Quantum State Sharing Research Articles

Three-Party Quantum State Sharing of an Arbitrary Unknown Two-Qubit State Based on Entanglement Swapping and Bell-State Measurements

We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using a four-qubit cluster-class state and a Bell state as a quantum channel. With a quantum controlled phase gate (QCPG) operation and a local unitary operation, any one of the two agents has the access to reconstruct the original state if he/she collaborates with the other one, whilst individual agent obtains no information. As all quantum resource can be used to carry the useful information, the intrinsic efficiency of qubits approaches the maximal value. Moreover, the present scheme is more feasible with present-day technique.

Scheme for Generalized Quantum State Sharing of a Single-Qubit State in Cavity QED

An experimentally feasible scheme for generalized quantum state sharing of an arbitrary unknown single-qubit state in cavity QED is presented. Using a generalized Greenberger–Horne–Zeilinger (GHZ) state as the quantum channel among the three parties, the quantum information (i.e. the single-qubit state) from the sender can be split in such a way that the information can be recovered if and only if both receivers collaborate. Moreover, the scheme is insensitive to both the effects of thermal field and cavity decay.

Quantum teleportation and state sharing using a genuinely entangled six-qubit state

The usefulness of the genuinely entangled six-qubit state that has recently been introduced by Borras et al (2007 J. Phys. A: Math. Theor. 40 13407) is investigated for the quantum teleportation of an arbitrary three-qubit state and for quantum state sharing (QSTS) of an arbitrary two-qubit state. We construct two distinct protocols for QSTS of an arbitrary two-qubit state using this state as an entangled channel. We construct 16 orthogonal four-qubit states which can lock an arbitrary two-qubit state between two parties.

Geometric measure of entanglement and shared quantum states

We give an explicit expression for the geometric measure of entanglement for three-qubit states that are linear combinations of four orthogonal product states. It turns out that the geometric measure for these states has three different expressions depending on the range of definition in parameter space. Each expression of the measure has its own geometrically meaningful interpretation. Such an interpretation allows oneself to take one step toward a complete understanding for the general properties of the entanglement measure. The states that lie on joint surfaces separating different ranges of definition, designated as shared states, seem to have particularly interesting features. The properties of the shared states are fully discussed.

MULTIPARTY QUANTUM STATE SHARING OF m-QUBIT STATE

A scheme for quantum state sharing (QSTS) of a one-particle state is proposed for a three-particle GHZ state utilized as a quantum channel. After the sender (Alice) makes Bell-state measurements (BM) on her particles, and the controller (Charlie) performs a computational basis measurement (CM), the recipient (Bob) only needs to carry out a unitary transformation of the classical information from the sender and the controller. Finally, the scheme is generalized to multiparty QSTS of a one-qubit state with n agents and an m-qubit state with n agents.

Bounding the Set of Quantum Correlations

We introduce a hierarchy of conditions necessarily satisfied by any distribution P_{alphabeta} representing the probabilities for two separate observers to obtain outcomes alpha and beta when making local measurements on a shared quantum state. Each condition in this hierarchy is formulated as a semidefinite program. Among other applications, our approach can be used to obtain upper bounds on the quantum violation of an arbitrary Bell inequality. It yields, for instance, tight bounds for the violations of the Collins et al. inequalities.

Quantum State Sharing by Using Two-Mode and Single-ModeSqueezed State Lights

We propose a quantum state sharing scheme for continuous variables using bright two-modesqueezed state and single-mode squeezed state light. Thesqueezing of a single-mode state is applied to enhance the security ofinformation in quantum teleportation network. The signal-to-noise ratio ofcommunication and the fidelity between the secret and reconstruction stateare analysed. It is shown that both the receivers of Bob and Charlie cannotextract information with a high signal-to-noise ratio because of the largenoise come from the other quadrature component of single mode squeezedstate. Anyone of Bob and Charlie can retrieve the quantum state with a highsignal-to-noise ratio if and only if the other one cooperates with the measurement.

Huge Quantum Broadcast Channels and Cryptographic Applications for Separable States

Quantum information-theoretic models of secret source-sharing are developed using a general LOCC scheme, i.e. a protocol involving only local operations and classical communication. This is in order to generate a common random key from a shared quantum state at two terminals without allowing an eavesdropper to obtain information about this key. Coding theorems for special separable states are obtained, and bounds to secret key capacity are also derived for more general quantum source states and other models later. In order to prove results for secret source-sharing schemes with a quantum source state also shared with a wiretapper, multi-user systems are studied and the capacity region for the degraded quantum broadcast channel is started to be determined. Using the results of the foregoing chapters, a sufficient bound on the error rate for unconditional security of the BB84 quantum key distribution protocol is proved.

Secure Key from Bound Entanglement

We characterize the set of shared quantum states which contain a cryptographically private key. This allows us to recast the theory of privacy as a paradigm closely related to that used in entanglement manipulation. It is shown that one can distill an arbitrarily secure key from bound entangled states. There are also states that have less distillable private keys than the entanglement cost of the state. In general, the amount of distillable key is bounded from above by the relative entropy of entanglement. Relationships between distillability and distinguishability are found for a class of states which have Bell states correlated to separable hiding states. We also describe a technique for finding states exhibiting irreversibility in entanglement distillation.

Hiding bits in bell states.

We present a scheme for hiding bits in Bell states that is secure even when the sharers, Alice and Bob, are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in n, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.