Arbitrary Qubit State Research Articles

Constructions of optimal-speed quantum evolutions: a comparative study

We present a comparative analysis of two different constructions of optimal-speed quantum Hamiltonian evolutions on the Bloch sphere. In the first approach (Mostafazadeh’s approach), the evolution is specified by a traceless stationary Hermitian Hamiltonian and occurs between two arbitrary qubit states by maximizing the energy uncertainty. In the second approach (Bender’s approach), instead, the evolution is characterized by a stationary Hermitian Hamiltonian which is not traceless and occurs between an initial qubit state on the north pole and an arbitrary final qubit state. In this second approach, the evolution occurs by minimizing the evolution time subject to the constraint that the difference between the largest and the smallest eigenvalues of the Hamiltonian is kept fixed. For both approaches we calculate explicitly the optimal Hamiltonian, the optimal unitary evolution operator and, finally, the optimal magnetic field configuration. Furthermore, we show in a clear way that Mostafazadeh’s and Bender’s approaches are equivalent when we extend Mostafazadeh’s approach to Hamiltonians with nonzero trace and, at the same time, focus on an initial quantum state placed on the north pole of the Bloch sphere. Finally, we demonstrate in both scenarios that the optimal unitary evolution operator is a rotation about an axis that is orthogonal to the unit Bloch vectors that correspond to the initial and final qubit states.

Efficient high-fidelity flying qubit shaping

Matter qubit to traveling photonic qubit conversion is the cornerstone of numerous quantum technologies such as distributed quantum computing, as well as several quantum internet and networking protocols. We formulate a theory for stimulated Raman emission which is applicable to a wide range of physical systems, including quantum dots, solid-state defects, and trapped ions, as well as various parameter regimes. We find the upper bound for the photonic pulse emission efficiency of arbitrary matter qubit states for imperfect emitters and show a path forward to optimizing the fidelity. Based on these results, we propose a paradigm shift from optimizing the drive to directly optimizing the temporal mode of the flying qubit using a closed-form expression. Protocols for the production of time-bin encoding and spin-photon entanglement are proposed. Furthermore, the mathematical idea to use input-output theory for pulses to absorb the dominant emission process into the coherent dynamics, followed by a non-Hermitian Schrödinger equation approach, has great potential for studying other physical systems. Published by the American Physical Society 2024

The origin of improving the fidelity of the joint remote state preparation of an arbitrary qubit state affected by amplitude-damping noise

The origin of improving the fidelity of the joint remote state preparation of an arbitrary qubit state affected by amplitude-damping noise

Quantum neural networks for the discovery and implementation of quantum error-correcting codes.

We implement and use quantum neural networks that exploit bit-flip quantum error-correcting codes that correct bit-flip errors in arbitrary logical qubit states. We introduce conjugate layer quantum autoencoders and use them in order to restore states impacted by amplitude damping through the utilization of an approximative four-qubit error-correcting codeword. Our specific implementation avoids barren plateaus of the cost function and improves the training time. Moreover, we propose a strategy that allows one to discover new encryption protocols tailored for specific quantum channels. This is exemplified by learning to generate logical qubits explicitly for the bit-flip channel. Our modified quantum neural networks consistently outperform the standard implementations across all tasks.

Experimental Direct Measurement of the Relative Entropy of Coherence

Quantum coherence is the most distinguished feature of quantum mechanics, which characterizes the superposition properties of quantum states. It plays a critical role in various fields, ranging from quantum information technology to quantum biology. Although various coherence quantifiers have been proposed since the resource theory of coherence was established, there are a lack of experimental methods to estimate them efficiently, which restricts the applications of coherence. Relative entropy of coherence is one of the main quantifiers of coherence, and is frequently used in quantum information science. Such nonlinear properties of quantum states are usually calculated from full descriptions of the quantum state, although they are not related to all parameters that specify the state. Here, we experimentally measure the relative entropy of coherence for the arbitrary qubit states directly in the photonic system without using standard state tomography. In the experiment, we directly measure the von Neumann entropy of the quantum states through interference, thus obtaining the relative entropy of coherence, and finding that the experimental results are in good agreement with the theory. Our work provides a nice alternative experimental scheme for measuring the relative entropy of coherence.

Proposal for Optomagnonic Teleportation and Entanglement Swapping

A protocol for realizing discrete-variable quantum teleportation in an optomagnonic system is provided. Using optical pulses, an arbitrary photonic qubit state encoded in orthogonal polarizations is transferred onto the joint state of a pair of magnonic oscillators in two macroscopic yttrium-iron-garnet (YIG) spheres that are placed in an optical interferometer. We further show that optomagnonic entanglement swapping can be realized in an extended dual-interferometer configuration with a joint Bell-state detection. Consequently, magnon Bell states are prepared. We analyze the effect of the residual thermal occupation of the magnon modes on the fidelity in both the teleportation and entanglement swapping protocols. The work may find applications in the study of macroscopic quantum states, quantum information processing, and hybrid quantum networks based on magnonics.

Qubit teleportation between non-neighbouring nodes in a quantum network

Future quantum internet applications will derive their power from the ability to share quantum information across the network1,2. Quantum teleportation allows for the reliable transfer of quantum information between distant nodes, even in the presence of highly lossy network connections3. Although many experimental demonstrations have been performed on different quantum network platforms4–10, moving beyond directly connected nodes has, so far, been hindered by the demanding requirements on the pre-shared remote entanglement, joint qubit readout and coherence times. Here we realize quantum teleportation between remote, non-neighbouring nodes in a quantum network. The network uses three optically connected nodes based on solid-state spin qubits. The teleporter is prepared by establishing remote entanglement on the two links, followed by entanglement swapping on the middle node and storage in a memory qubit. We demonstrate that, once successful preparation of the teleporter is heralded, arbitrary qubit states can be teleported with fidelity above the classical bound, even with unit efficiency. These results are enabled by key innovations in the qubit readout procedure, active memory qubit protection during entanglement generation and tailored heralding that reduces remote entanglement infidelities. Our work demonstrates a prime building block for future quantum networks and opens the door to exploring teleportation-based multi-node protocols and applications2,11–13.

Optomechanical quantum teleportation

Quantum teleportation, the faithful transfer of an unknown input state onto a remote quantum system, is a key component in long distance quantum communication protocols and distributed quantum computing. At the same time, high frequency nano-optomechanical systems hold great promise as nodes in a future quantum network, operating on-chip at low-loss optical telecom wavelengths with long mechanical lifetimes. Recent demonstrations include entanglement between two resonators, a quantum memory and microwave to optics transduction. Despite these successes, quantum teleportation of an optical input state onto a long-lived optomechanical memory is an outstanding challenge. Here we demonstrate quantum teleportation of a polarization-encoded optical input state onto the joint state of a pair of nanomechanical resonators. Our protocol also allows for the first time to store and retrieve an arbitrary qubit state onto a dual-rail encoded optomechanical quantum memory. This work demonstrates the full functionality of a single quantum repeater node, and presents a key milestone towards applications of optomechanical systems as quantum network nodes.

Optimal convex approximation of qubit states and geometry of completely represented states

We investigate the optimal convex approximation, optimally approximating a desired and unavailable qubit state by the convex mixing of a given set of available states. When the available states are the eigenvectors of three Pauli matrices, we present the complete exact solution for the optimal convex approximation of an arbitrary qubit state based on the fidelity distance. By the comparison of optimal states based on fidelity and trace norm, the advantages and disadvantages of the optimal convex approximation are identified. Several examples are provided to support this. We also analyze the geometrical properties of the target states which can be completely represented by a set of available states. Using the feature of convex combination, we derive the maximum range of completely represented states and clearly illustrate that any qubit state can be optimally prepared by at most three available states in known useable states.

Molecular Machines for Quantum Error Correction

Inspired by biological molecular machines we explore the idea of an active quantum robot whose purpose is delaying decoherence. A conceptual model capable of partially protecting arbitrary logical qubit states against single physical qubit errors is presented. Implementation of an instance of that model - the entanglement qubot - is proposed using laser-dressed Rydberg atoms. Dynamics of the system is studied using stochastic wavefunction methods.

Toward Atomic-Resolution Quantum Measurements with Coherently Shaped Free Electrons.

Free electrons provide a powerful tool for probing material properties at atomic resolution. Recent advances in ultrafast electron microscopy enable the manipulation of free-electron wave functions using laser pulses. It would be of great importance if one could combine the spatial resolution of electron microscopes with the ability of laser pulses to probe coherent phenomena in quantum systems. To this end, we propose a novel concept that leverages free electrons that are coherently shaped by laser pulses to measure quantum coherence in materials. We develop the quantum theory of interactions between shaped electrons and arbitrary qubit states in materials, and show how the postinteraction electron energy spectrum enables measuring the qubit state (on the Bloch sphere) and the decoherence or relaxation times (T_{2}/T_{1}). Finally, we describe how such electrons can detect and quantify superradiance from multiple qubits. Our scheme can be implemented in ultrafast transmission electron microscopes (UTEM), opening the way toward the full characterization of the state of quantum systems at atomic resolution.

Experimental realization of controlled quantum teleportation of arbitrary qubit states via cluster states

Controlled quantum teleportation involves a third party as a controller for the teleportation of state. Here, we present the novel protocols for controlling teleportation of the arbitrary two-qubit and three-qubit states through five-qubit and seven-qubit cluster states respectively. In these schemes, Alice sends the arbitrary qubit states to the remote receiver Bob through the cluster states as quantum channels under the control of Charlie. Bob can recover the mentioned states by making appropriate unitary operations, and we point out that the efficiency in our schemes is 100%. In the process of our analysis, we find the classical communication cost in our protocols is remarkably reduced when compared to the previous protocols. We perform the experimental realization of the above protocols on “IBM 16 Melbourne” quantum computer and “IBM quantum simulator” and we calculate the fidelity. We also examine the security analysis against Charlie, and these schemes which we considered here are secure against Charlie’s attacks.

Generation of arbitrary qubit states by adiabatic evolution split by a phase jump

We propose a technique for accurate, flexible and robust generation of arbitrary coherent superpositions of two quantum states. It uses a sequence of two adiabatic pulses split by a phase jump serving as a control parameter. Each pulse has a chirped detuning, which induces a half crossing, and acts as a $\pi/2$ pulse in the adiabatic regime. The phase jump is imprinted onto the population ratio of the created superposition state. Of the various possible relations between the two pulses, we select the case when the Rabi frequency and the detuning of the second pulse are mirror images of those of the first pulse, and the two detunings have opposite signs. Then the mixing angle of the superposition state depends on the phase jump only. For other arrangements, the superposition mixing angle is shifted by the dynamic phases of the propagators, which makes these cases suitable for state tomography. This twin setup comes along with the advantage that it reduces the error $\epsilon$ of each individual pulse down to $4\epsilon^2$ overall. Therefore, the proposed technique combines the benefits of robustness stemming from adiabatic evolution with accuracy generated by the twin-pulse error suppression, and flexibility of the superposition state controlled by the phase jump $\phi$. In addition, we present a simple exactly soluble trigonometric model in order to illustrate the proposed technique. In this model, when the pulse area $A$ increases the nonadiabatic oscillations are damped as $A^{-1}$ for a single pulse and $A^{-2}$ for the two-pulse sequence. Finally, the proposed technique is extended to sequences of $N=2^n$ pulses by concatenating $\pi/2$ sequences and splitting them by a phase jump, thereby further reducing the nonadiabatic error $\epsilon$ to $(2\epsilon)^{N}$. This makes the proposed technique suitable for generating high-fidelity quantum rotation gates.

Optimal fidelity for quantum teleportation protocol of an arbitrary qubit state affected by amplitude-damping noise: causes and results

The improvement of the average fidelity of the quantum teleportation protocol of an arbitrary qubit state has been researched. The initial quantum channel is chosen as the non-maximally entangled state, and this state depends on a free parameter. One qubit of this quantum channel is influenced by the amplitude-damping noise environment in the Markovian regime or the non-Markovian regime. The average fidelity is enhanced efficiently through the appropriately selected free parameter of the initial quantum channel. The optimization could not be attributed to the probability as well as the noise environment that makes the initial quantum channel becomes the closest quantum channel to the maximally entangled one. Our study shows that the average fidelity is enhanced as the quantum entanglement of the initial quantum channel is harmoniously redistributed into the entanglement of quantum channel influenced by the noise environment and the entanglement between each of the qubits in this quantum channel and the noise environment.

All-Optical Storage of Phase-Sensitive Quantum States of Light

We experimentally demonstrate storage and on-demand release of phase-sensitive, photon-number superposition states of the form α|0⟩+βe^{iθ}|1⟩ for an optical quantized oscillator mode. For this purpose, we newly developed a phase-probing mechanism compatible with a storage system composed of two concatenated optical cavities, which was previously employed for storage of phase-insensitive single-photon states [Phys. Rev. X 3, 041028 (2013)PRXHAE2160-330810.1103/PhysRevX.3.041028]. This is the first demonstration of all-optically storing highly nonclassical and phase-sensitive quantum states of light. The strong nonclassicality of the states after storage becomes manifest as a negative region in the corresponding Wigner function shifted away from the origin in phase space. This negativity is otherwise, without the phase information of the memory system, unobtainable. While our scheme includes the possibility of optical storage, on-demand release and synchronization of arbitrary single-rail qubit states, it is not limited to such states. In fact, our technique is extendible to more general phase-sensitive states such as multiphoton superposition or entangled states, and thus it represents a significant step toward advanced optical quantum information processing, where highly nonclassical states are utilized as resources.

Apollonius Representation and Complex Geometry of Entangled Qubit States

A representation of one qubit state by points in complex plane is proposed, such that the computational basis corresponds to two fixed points at a finite distance in the plane. These points represent common symmetric states for the set of quantum states on Apollonius circles. It is shown that, the Shannon entropy of one qubit state depends on ratio of probabilities and is a constant along Apollonius circles. For two qubit state and for three qubit state in Apollonius representation, the concurrence for entanglement and the Cayley hyperdeterminant for tritanglement correspondingly, are constant on the circles as well. Similar results are obtained also for n-tangle hyperdeterminant with even number of qubit states. It turns out that, for arbitrary multiple qubit state in Apollonius representation, fidelity between symmetric qubit states is also constant on Apollonius circles. According to these, the Apollonius circles are interpreted as integral curves for entanglement characteristics. The bipolar and the Cassini representations for qubit state are introduced, and their relations with qubit coherent states are established. We proposed the differential geometry for qubit states in Apollonius representation, defined by the metric on a surface in conformal coordinates, as square of the concurrence. The surfaces of the concurrence, as surfaces of revolution in Euclidean and Minkowski spaces are constructed. It is shown that, curves on these surfaces with constant Gaussian curvature becomes Cassini curves.

Bidirectional controlled quantum teleportation by a genuine entangled 9-qubit state

Since the first protocol of quantum teleportation based on an EPR pair was presented by Bennett et al. in 1993, it has become a hot topic in quantum communication. It is known that entanglement plays a key role in quantum teleportation. Various schemes of controlled quantum teleportation and bidirectional controlled quantum teleportation have been developed by using all kinds of multi-parties entangled states as a quantum channel, e.g. GHZ states, W states, 5-qubit cluster states, 6-qubit cluster states, 7-qubit cluster states, maximally entangled 5-qubit states, maximally entangled 6-qubit states, genuine entangled 6-qubit states, genuine entangled 7-qubit states, genuine entangled 8-qubit states. In this paper, a genuine entangled 9-qubit state is used as channel of quantum teleportation, and two schemes of bidirectional controlled quantum teleportation are proposed. One scheme is that with the control of Charlie Alice can transmit an arbitrary unknown qubit state to Bob and Bob can transmit an arbitrary unknown 3-qubit state to Alice in the same time. Another scheme is that with the control of Charlie Alice and Bob can transmit an arbitrary unknown 2-qubit to each other simultaneously. Compared with the existed schemes, our scheme can transmit more qubits of arbitrary state in total by an entangled state, and the intrinsic efficiency of our scheme is maybe the best. Moreover, the genuine entangled 9-qubit state used in our scheme can be produced through some simple quantum unitary gates.

Universal stabilization of single-qubit states using a tunable coupler

We theoretically analyze a scheme for fast stabilization of arbitrary qubit states with high fidelities, extending a protocol recently demonstrated experimentally [Lu et al., Phys. Rev. Lett. 119, 150502 (2017)]. That experiment utilized red and blue sideband transitions in a system composed of a fluxonium qubit, a low-Q LC-oscillator, and a coupler enabling us to tune the interaction between them. Under parametric modulations of the coupling strength, the qubit can be steered into any desired pure or mixed single-qubit state. For realistic circuit parameters, we predict that stabilization can be achieved within 100 ns. By varying the ratio between the oscillator's damping rate and the effective qubit-oscillator coupling strength, we can switch between under-damped, critically-damped, and over-damped stabilization and find optimal working points. We further analyze the effect of thermal fluctuations and show that the stabilization scheme remains robust for realistic temperatures.

Complete optimal convex approximations of qubit states under B_2 distance

We consider the optimal approximation of arbitrary qubit states with respect to an available states consisting the eigenstates of two of three Pauli matrices, the B_2-distance of an arbitrary target state. Both the analytical formulae of the B_2-distance and the corresponding complete optimal decompositions are obtained. The trade-off relations for both the sum and the squared sum of the B_2-distances have been analytically and numerically investigated.

Controlled cyclic remote state preparation of arbitrary qubit states

Quantum secure communications could securely transmit quantum information by using quantum resource. Recently, novel applications such as bidirectional and asymmetric quantum protocols have been developed. In this paper, we propose a new method for generating entanglement which is highly useful for multiparty quantum communications such as teleportation and Remote State Preparation (RSP). As one of its applications, we propose a new type of quantum secure communications, i.e. cyclic RSP protocols. Starting from a four-party controlled cyclic RSP protocol of one-qubit states, we show that this cyclic protocol can be generalized to a multiparty controlled cyclic RSP protocol for preparation of arbitrary qubit states. We point out that previous bidirectional and asymmetric protocols can be regarded as a simpler form of our cyclic RSP protocols.