Local Projective Measurements Research Articles

Optimal verification and fidelity estimation of maximally entangled states

We study the verification of maximally entangled states by virtue of the simplest measurement settings: local projective measurements without adaption. We show that optimal protocols are in one-to-one correspondence with complex projective 2-designs constructed from orthonormal bases. Optimal protocols with minimal measurement settings are in one-to-one correspondence with complete sets of mutually unbiased bases. Based on this observation, optimal protocols are constructed explicitly for any local dimension, which can also be applied to estimating the fidelity with the target state and to detecting entanglement. In addition, we show that incomplete sets of mutually unbiased bases are optimal for verifying maximally entangled states when the number of measurement settings is restricted. Moreover, we construct optimal protocols for the adversarial scenario in which state preparation is not trusted. The number of tests has the same scaling behavior as the counterpart for the nonadversarial scenario; the overhead is no more than three times. We also show that the entanglement of the maximally entangled state can be certified with any given significance level using only one test as long as the local dimension is large enough.

$(t,n)$ -Threshold Quantum Secret Sharing Based on One-Way Local Distinguishability

We propose a quantum secret sharing protocol with a set of orthogonal generalized Bell states and one-way local distinguishability. In the proposed protocol, the participants use local projective measurements and one-way classical communication to distinguish among four Bell states, and we combine with the Shamir $(t,n)$ -threshold scheme to realize $(t,n)$ -threshold access structure. Compared to the existing schemes, the practical communication costs are dramatically improved as there is need for one-way classic communication between the two participants in our protocol. In addition, the efficiency in the process of information transmission will also be improved, as the number of communications will be reduced. At last, we demonstrate our protocol to be secure against both eavesdropping and dishonest participants.

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.

Closing the detection loophole in multipartite Bell experiments with a limited number of efficient detectors

The problem of closing the detection loophole in Bell tests is investigated in the presence of a limited number of efficient detectors using emblematic multipartite quantum states. To this end, a family of multipartite Bell inequalities is introduced basing on local projective measurements conducted by $N-k$ parties and applying a $k$-party Bell inequality on the remaining parties. Surprisingly, we find that most of the studied pure multipartite states involving e.g. cluster states, the Dicke states, and the Greenberger-Horne-Zeilinger states can violate our inequalities with only the use of two efficient detectors, whereas the remaining detectors may have arbitrary small efficiencies. We believe that our inequalities are useful in Bell experiments and device-independent applications if only a small number of highly efficient detectors are in our disposal.

Additivity of entropic uncertainty relations

We consider the uncertainty between two pairs of local projective measurements performed on a multipartite system. We show that the optimal bound in any linear uncertainty relation, formulated in terms of the Shannon entropy, is additive. This directly implies, against naive intuition, that the minimal entropic uncertainty can always be realized by fully separable states. Hence, in contradiction to proposals by other authors, no entanglement witness can be constructed solely by comparing the attainable uncertainties of entangled and separable states. However, our result gives rise to a huge simplification for computing global uncertainty bounds as they now can be deduced from local ones. Furthermore, we provide the natural generalization of the Maassen and Uffink inequality for linear uncertainty relations with arbitrary positive coefficients.

Maximal qubit violation of n-locality inequalities in a star-shaped quantum network

Bell's theorem was a cornerstone for our understanding of quantum theory and the establishment of Bell non-locality played a crucial role in the development of quantum information. Recently, its extension to complex networks has been attracting growing attention, but a deep characterization of quantum behavior is still missing for this novel context. In this work we analyze quantum correlations arising in the bilocality scenario, that is a tripartite quantum network where the correlations between the parties are mediated by two independent sources of states. First, we prove that non-bilocal correlations witnessed through a Bell-state measurement in the central node of the network form a subset of those obtainable by means of a local projective measurement. This leads us to derive the maximal violation of the bilocality inequality that can be achieved by arbitrary two-qubit quantum states and arbitrary local projective measurements. We then analyze in details the relation between the violation of the bilocality inequality and the CHSH inequality. Finally, we show how our method can be extended to the n-locality scenario consisting of n two-qubit quantum states distributed among nodes of a star-shaped network.

Universal Bell Correlations Do Not Exist.

We prove that there is no finite-alphabet nonlocal box that generates exactly those correlations that can be generated using a maximally entangled pair of qubits. More generally, we prove that if some finite-alphabet nonlocal box is strong enough to simulate arbitrary local projective measurements of a maximally entangled pair of qubits, then that nonlocal box cannot itself be simulated using any finite amount of entanglement. We also give a quantitative version of this theorem for approximate simulations, along with a corresponding positive result.

Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constantKG(3)

We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner stateρ=v|ψ−⟩⟨ψ−|+(1−v)14via a local hidden variable (LHV) model, where|ψ−⟩denotes the singlet state. We show analytically that these correlations are local forv=999×689×10−6cos2⁡(π/50)≃0.6829. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constantKG(3)≤1/v≃1.4644. We also present a LHV model for reproducing the statistics of arbitrary POVMs on the Werner state forv≃0.4553. The techniques we develop can be adapted to construct LHV models for other entangled states, as well as bounding other Grothendieck constants.

Conditional purity and quantum correlation measures in two qubit mixed states

We analyze and show experimental results of the conditional purity, the quantum discord and other related measures of quantum correlation in mixed two-qubit states constructed from a pair of photons in identical polarization states. The considered states are relevant for the description of spin pair states in interacting spin chains in a transverse magnetic field. We derive clean analytical expressions for the conditional local purity and other correlation measures obtained as a result of a remote local projective measurement, which are fully verified by the experimental results. A simple exact expression for the quantum discord of these states in terms of the maximum conditional purity is also derived.

Unified entropic measures of quantum correlations induced by local measurements

We introduce quantum correlations measures based on the minimal change in unified entropies induced by local rank-one projective measurements, divided by a factor that depends on the generalized purity of the system in the case of non-additive entropies. In this way, we overcome the issue of the artificial increasing of the value of quantum correlations measures based on non-additive entropies when an uncorrelated ancilla is appended to the system without changing the computability of our entropic correlations measures with respect to the previous ones. Moreover, we recover as limiting cases the quantum correlations measures based on von Neumann and R\'enyi entropies (i.e., additive entropies), for which the adjustment factor becomes trivial. In addition, we distinguish between total and semiquantum correlations and obtain some relations between them. Finally, we obtain analytical expressions of the entropic correlations measures for typical quantum bipartite systems.

Optimal randomness certification from one entangled bit

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.

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.

HIERARCHY OF CORRELATIONS VIA LÜDERS MEASUREMENTS

The classification and quantification of correlations (classical and quantum) in composite quantum systems are of fundamental significance for quantum information processing. While the paradigm of separability versus entanglement has been intensively studied, the scenario of classicality versus quantumness, with focus on the quantum discord, has also attracted many recent interests. In this paper, pursuing further the latter scenario and exploiting the intrinsic structure of bipartite quantum states via local projective measurements, we introduce the notion of coherent dimension of correlations in terms of the Lüders measurements. The coherent dimension can alternatively be regarded as a generalization of the Schmidt number of a pure state. Furthermore, we propose some families of measures for correlations, which extend naturally both the quantum discord and the quantum mutual information (total correlations), and furthermore interpolate between them. These quantities reveal some hierarchial structures, and provide a more complete description, of both classical and quantum correlations in the quantum realm.

Erratum: Entanglement in bipartite pure states of an interacting boson gas obtained by local projective measurements [Phys. Rev. A84, 032330 (2011)

Received 25 September 2012DOI:https://doi.org/10.1103/PhysRevA.86.049901©2012 American Physical Society

Instantaneous spatially local projective measurements are consistent in a relativistic quantum field

Suppose the postulate of measurement in quantum mechanics can be extended to quantum field theory; then a local projective measurement at some moment on an object locally coupled with a relativistic quantum field will result in a projection or collapse of the wavefunctional of the combined system defined on the whole time-slice associated with the very moment of the measurement, if the relevant degrees of freedom have nonzero correlations. This implies that the wavefunctionals in the same Hamiltonian system but defined in different reference frames would collapse on different time-slices passing through the same local event where the measurement was done. Are these post-measurement states consistent with each other? We illustrate that the quantum states of the Raine–Sciama–Grove detector–field system started with the same initial Gaussian state defined on the same initial time-slice, then collapsed by the measurements on the pointlike detectors on different time-slices in different frames, will evolve to the same state of the combined system up to a coordinate transformation when compared on the same final time-slice. Such consistency is guaranteed by the spatial locality of interactions and the general covariance in a relativistic system, together with the spatial locality of measurements and the linearity of quantum dynamics in its quantum theory.

Controlled-Joint Remote Preparation of an Arbitrary Two-Qubit State via Non-maximally Entangled Channel

In this paper, we make a study on how to efficiently transmit an arbitrary two-qubit pure state to remote receiver via non-maximal entangled quantum channel. As a special case, in the first section we present a controlled-joint remote state preparation scheme based on maximally entangled channel. By some local convertible projective measurement bases, two message carriers and one controller can help the receiver Charlie reconstruct the desired state with success probability p=100 %. Then, we extend it to the case of non-maximally entangled channel. Utilizing positive operator-valued measure (POVM) measurement instead of projective measurement, the controller can assist the two senders to fulfill the task. Compared with some previous schemes, our protocol will succeed with a higher probability. And success or failure will only depend on the controller’s measurement outcome, but has nothing to do with two senders’ measurement results.

Scalable one-way quantum computer using on-chip resonator qubits

We propose a scalable and robust architecture for one-way quantum computation using coupled networks of superconducting transmission line resonators. In our protocol, quantum information is encoded into the long-lived photon states of the resonators, which have a much longer coherence time than the usual superconducting qubits. Each resonator contains a charge qubit used for the state initialization and local projective measurement of the photonic qubit. Any pair of neighboring photonic qubits are coupled via a mediator charge qubit, and large photonic cluster states can be created by applying Stark-shifted Rabi pulses to these mediator qubits. The distinct advantage of our architecture is that it combines both the excellent scalability of the solid-state systems and the long coherence time of the photonic qubits. Furthermore, this architecture is very robust against the parameter variations.

Quantum states and local projective measurement in a relativistic field

In an explicitly covariant system with point-like detectors coupled to a relativistic quantum field, the Gaussian states of the combined system and the reduced states of the detectors derived from them are consistent, but not have to be covariant, in different frames of different observers. Even in the presence of spatially local projective measurements, which result instantaneous wave functional collapses on different time-slices in different reference frames, the consistency still holds.

Entanglement in bipartite pure states of an interacting boson gas obtained by local projective measurements

We quantify the extractable entanglement of excited states of a Lieb-Liniger gas that are obtained from coarse-grained measurements on the ground state in which the boson number in one of two complementary contiguous partitions of the gas is determined. Numerically exact results obtained from the coordinate Bethe ansatz show that the von Neumann entropy of the resulting bipartite pure state increases monotonically with the strength of repulsive interactions and saturates to the impenetrable-boson limiting value. We also present evidence indicating that the largest amount of entanglement can be extracted from the most probable projected state having half the number of bosons in a given partition. Our study points to a fundamental difference between the nature of the entanglement in free-bosonic and free-fermionic systems, with the entanglement in the former being zero after projection, while that in the latter (corresponding to the impenetrable-boson limit) being nonzero.

Distinguishability of hyperentangled Bell states by linear evolution and local projective measurement

Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell-state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend known bounds for Bell-state distinguishability in one and two variables to the general case of entanglement in $n$ two-state variables. We show that at most ${2}^{n+1}\ensuremath{-}1$ classes out of ${4}^{n}$ hyper-Bell states can be distinguished with one copy of the input state. With two copies, complete distinguishability is possible. We present optimal schemes in each case.