Probabilistic analysis of three-player symmetric quantum games played using the Einstein-Podolsky-Rosen-Bohm setting

This Letter extends our probabilistic framework for two-player quantum games to the multiplayer case, while giving a unified perspective for both classical and quantum games. Considering joint probabilities in the Einstein-Podolsky-Rosen-Bohm (EPR-Bohm) setting for three observers, we use this setting in order to play general three-player noncooperative symmetric games. We analyze how the peculiar non-factorizable joint probabilities provided by the EPR-Bohm setting can change the outcome of a game, while requiring that the quantum game attains a classical interpretation for factorizable joint probabilities. In this framework, our analysis of the three-player generalized Prisoner's Dilemma (PD) shows that the players can indeed escape from the classical outcome of the game, because of non-factorizable joint probabilities that the EPR setting can provide. This surprising result for three-player PD contrasts strikingly with our earlier result for two-player PD, played in the same framework, in which even non-factorizable joint probabilities do not result in escaping from the classical consequence of the game.     

Conditional strategies in iterated quantum games

Iterated bipartite quantum games are implemented in terms of the discrete-time quantum walk on the line. Our proposal allows for conditional strategies, as two rational agents make a choice from a restricted set of two-qubit unitary operations. We discuss how several classical strategies are related to families of quantum strategies. A quantum version of the well known Prisoner’s Dilemma bipartite game, in which both players use mixed strategies, is presented as a specific example.     

Quantum controlled phase gate and cluster states generation via two superconducting quantum interference devices in a cavity

A scheme for implementing 2-qubit quantum controlled phase gate (QCPG) is proposed with two superconducting quantum interference devices (SQUIDs) in a cavity. The gate operations are realized within the two lower flux states of the SQUIDs by using a quantized cavity field and classical microwave pulses. Our scheme is achieved without any type of measurement, does not use the cavity mode as the data bus and only requires a very short resonant interaction of the SQUID-cavity system. As an application of the QCPG operation, we also propose a scheme for generating the cluster states of many SQUIDs.     

Quantum Prisoner’s Dilemma game on hypergraph networks

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.     

Classical and quantum transport through entropic barriers modeled by hardwall hyperboloidal constrictions

We study the quantum transport through entropic barriers induced by hardwall constrictions of hyperboloidal shape in two and three spatial dimensions. Using the separability of the Schrödinger equation and the classical equations of motion for these geometries, we study in detail the quantum transmission probabilities and the associated quantum resonances, and relate them to the classical phase structures which govern the transport through the constrictions. These classical phase structures are compared to the analogous structures which, as has been shown only recently, govern reaction type dynamics in smooth systems. Although the systems studied in this paper are special due their separability they can be taken as a guide to study entropic barriers resulting from constriction geometries that lead to non-separable dynamics.     

Remote preparation of a class of three-qubit states

We propose a remote state preparation (RSP) scheme of a three-particle Greenberger-Horne-Zeilinger (GHZ) class state by using three 2-qubit maximally entangled states as the quantum channel. The success probability of preparation and classical communication cost are calculated. Generally speaking, conditioned on Alice’s classical message, with probability 1/4 Bob can successfully prepare the original state by performing one appropriate unitary operation. However, for four kinds of special states, the success probability of preparation can be increased to 1/2 or even 1 after consuming some extra bits.     

Preparation of pseudo-pure states for NMR quantum computing with one ancillary qubit

Quantum state preparation plays an equally important role as quantum operations and measurements in quantum information processing. The previous methods for initialization require either an exponential number of experiments, or cause signal reduction or place restrictions on molecular structures. In this study, we propose three types of quantum circuits for preparing the pseudo-pure states of(n-1) qubits in the n-coupled Hilbert space, which simply needs the assistance of one ancilla spin and two different experiments independent of n. Most importantly, our methods work well on homo-nuclear and hetero-nuclear molecules without the reduction of signals in the gradient field. As a proof-of-principle demonstration, we experimentally prepared the pseudo-pure states of heteronuclear 2-qubit and homonuclear 4-qubit molecules using a nuclear magnetic resonance quantum information processor.     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

Quantum teleportation using entangled 3-qubit states and the ‘magic bases’

We study quantum teleportation of single qubit information state using 3-qubit general entangled states. We propose a set of 8 GHZ-like states which gives (i) standard quantum teleportation (SQT) involving two parties and 3-qubit Bell state measurement (BSM) and (ii) controlled quantum teleportation (CQT) involving three parties, 2-qubit BSM and an independent measurement on one qubit. Both are obtained with perfect success and fidelity and with no restriction on destinations (receiver) of any of the three entangled qubits. For SQT, for each designated one qubit which is one of a pair going to Alice, we obtain a magic basis containing eight basis states. The eight basis states can be put in two groups of four, such that states of one group are identical with the corresponding GHZ-like states and states of the other differ from the corresponding GHZ-like states by the same phase factor. These basis states can be put in two different groups of four-states each, such that if any entangled state is a superposition of these with coefficients of each group having the same phase, perfect SQT results. Also, for perfect CQT, with each set of given destinations of entangled qubits, we find a different magic basis. If no restriction on destinations of any entangled qubit exists, three magic semi-bases, each with four basis states, are obtained, which lead to perfect SQT. For perfect CQT, with no restriction on entangled qubits, we find four magic quarter-bases, each having two basis states. This gives perfect SQT also. We also obtain expressions for co-concurrences and conditional concurrences.     

Locking classical correlations in quantum States

We show that there exist bipartite quantum states which contain a large locked classical correlation that is unlocked by a disproportionately small amount of classical communication. In particular, there are (2n+1)-qubit states for which a one-bit message doubles the optimal classical mutual information between measurement results on the subsystems, from n/2 bits to n bits. This phenomenon is impossible classically. However, states exhibiting this behavior need not be entangled. We study the range of states exhibiting this phenomenon and bound its magnitude.     

Probabilistic Controlled Teleportation of a Triplet W State with Combined Channel of Non-Maximally Entangled Einstein-Podolsky-Rosen and Greenberger-Horne-Zeilinger States

A scheme for probabilistic controlled teleportation of a triplet W state using combined non-maximally entangled channel of two Einstein-Podolsky-Rosen （EPR） states and one Creenberger-Horne-Zeilinger （CHZ） state is proposed. In this scheme, an （m ＋ 2）-qubit CHZ state serves not only as the control parameter but also as the quantum channel. The m control qubits are shared by m supervisors. With the aid of local operations and individual measurements, including Bell-state measurement, Von Neumann measurement, and mutual classical communication etc., Bob can faithfully reconstruct the original state by performing relevant unitary transformations. The total probability of successful teleportation is only dependent on channel coefficients of EPR states and GHZ, independent of the number of supervisor m. This protocol can also be extended to probabilistic controlled teleportation of an arbitrary N-qubit state using combined non-maximally entangled channel of N- 1 EPR states and one （m ＋ 2）-qubit GHZ.     

Discussion of the entanglement classification of a 4-qubit pure state

We classify 4-qubit pure states under the stochastic local operation and classical communication (SLOCC). There exist twenty three essentially different classes of states, giving rise to a four-graded partially ordered structure. We also give the criterion to judge which class an arbitrary 4-qubit state belongs to. We re-classify the 4-qubit pure state into 2×2×4, 4×4 aspects. Finally, we give our analysis of the classification difference of methods for the 3-qubit pure state.     

Perfect quantum teleportation and dense coding protocols via the 2N-qubit W state

In this paper, we investigate perfect quantum teleportation and dense coding by using an 2N-qubit W state channel. In the quantum teleportation scheme, an unknown N-qubit entangled state can be perfectly teleported. One ebit of entanglement and two bits of classical communication are consumed in the teleportation process, just like when using the Bell state channel. While N+1 bits of classical information can be transmitted by only sending N particles in the dense coding protocol.     

Quantum Fisher Information of a 3-Qubit State

We investigate the properties of quantum Fisher information in a general superposition of a 3-qubit GHZ state and two W states. Numerical calculation for quantum Fisher information of the 3-qubit state is given. It is shown that the mean spin direction, the length of mean spin and quantum Fisher information are determined by the coefficients of superposition and the relative phase between the GHZ state and the W states.     

Improved Protocols of Secure Quantum Communication Using W States

Recently, Hwang et al. (Eur. Phys. J. D 61:785, 2011) and Yuan et al. (Int. J. Theor. Phys. 50:2403, 2011) have proposed two efficient protocols of secure quantum communication using 3-qubit and 4-qubit symmetric W state respectively. These two dense coding based protocols are generalized and their efficiencies are considerably improved. Simple bounds on the qubit efficiency of deterministic secure quantum communication (DSQC) and quantum secure direct communication (QSDC) protocols are obtained and it is shown that dense coding is not essential for designing of maximally efficient DSQC and QSDC protocols. This fact is used to design maximally efficient protocols of DSQC and QSDC using 3-qubit and 4-qubit W states.     

Scheme for implementing perfect quantum dense coding with three-atom W-class state in cavity QED

We propose an experimentally feasible scheme of implementing perfect quantum dense coding with three-atom W-class state in cavity QED. In this scheme atoms interact simultaneously with a highly detuned cavity field and the cavity is only virtually excited, thus the scheme is insensitive to the cavity decay, which is very important in view of experiment. Moreover, we also propose a scheme of transmitting three bits of classical information by sending one qubit and one classical bit with 3-qubit W-class and GHZ states.     

Exact results on decoherence and entanglement in a system of N driven atoms and a dissipative cavity mode

We solve the dynamics of an open quantum system where N strongly driven two-level atoms are equally coupled on resonance to a dissipative cavity mode. Analytical results are derived on decoherence, entanglement, purity, atomic correlations and cavity field mean photon number. We predict decoherencefree subspaces for the whole system and the N-qubit subsystem, the monitoring of quantum coherence and purity decay by atomic populations measurements, the conditional generation of atomic multi-partite entangled states and of cavity cat-like states. We show that the dynamics of atoms prepared in states invariant under permutation of any two components remains restricted within the subspace spanned by the completely symmetric Dicke states. We discuss examples and applications in the cases N = 3, 4. An erratum to this article can be found at     

A Macroscopic Device for Quantum Computation

We show how a compound system of two entangled qubits in a non-product state can be described in a complete way by extracting entanglement into an internal constraint between the two qubits. By making use of a sphere model representation for the spin 1/2, we derive a geometric model for entanglement. We illustrate our approach on 2-qubit algorithms proposed by Deutsch, respectively Arvind. One of the advantages of the 2-qubit case is that it allows for a nice geometrical representation of entanglement, which contributes to a more intuitive grasp of what is going on in a 2-qubit quantum computation.     

Arbiter as the Third Man in Classical and Quantum Games

We study the possible influence of a not necessarily sincere arbiter on the course of classical and quantum 2×2 games and we show that this influence in the quantum case is much bigger than in the classical case. Extreme sensitivity of quantum games on initial states of quantum objects used as carriers of information in a game shows that a quantum game, contrary to a classical game, is not defined by a payoff matrix alone but also by an initial state of objects used to play a game. Therefore, two quantum games that have the same payoff matrices but begin with different initial states should be considered as different games.     

From quantum mechanics to classical statistical physics: Generalized Rokhsar-Kivelson Hamiltonians and the “Stochastic Matrix Form” decomposition

Quantum Hamiltonians that are fine-tuned to their so-called Rokhsar-Kivelson (RK) points, first presented in the context of quantum dimer models, are defined by their representations in preferred bases in which their ground state wave functions are intimately related to the partition functions of combinatorial problems of classical statistical physics. We show that all the known examples of quantum Hamiltonians, when fine-tuned to their RK points, belong to a larger class of real, symmetric, and irreducible matrices that admit what we dub a Stochastic Matrix Form (SMF) decomposition. Matrices that are SMF decomposable are shown to be in one-to-one correspondence with stochastic classical systems described by a Master equation of the matrix type, hence their name. It then follows that the equilibrium partition function of the stochastic classical system partly controls the zero-temperature quantum phase diagram, while the relaxation rates of the stochastic classical system coincide with the excitation spectrum of the quantum problem. Given a generic quantum Hamiltonian construed as an abstract operator defined on some Hilbert space, we prove that there exists a continuous manifold of bases in which the representation of the quantum Hamiltonian is SMF decomposable, i.e., there is a (continuous) manifold of distinct stochastic classical systems related to the same quantum problem. Finally, we illustrate with three examples of Hamiltonians fine-tuned to their RK points, the triangular quantum dimer model, the quantum eight-vertex model, and the quantum three-coloring model on the honeycomb lattice, how they can be understood within our framework, and how this allows for immediate generalizations, e.g., by adding non-trivial interactions to these models.