟩=a|0⟩L+b|1⟩L. Thus, we explored the effectiveness of dynamical decoupling with a large set of two-qubit |ψab⟩ states, where a and b are real amplitudes. With this, we also determined that the |ψab⟩ states most benefiting from this dynamical decoupling approach and slowed down the decay of their survival probability.

Entanglement-assisted quantum communication with simple measurements

Dense coding is the seminal example of how entanglement can boost qubit communication, from sending one bit to sending two bits. This is made possible by projecting separate particles onto a maximally entangled basis. We investigate more general communication tasks, in both theory and experiment, and show that simpler measurements enable strong and sometimes even optimal entanglement-assisted qubit communication protocols. Using only partial Bell state analysers for two qubits, we demonstrate quantum correlations that cannot be simulated with two bits of classical communication. Then, we show that there exists an established and operationally meaningful task for which product measurements are sufficient for the strongest possible quantum predictions based on a maximally entangled two-qubit state. Our results reveal that there are scenarios in which the power of entanglement in enhancing quantum communication can be harvested in simple and scalable optical experiments.

Dynamics of quantum correlations in two 2-level atoms coupled to thermal reservoirs

In this paper, we examine the dynamics of quantum correlations in two noninteractive two-level atoms coupled to two separate identical thermal reservoirs. The two atoms are initially produced in a Gisin state, which is a blend of a maximally entangled two-qubit state and a separable mixed state. Quantum entanglement is measured by logarithmic negativity, while the nonclassical correlations are characterized by trace distance discord and local quantum uncertainty. Using the mean photon number of reservoirs and spontaneous emission rates of atoms as inputs, we explore how these quantum resources behave. Consequently, we demonstrate that the dynamics of quantum entanglement and quantum correlations depend upon the parameters driving the system. Significantly, we further demonstrate that specific parameters may be tweaked to preserve the quantum resources in the system. The results give a full grasp of the quantum features of such a two-level atomic system, showing capabilities to construct quantum technology.

Hierarchical Quantum Information Splitting of an Arbitrary Two-Qubit State Based on a Decision Tree

Quantum informatics is a new subject formed by the intersection of quantum mechanics and informatics. Quantum communication is a new way to transmit quantum states through quantum entanglement, quantum teleportation, and quantum information splitting. Based on the research of multiparticle state quantum information splitting, this paper innovatively combines the decision tree algorithm of machine learning with quantum communication to solve the problem of channel particle allocation in quantum communication, and experiments showed that the algorithm can make the optimal allocation scheme. Based on this scheme, we propose a two-particle state hierarchical quantum information splitting scheme based on the multi-particle state. First, Alice measures the Bell states of the particles she owns and tells the result to the receiver through the classical channel. If the receiver is a high-level communicator, he only needs the help of one of the low-level communicators and all the high-level communicators. After performing a single particle measurement on the z-basis, they send the result to the receiver through the classical channel. When the receiver is a low-level communicator, all communicators need to measure the particles they own and tell the receiver the results. Finally, the receiver performs the corresponding unitary operation according to the received results. In this regard, a complete hierarchical quantum information splitting operation is completed. On the basis of theoretical research, we also carried out experimental verification, security analysis, and comparative analysis, which shows that our scheme is reliable and has high security and efficiency.

Non-locality ≠ quantum entanglement

The unique entanglement measure is concurrence in a two-qubit pure state. The maximum violation of Bell’s inequality is monotonically increasing for this quantity. Therefore, people expect that pure state entanglement is relevant to the non-locality. For justification, we extend the study to three qubits. We consider all possible three-qubit operators with a symmetric permutation. When only considering one entanglement measure, the numerical result contradicts expectation. Therefore, we conclude ‘non-locality ≠ quantum entanglement’. We propose the generalized R-matrix or correlation matrix for the new diagnosis of quantum entanglement. We then demonstrate the evidence by restoring the monotonically increasing result. PACS numbers: 00.00, 20.00, 42.10

A Secured Half-Duplex Bidirectional Quantum Key Distribution Protocol against Collective Attacks

Quantum Key Distribution is a secure method that implements cryptographic protocols. The applications of quantum key distribution technology have an important role: to enhance the security in communication systems. It is originally inspired by the physical concepts associated with quantum mechanics. It aims to enable a secure exchange of cryptographic keys between two parties through an unsecured quantum communication channel. This work proposes a secure half-duplex bidirectional quantum key distribution protocol. The security of the proposed protocol is proved against collective attacks by estimating the interception of any eavesdropper with high probability in both directions under the control of the two parties. A two-qubit state encodes two pieces of information; the first qubit represents the transmitted bit and the second qubit represents the basis used for measurement. The partial diffusion operator is used to encrypt the transmitted qubit state as an extra layer of security. The predefined symmetry transformations induced by unitary in conjunction with the asymmetrical two-qubit teleportation scheme retain the protocol’s secrecy. Compared to the previous protocols, the proposed protocol has better performance on qubit efficiency.

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix \(\chi \) corresponding to various two- and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed \(\chi \) matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately 5–6 times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various J-coupling interactions.

Self-testing of different entanglement resources via fixed measurement settings

Self-testing, which refers to device independent characterization of the state and the measurement, enables the security of quantum information processing task certified independently of the operation performed inside the devices. Quantum states lie in the core of self-testing as key resources. However, for the different entangled states, usually different measurement settings should be taken in self-testing recipes. This may lead to the redundancy of measurement resources. In this work, we use fixed two-binary measurements and answer the question that what states can be self-tested with the same settings. By investigating the structure of generalized tilted-CHSH Bell operators with sum of squares decomposition method, we show that a family of two-qubit entangled states can be self-tested by the same measurement settings. The robustness analysis indicates that our scheme is feasible for practical experiment instrument. Moreover, our results can be applied to various quantum information processing tasks.

Resource-theoretic efficacy of the single copy of a two-qubit entangled state in a sequential network

How best one can recycle a given quantum resource, mitigating the various difficulties involved in its preparation and preservation, is of considerable importance for ensuring efficient applications in quantum technology. Here, we demonstrate quantitatively the resource-theoretic advantage of reusing a single copy of a two-qubit entangled state toward information processing. To this end, we consider a scenario of sequential entanglement detection of a given two-qubit state by multiple independent observers on each of the two spatially separated wings. In particular, we consider equal numbers of sequential observers on the two wings. We first determine the upper bound on the number of observers who can detect entanglement employing suitable entanglement witness operators. In terms of the parameters characterizing the entanglement consumed and the robustness of measurements, we then compare the above scenario with the corresponding scenario involving multiple pairs of entangled qubits shared among the two wings. This reveals a clear resource-theoretic advantage of recycling a single copy of a two-qubit entangled state in the sequential network.

A complementary resource relation of concurrence and roughness for a two-qubit state

Quantum resources lie at the core of quantum computation as they are responsible for the computational advantage in many tasks. The complementary relations are a pathway to understanding how the physical quantities are related. This work presents a complementary relationship between the quantumness of a two qubits state and the degree of entanglement, respectively measured by roughness and concurrence. There is a finite R2 region that can be used to characterize the two qubits subspace. Heat maps for accumulation points over the surfaces of pure and non-pure randomly sampled states are presented, also an investigation of a decoherence process using a bath under zero and non-zero temperature is performed using the roughness versus concurrence parameter space.

Quantum kinematics in terms of observable quantities and the chirality of entangled two-qubit states.

We consider the kinematics of bipartite quantum states as determined by observable quantities, in particular the Bloch vectors of the subsystems. In examining the simplest case of a pair of two-level systems, there is a remarkable connection between the presence of non-classical correlations and the chirality of the two bases generated by the singular value decomposition of the correlation matrix of the Bloch vectors. We investigate the limits imposed by quantum mechanics of this effect and its relationship with other methods on quantifying the system's non-classical behavior.

Thermal quantum memory, Bell-non-locality, and entanglement behaviors in a two-spin Heisenberg chain model

This paper explores thermal quantum memory-assisted entropic uncertainty, Bell-non-locality, and entanglement in a two-qubit Heisenberg XXX chain with x-directional Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions in thermal equilibrium. We find this crucial that the initial degree of nonlocality and entanglement in the two-qubit state entirely depends upon the temperature, orientation, and strength of the DM and KSEA interaction of the magnetic field. Among many other situations, the magnetic field characterized by DM interaction with minimal temperature, exchange coupling strength, and KSEA interaction is the most reliable for generating and maintaining maximal nonlocality and entanglement while completely suppressing entropic uncertainty. On the other hand, repeated revivals and non-Markovian dynamics have been observed when the magnetic field is characterized by exchange coupling constant, DM and KSEA interaction with a higher temperature limit. Except for temperature-based magnetic fields, we show that maximal entanglement and nonlocality are generated and preserved in the two qubits with zero-order entropic uncertainty, which we believe is a better result than previous studies.

Bidirectional Controlled Quantum Teleportation of Arbitrary Two-qubit States Using Ten-qubit Entangled Channel in Noisy Environment

Bidirectional Controlled Quantum Teleportation of Arbitrary Two-qubit States Using Ten-qubit Entangled Channel in Noisy Environment

High fidelity two-qubit gates on fluxoniums using a tunable coupler

Superconducting fluxonium qubits provide a promising alternative to transmons on the path toward large-scale superconductor-based quantum computing due to their better coherence and larger anharmonicity. A major challenge for multi-qubit fluxonium devices is the experimental demonstration of a scalable crosstalk-free multi-qubit architecture with high-fidelity single-qubit and two-qubit gates, single-shot readout, and state initialization. Here, we present a two-qubit fluxonium-based quantum processor with a tunable coupler element. We experimentally demonstrate fSim-type and controlled-Z-gates with 99.55 and 99.23% fidelities, respectively. The residual ZZ interaction is suppressed down to the few kHz levels. Using a galvanically coupled flux control line, we implement high-fidelity single-qubit gates and ground state initialization with a single arbitrary waveform generator channel per qubit.

Device-independent randomness certification using multiple copies of entangled states

We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension of the system implies a higher amount of randomness, the non-triviality lies in the device-independent simultaneous certification of generated randomness from many copies of entangled states. This is because, most of the two-outcome Bell inequalities (viz., Clauser-Horne-Shimony-Holt, Elegant, or Chain Bell inequality) are optimized for a single copy of two-qubit entangled state. Thus, such Bell inequalities can certify neither many copies of entangled states nor a higher amount of randomness. In this work, we suitably invoke a family of n-settings Bell inequalities which is optimized for ⌊n/2⌋ copies of maximally entangled two-qubit states, thereby, possess the ability to certify more randomness from many copies of two-qubit entangled state.

The masking condition for the quantum state in two-dimensional Hilbert space

This paper focuses on quantum information masking for the quantum state in two-dimensional Hilbert space. We present a system of equations as the condition of quantum information masking. It is shown that quantum information contained in a single qubit state can be masked, if and only if the coefficients of the quantum state satisfy the given system of equations. By observing the characteristics of non-orthogonal maskable quantum states, we obtain a related conclusion, namely, if two non-orthogonal two-qubit quantum states can mask a single qubit state, they have the same number of terms and the same basis. Finally, for maskable orthogonal quantum states, we analyze two special examples and give their images for an intuitive description.