N-qubit States Research Articles

Shortcut to adiabatic gate teleportation

We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In this scenario, we provide the counterdiabatic driving for arbitrary n-qubit gates, which allows to achieve universality through a variety of gate sets. Remarkably, our approach maps the superadiabatic Hamiltonian for an arbitrary n-qubit gate teleportation into the implementation of a rotated superadiabatic dynamics of an n-qubit state teleportation. This result is rather general, with the speed of the evolution only dictated by the quantum speed limit. In particular, we analyze the energetic cost for different Hamiltonian interpolations in the context of the energy-time complementarity.

3-Uniform states and orthogonal arrays

We propose a criterion for the k-uniform state via local unitary transformation invariant and find for what N there are 3-uniform states of N-qubits. We also demonstrate the existence of 3-uniform states of N-qubits for N=11, 12, 13, 14 and 15.

More communication with less entanglement

We exhibit the intriguing phenomena of “Less is More” using a set of multipartite entangled states. We consider the quantum communication protocols for the exact teleportation, superdense coding, and quantum key distribution. We find that sometimes less entanglement is more useful. To understand this phenomena we obtain a condition that a resource state must satisfy to communicate a n-qubit pure state which has m terms. We find that an appropriate partition of the resource state should have a von-Neumann entropy of log2 m. Furthermore, it is shown that some states may be suitable for exact superdense coding, but not for exact teleportation.

Highly noise resistant multiqubit quantum correlations

We analyze robustness of correlations of the N-qubit GHZ and Dicke states against white noise admixture. For sufficiently large N, the Dicke states (for any number of excitations) lead to more robust violation of local realism than the GHZ states (e.g. for N > 8 for the W state). We also identify states that are the most resistant to white noise. Surprisingly, it turns out that these states are the GHZ states augmented with fully product states. Based on our numerical analysis conducted up to N = 8, and an analytical formula derived for any N parties, we conjecture that the three-qubit GHZ state augmented with a product of (N − 3) pure qubits is the most robust against white noise admixture among any N-qubit state. As a by-product, we derive a single Bell inequality and show that it is violated by all pure entangled states of a given number of parties. This gives an alternative proof of Gisin’s theorem.

Monogamous nature of symmetric N-qubit states of the W class: Concurrence and negativity tangle**Project supported by Department of Science and Technology, Government of India through the award of INSPIRE fellowship.

Using Majorana representation of symmetric N-qubit pure states, we have examined the monogamous nature of the family of states with two-distinct spinors, the W class of states. We have evaluated the N-concurrence tangle and showed that all the states in this family have vanishing concurrence tangle. The negativity tangle for the W class of states is shown to be non-zero, illustrating the fact that the concurrence tangle is always lesser than or equal to the negativity tangle in a pure N-qubit state.

Maximal entanglement concentration for a set of $$(n+1)$$ ( n + 1 ) -qubit states

We propose two schemes for concentration of $$(n+1)$$(n+1)-qubit entangled states that can be written in the form of $$\left( \alpha |\varphi _{0}\rangle |0\rangle +\beta |\varphi _{1}\rangle |1\rangle \right) _{n+1}$$?|?0?|0?+s|?1?|1?n+1 where $$|\varphi _{0}\rangle $$|?0? and $$|\varphi _{1}\rangle $$|?1? are mutually orthogonal n-qubit states. The importance of this general form is that the entangled states such as Bell, cat, GHZ, GHZ-like, $$|\varOmega \rangle $$|Ω?, $$|Q_{5}\rangle $$|Q5?, 4-qubit cluster states and specific states from the nine SLOCC-nonequivalent families of 4-qubit entangled states can be expressed in this form. The proposed entanglement concentration protocol is based on the local operations and classical communications (LOCC). It is shown that the maximum success probability for ECP using quantum nondemolition technique (QND) is $$2\beta ^{2}$$2s2 for $$(n+1)$$(n+1)-qubit states of the prescribed form. It is shown that the proposed schemes can be implemented optically. Further, it is also noted that the proposed schemes can be implemented using quantum dot and microcavity systems.

Quantum Teleportation of an Arbitrary N-qubit State via GHZ-like States

Recently Zhu (Int. J. Theor. Phys. 53, 4095, 2014) had shown that using GHZ-like states as quantum channel, it is possible to teleport an arbitrary unknown two-qubit state. We investigate this channel for the teleportation of an arbitrary N-qubit state. The strict proof through mathematical induction is presented and the rule for the receiver to reconstruct the desired state is explicitly derived in the most general case. We also discuss that if a system of quantum secret sharing of classical message is established, our protocol can be transformed to a N-qubit perfect controlled teleportation scheme from the controller’s point of view.

Monogamy of [formula omitted]th power entanglement measurement in qubit systems

In this paper, we study the αth power monogamy properties related to the entanglement measure in bipartite states. The monogamy relations related to the αth power of negativity and the Convex-Roof Extended Negativity are obtained for N-qubit states. We also give a tighter bound of hierarchical monogamy inequality for the entanglement of formation. We find that the GHZ state and W state can be used to distinguish both the αth power of the concurrence for 0<α<2 and the αth power of the entanglement of formation for 0<α≤12. Furthermore, we compare concurrence with negativity in terms of monogamy property and investigate the difference between them.

A recursive approach for geometric quantifiers of quantum correlations in multiqubit Schrödinger cat states

A recursive approach to determine the Hilbert–Schmidt measure of pairwise quantum discord in a special class of symmetric states of k qubits is presented. We especially focus on the reduced states of k qubits obtained from a balanced superposition of symmetric n-qubit states (multiqubit Schrödinger cat states) by tracing out n-k particles (k = 2, 3, …, n-1). Two pairing schemes are considered. In the first one, the geometric discord measuring the correlation between one qubit and the parity grouping (k-1) qubits is explicitly derived. This uses recursive relations between the Fano–Bloch correlation matrices associated with subsystems comprising k, k-1, … and two particles. A detailed analysis is given for two-, three- and four-qubit systems. In the second scheme, the subsystem comprising the (k-1) qubits is mapped into a system of two logical qubits. We show that these two bipartition schemes are equivalents in evaluating the pairwise correlation in multiqubits systems. The explicit expressions of classical states presenting zero discord are derived.

Context-Invariant and Local Quasi Hidden Variable (qHV) Modelling Versus Contextual and Nonlocal HV Modelling

For all the joint von Neumann measurements on a D-dimensional quantum system, we present the specific example of a context-invariant quasi hidden variable (qHV) model, proved in [Loubenets, J. Math. Phys. 56, 032201 (2015)] to exist for each Hilbert space. In this model, a quantum observable X is represented by a variety of random variables satisfying the functional condition required in quantum foundations but, in contrast to a contextual model, each of these random variables equivalently models X under all joint von Neumann measurements, regardless of their contexts. This, in particular, implies the specific local qHV (LqHV) model for an N-qudit state and allows us to derive the new exact upper bound on the maximal violation of 2x...x2-setting Bell-type inequalities of any type (either on correlation functions or on joint probabilities) under N-partite joint von Neumann measurements on an N-qudit state. For d=2, this new upper bound coincides with the maximal violation by an N-qubit state of the Mermin-Klyshko inequality. Based on our results, we discuss the conceptual and mathematical advantages of context-invariant and local qHV modelling.

Inseparability criteria based on bipartitions of $$N$$ N -qubit systems

We present a new set of inequalities to detect inseparability in $$N$$N-qubit states. These are based on negative partial transposition and involve collective qubit---qubit correlations of any two partitions of the entire system. They reveal the rich texture of partial separability for different partitions and can discriminate between GHZ-type and W-type entanglement, as well. We introduce a new concept of relative entanglement of two different systems and two different partitions in a qubit-ensemble. The criteria in its generic form are also applicable to non-symmetric states and states with odd or even $$N$$N.

Analysis ofN-qubit perfect controlled teleportation schemes from the controller's point of view

We quantitatively analyze and evaluate the controller's power in $N$-qubit controlled teleportation schemes. We calculate the minimum control power required to ensure the controller's authority such that the teleportation fidelity without the controller's permission is no more than the classical bound. We revisit several typical controlled teleportation schemes from the controller's point of view and evaluate the control power in these schemes. We find that for teleporting arbitrary N-qubit states, each controller should control at least N bits of useful information to ensure his/her authority over the protocol. We also discuss the general rules that must be satisfied by controlled teleportation schemes to ensure both teleportation fidelity and control power.

Atomic and Photonic Entanglement Generation in n Coupled Atom-Cavity Systems

Based on two-photon Jaynes-Cummings Hamiltonian for the n coupled optical cavities each of them containing a single three level atom, the n-qubit and n-photonic state transfer between the corresponding atoms and cavities is investigated. In fact, we consider that the cavities are located at the nodes (vertices) of the complete network (graph) K n at which all of the nodes are connected, so that the cavities are interact with each other (via two photon exchange) completely. Then, quantum state transfer, photon transition between cavities and entanglement generations between n atoms are discussed. More clearly, by employing the consistency of number of photons and atomic excitations (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from 3 n dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times T at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength ξ between cavities.

A classification of multipartite states by degree of non-locality

We propose a novel form of classification of multipartite states, in terms of the maximum degree of non-locality they can exhibit under any choice of local observables. This uses the hierarchy of notions previously introduced by Abramsky and Brandenburger: strong contextuality, logical contextuality, and probabilistic contextuality. We study n-qubit pure states. We conjecture that for more than 2 parties, all entangled states are logically contextual. We prove a number of results in support of this conjecture: (1) We show that all permutation-symmetric states are logically non-local. (2) We study the class of balanced states with functional dependencies. These states are described by Boolean functions and have a rich structure, allowing a detailed analysis, which again confirms the conjecture in this case.

One-party controlled minimum remote state preparation of equatorial n-qubit states

This paper offers a theoretical protocol for one-party controlled remote state preparation (RSP) of n-qubit states with minimum resources consumption. We are mainly focused on the case of the n-qubit state chosen from equatorial circle on a Bloch sphere. We use n - 1 EPR pairs and one GHZ state as quantum channel and show that only n + 1 cbits, n ebits and 2n + 1 qubits are consumed during the controlled RSP processing.

A bonding model of entanglement for N-qubit graph states

The class of entangled N-qubit states known as graph states, and the corresponding stabilizer groups of N-qubit Pauli observables, have found a wide range of applications in quantum information processing and the foundations of quantum mechanics. A review of the properties of graph states is given and core spaces of graph states are introduced and discussed. A bonding model of entanglement for generalized graph states is then presented, in which the presence or absence of a bond between two qubits unequivocally specifies whether or not they are entangled. A physical interpretation of these bonds is given, along with a characterization of how they can be created or destroyed by entangling unitary operations and how they can be destroyed by local Pauli measurements. It is shown that local unitary operations do not affect the bond structure of a graph state, and therefore that if two graph states have nonisomorphic bond structures, then local unitary operations and/or reordering of qubits cannot change one into the other. Color multigraphs are introduced to depict the bond structures of graph states and to make some of their properties more apparent.

Entanglement monogamy relations of qubit systems

We investigate the monogamy relations related to the concurrence and the entanglement of formation. General monogamy inequalities given by the {\alpha}th power of concurrence and entanglement of formation are presented for N-qubit states. The monogamy relation for entanglement of assistance is also established. Based on these general monogamy relations, the residual entanglement of concurrence and entanglement of formation are studied. Some relations among the residual entanglement, entanglement of assistance, and three tangle are also presented.

Test of genuine multipartite nonlocality without inequalities.

In this Letter we propose a set of conditions on the joint probabilities as a test of genuine multipartite nonlocality without inequality. Our test is failed by all nonsignaling local models in which even nonlocal correlations among some observables (not all) are allowed as long as these correlations respect the nonsignaling principle. A pass of our test by a state therefore indicates that this state cannot be simulated by any nonsignaling local models; i.e., the state exhibits genuine multipartite nonlocality. It turns out that all entangled symmetric n-qubit (n≥3) states pass our test and therefore are n-way nonlocal. Also we construct two Bell-type inequalities from our proposed test whose violations indicate genuine multipartite nonlocal correlations.

Analytical characterization of the genuine multiparticle negativity

The genuine multiparticle negativity is a measure of genuine multiparticle entanglement which can be numerically calculated. We present several results of how this entanglement measure can be characterized in an analytical way. First, we show that with an appropriate normalization this measure can be seen as coming from a mixed convex roof construction. Based on this, we determine its value for n-qubit GHZ-diagonal states and four-qubit cluster-diagonal states.

Multidimensional color image storage, retrieval, and compression based on quantum amplitudes and phases

In this study, we propose a new representation method for multidimensional color images, called an n-qubit normal arbitrary superposition state (NASS), where n qubits represent the colors and coordinates of 2n pixels (e.g., a three-dimensional color image of 1024×1024×1024 using only 30 qubits). Based on NASS, we present an (n+1)-qubit normal arbitrary superposition state with relative phases (NASSRP) and an (n+2)-qubit normal arbitrary superposition state with three components (NASSTC) for lossless and lossy quantum compression, respectively. We also design three general quantum circuits to generate NASS, NASSRP, and NASSTC states, where we retrieve an image from a quantum system using different projection measurement operators. Finally, we define the quantum compression ratio and analyze lossless and lossy quantum compression algorithms of multidimensional quantum images. For the first time, we implemented the compression of multidimensional color images on a quantum computer. Thus, we address the theoretical and practical aspects of image processing on a quantum computer.