Von Neumann Projective Measurements Research Articles

General quantum correlation from nonreal values of Kirkwood–Dirac quasiprobability over orthonormal product bases

We propose a characterization and a quantification of the general quantum correlation which is exhibited even by a separable (unentangled) mixed bipartite state in terms of the nonclassical values of the associated Kirkwood–Dirac (KD) quasiprobability. Such a general quantum correlation, wherein entanglement is a subset, is not only intriguing from a fundamental point of view, but it has also been recognized as a resource in a variety of schemes of quantum information processing and quantum technology. Given a bipartite state, we construct a quantity based on the imaginary part the associated KD quasiprobability defined over a pair of orthonormal product bases and an optimization procedure over all pairs of such bases. We show that it satisfies certain requirements expected for a quantifier of general quantum correlations. It gives a lower bound to the total sum of the quantum standard deviation of all the elements of the product (local) basis, minimized over all such bases. It suggests an interpretation as the minimum genuine quantum share of uncertainty in all local von-Neumann projective measurements. Moreover, it is a faithful witness for entanglement and measurement-induced nonlocality of pure bipartite states. We then discuss a variational scheme for its estimation, and based on this, we offer information theoretical meanings of the general quantum correlation. Our results suggest a deep connection between the nonclassical concept of general quantum correlation and the nonclassical values of the KD quasiprobability and the associated strange weak values.

Characterizing nonclassical correlations of tensorizing states in a bilocal scenario

In the present paper, we attempt to address the question of “can tensorizing states $$(\rho \otimes \rho \; \text {or}\;\rho \otimes \rho ')$$ have quantum advantages?”. To answer this question, we exploit the notion of measurement-induced nonlocality (MIN) and advocate a fidelity-based nonbilocal measure to capture the nonlocal effects of tensorizing states due to locally invariant von Neumann projective measurements. We show that the properties of the fidelity-based nonbilocal measures are retrieved from that of MIN. Analytically, we evaluate the nonbilocal measure for any arbitrary pure state. The upper bounds of the nonbilocal measure based on fidelity are also obtained in terms of eigenvalues of correlation matrix. As an illustration, we have computed the nonbilocality for some popular input states.

Measurement-induced nonlocality quantified by Hellinger distance and weak measurements

In this article, we propose measurement-induced nonlocality (MIN) quantified by Hellinger distance using von Neumann projective measurement. The proposed MIN is a bonafide measure of nonlocal correlation and is resistant to local ancilla problem. We obtain an analytical expression of the Hellinger distance MIN for general pure and 2×n mixed states. In addition to comparing with similar measures, we explore the role of weak measurement in capturing nonlocal correlation.

Measurement-induced nonlocality based on affinity

Measurement-induced nonlocality (MIN), a quantum correlation measure for bipartite systems, is an indicator of maximal global effects due to locally invariant von Neumann projective measurements. It is originally defined as the maximal square of the Hilbert–Schmidt norm of the difference between pre- and post-measurement states. In this article, we propose a new form of MIN based on affinity. This quantity satisfies all the criteria of a bona fide measure of quantum correlation measures. This quantity is evaluated for both arbitrary pure and 2 × n dimensional (qubit–qudit) mixed states. The operational meaning of the proposed quantity is interpreted in terms of the interferometric power of the quantum state. We apply these results on two-qubit mixed states, such as the Werner, isotropic and Bell diagonal states.

Quantum Teleportation of Ten-qubit State Based on the Cluster State Quantum Channel

We propose a novel and applicable teleportation protocol for certain class of ten-qubit state by utilizing an eight-qubit entangled state as a quantum channel. In this scheme, the sender applies a four-qubit C-NOT gate and an eight-qubit von-Neumann projective measurement. Based on this channel we explicitly demonstrate how the protocol works by recurring the original quantum state of ten-qubit state at the receiver terminal with considerable efficiency.

Characterizing nonclassical correlation using affinity

Geometric discord, a measure of quantumness of bipartite system, captures minimal nonlocal effects of a quantum state due to locally invariant von Neumann projective measurements. Original version of this measure is suffered by the local ancilla problem. In this article, we propose a new version of geometric discord using affinity. This quantity satisfies all criteria of a good measure of quantum correlation of the bipartite system and resolves local ancilla problem of Hilbert-Schmidt norm based discord. We evaluate analytically the proposed quantity for both pure and mixed states. For an arbitrary pure state, it is shown that affinity based geometric discord equal to geometric measure of entanglement. Further, we obtain a lower bound of this measure for m \times n dimensional arbitrary mixed state and a closed formula of proposed version of geometric discord for 2 \times n dimensional mixed state is obtained. Finally, as an illustration, we have studied the nonlocality of Bell diagonal state, isotropic and Werner states.

Dynamics of measurement-induced nonlocality under decoherence

Measurement Induced Nonlocality (MIN) captures nonlocal effects of a quantum state due to local von Neumann projective measurements, is a bonafide measure of quantum correlation between constituents of a composite system. In this paper, we study the dynamical behavior of entanglement (measured by concurrence), Hilber-Schmidt MIN and fidelity based MIN (FMIN) under local noisy channels such as hybrid (consists of bit, phase, bit and phase flip), generalized amplitude damping (GAD) and depolarizing channels for the initial Bell diagonal state. We observed that while sudden death of entanglement occur in hybrid and GAD channels, MIN and FMIN are more robust against such noise. Finally, we demonstrate the revival of MIN and FMIN after a dark point of time against depolarizing noise.

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.

An efficient quantum teleportation of six-qubit state via an eight-qubit cluster state

We present a scheme for teleporting a certain class of six-particle state via an eight-particle cluster state as quantum channel. In our scheme, the sender merely needs to perform an eight-particle von-Neumann projective measurement, and the receiver gives a corresponding general evolution to restore the original state. Our scheme is a deterministic scheme. Compared with other schemes proposed before, our scheme possesses higher intrinsic efficiency.

Faithful Pointer for Qubit Measurement

In the context of von Neumann projective measurement scenario for a qubit system, it is widely believed that the mutual orthogonality between the post-interaction pointer states is the sufficient condition for achieving the ideal measurement situation. However, for experimentally verifying the observable probabilities, the real space distinction between the pointer distributions corresponding to post-interaction pointer states play crucial role. It is implicitly assumed that mutual orthogonality ensures the support between the post-interaction pointer distributions to be disjoint. We point out that mutual orthogonality (formal idealness) does \emph{not} necessarily imply the real space distinguishability (operational idealness), but converse is true. In fact, for the commonly referred Gaussian wavefunction, it is possible to obtain a measurement situation which is formally ideal but fully nonideal operationally. In this paper, we derive a class of pointer states, that we call faithful pointers, for which the degree of formal (non)idealness is equal to the operational (non)idealness. In other words, for the faithful pointers, if a measurement situation is formally ideal then it is operationally ideal and vice versa.

Quantum Teleportation of Eight-Qubit State via Six-Qubit Cluster State

A novel quantum teleportation protocol for certain class of eight-qubit state is proposed. We utilize a six-qubit cluster state as quantum channel. In our scheme, the sender performs four controlled-NOT operations and a six-qubit von-Neumann projective measurement, the original state with deterministic probability can be reconstructed by the receiver. Higher efficiency can be achieved based on our results.

Quantum Teleportation of Five-qubit State

We propose a novel quantum teleportation protocol for certain class of five-qubit state with a seven-qubit cluster state as quantum channel. In our scheme, the sender merely needs to perform a seven-qubit von-Neumann projective measurement, the original state with deterministic probability can be reconstructed by the receiver after a series corresponding unitary transformations. Compared with other schemes proposed before, our scheme has the distinct advantages of requiring fewer quantum channels, possessing higher intrinsic efficiency, and transmitting more quantum information bits.

Deterministic and Efficient Quantum Key Distribution Using Entanglement Parity Bits and Ancillary Qubits

In this paper, we propose an efficient and deterministic quantum key distribution protocol for establishing a secret key between two untrusted users. In this protocol, a secret key is distributed to a sender and a receiver who share entangled states with a third trusted party but not with each other. This secret key is distributed by the means of special pure quantum states using remote state preparation and controlled gates. In addition, we employ the parity bits of the entangled pairs and the ancillary states to assist in preparing and measuring the secret states. Distributing a state to two users requires two maximally entangled pairs as the quantum channel and a two-particle von Neumann projective measurement. The proposed protocol is exact and deterministic. It distributes a secret key of $ d $ qubits by the means of $ 2d $ entangled pairs and, on average, $ d $ bits of classical communication. We demonstrate the security of this protocol against entanglement attacks and present a method of privacy amplification.

Sequential Measurement of Displacement and Conduction Currents in Electronic Devices

The extension of the Ramo–Schockley–Pellegrini theorem for quantum systems allows to define a positive-operator valued measure (POVM) for the total conduction plus displacement electrical current. The resulting current operator is characterized by two parameters, viz. the width of the associated Gaussian functions and the lapse of time between consecutive measurements. For large Gaussian dispersions and small time intervals, the operator obeys to a continuous weak-measurement scheme. Contrarily, in the limit of very narrow Gaussian widths and a single-shot measurement, the operator corresponds to a standard von Neumann (projective) measurement. We have implemented the resulting measurement protocol into a quantum electron transport simulator. Numerical results for a resonant tunneling diode show the great sensibility of current–voltage characteristics to different parameter configurations of the total current operator.

Quantum Teleportation of A Four-qubit State by Using Six-qubit Cluster State

We propose a scheme for perfect quantum teleportation of a special form of four-qubit state by using a six-qubit cluster state as quantum channel. In our scheme, the sender only needs six-qubit von-Neumann projective measurements, and the receiver can reconstruct the original four-qubit state by applying the appropriate unitary operation.

Quantum remote control: remotely and conclusively changing the overlap between two qubit states

We propose a scheme for Alice to change remotely and conclusively the overlap between Bob’s two nonorthogonal qubit states with a finite probability of success. The remote nonunitary evolution of Bob’s primary system could be generated by performing a proper nonlocal unitary transformation on Bob’s primary system and Alice’s auxiliary system, followed by a local von Neumann projective measurement on Alice’s ancilla. The various desired inner product modifications between Bob’s primary states can be efficiently and fully controlled by Alice’s auxiliary states. We build a quantum network for implementing rapidly the remote nonunitary transformation, and thus provide a feasible physical means to realize the remote and controllable inner product modification. This scheme is feasible for current experimental technology.

Generating genuine multipartite entanglement via X Y-interaction and via projective measurements

We have studied the generation of multipartite entangled states for the superconducting phase qubits. The experiments performed in this direction have the capacity to generate several specific multipartite entangled states for three and four qubits. Our studies are also important as we have used a computable measure of genuine multipartite entanglement whereas all previous studies analyzed certain probability amplitudes. As a comparison, we have reviewed the generation of multipartite entangled states via von Neumann projective measurements.

Quantum Teleportation of an Arbitrary Three-Qubit State Using GHZ-Like States

A new application of the GHZ-like state is investigated for teleportation of an arbitrary three-qubit state. We demonstrate that three sets of GHZ-like states can be used to realize the perfect teleportation of an arbitrary three-qubit state by performing only the three-qubit von-Neumann projective measurements.

Perfect Teleportation of an Arbitrary Two-Qubit State via GHZ-Like States

We propose a novel and efficient scheme for quantum teleportation of an arbitrary two-qubit state via GHZ-like states. In this scheme, the sender Alice performs two three-qubit von-Neumann projective measurements on the qubits, the receiver Bob can reconstruct the original state by making appropriate unitary transformations. This quantum teleportation scheme is perfect, i.e. the success probability can reach 1.

Entangled Three Qutrit Coherent States and Localizable Entanglement

Choosing I-concurrence as the measure of bipartite entanglement and using von Neumann projective local measurements, localizable entanglement (LE) in a three-qutrit system is studied. A superposition of the qutrit-coherentstate of this system is considered ant its LE is obtained and analyzed as a function of the relevant parameters. It is observed that one may achieve the maximal entanglement or no entanglement at all, depending on the choice of the parameters involved.