Quantum game players can have advantage without discord

The last two decades have witnessed a rapid development of quantum information processing, a new paradigm which studies the power and limit of "quantum advantages" in various information processing tasks. Problems such as when quantum advantage exists, and if existing, how much it could be, are at a central position of these studies. In a broad class of scenarios, there are, implicitly or explicitly, at least two parties involved, who share a state, and the correlation in this shared state is the key factor to the efficiency under concern. In these scenarios, the shared \emph{entanglement} or \emph{discord} is usually what accounts for quantum advantage. In this paper, we examine a fundamental problem of this nature from the perspective of game theory, a branch of applied mathematics studying selfish behaviors of two or more players. We exhibit a natural zero-sum game, in which the chance for any player to win the game depends only on the ending correlation. We show that in a certain classical equilibrium, a situation in which no player can further increase her payoff by any local classical operation, whoever first uses a quantum computer has a big advantage over its classical opponent. The equilibrium is fair to both players and, as a shared correlation, it does not contain any discord, yet a quantum advantage still exists. This indicates that at least in game theory, the previous notion of discord as a measure of non-classical correlation needs to be reexamined, when there are two players with different objectives.Comment: 15 page

Quantum Protocol for Decision Making and Verifying Truthfulness among NN-quantum Parties: Solution and Extension of the Quantum Coin Flipping Game

We devised a protocol that allows two parties, who may malfunction or intentionally convey incorrect information in communication through a quantum channel, to verify each other's measurements and agree on each other's results. This has particular relevance in a modified version of the quantum coin flipping game where the possibility of the players cheating is now removed. Furthermore, the analysis is extended to $N$-parties communicating with each other, where we propose multiple solutions for the verification of each player's measurement. The results in the $N$-party scenario could have particular relevance for the implementation of future quantum networks, where verification of quantum information is a necessity

A measure of quantum correlations that lies approximately between entanglement and discord

When a quantum system is divided into two local subsystems, measurements on the two subsystems can exhibit correlations beyond those possible in a classical joint probability distribution; these are partially explained by entanglement, and more generally by a wider class of measures such as the quantum discord. In this work, I introduce a simple thought experiment defining a new measure of quantum correlations, which I call the accord, and write the result as a minimax optimization over unitary matrices. I find the exact result for pure states as a simple function of the Schmidt coefficients and provide a complete proof, and I likewise provide and prove the result for several classes of mixed states, notably including all states of two qubits and the experimentally relevant case of a pure state mixed with colorless noise. I demonstrate that for two qubit states the accord provides a tight lower bound on the discord; for Bell diagonal states it is also an upper bound on entanglement.Comment: 15 pages, 5 figures; v2: removed claim of convexity, all other results unchanged; v3: typo-level correction

Payoffs and coherence of a quantum two-player game in a thermal environment

A two-player quantum game is considered in the presence of a thermal decoherence modeled in terms of a rigorous Davies approach. It is shown how the energy dissipation and pure decoherence affect the payoffs of the players of the (quantum version) of prisoner dilemma. The impact of the thermal environment on a coherence of game, as a quantum system, is also presented

Information Theoretic Resources in Quantum Theory

Resource identification and quantification is an essential element of both classical and quantum information theory. Entanglement is one of these resources, arising when quantum communication and nonlocal operations are expensive to perform. In the first part of this thesis we quantify the effective entanglement when operations are additionally restricted. For an important class of errors we find a linear relationship between the usual and effective higher dimensional generalization of concurrence, a measure of entanglement. In the second chapter we focus on nonlocality in the presence of superselection rules, where we propose a scheme that may be used to activate nongenuinely multipartite nonlocality with multiple copies of the state. We show that whenever the number of particles is insufficient, the genuinely multipartite nonlocality is degraded to nongenuinely multipartite. While in the first few chapters we focus on understanding the resources present in quantum states, in the final part we turn the picture around and instead treat operations themselves as a resource. We provide our observers with free access to classical operations - ie. those that cannot detect or generate quantum coherence. We show that the operation of interest can then be used to either generate or detect quantum coherence if and only if it violates a particular commutation relation. Using the relative entropy, the commutation relation provides us with a measure of nonclassicality of operations. We show that the measure is a sum of two contributions, the generating power and the distinguishing power, each of which is separately an essential ingredient in quantum communication and information processing. The measure also sheds light on the operational meaning of quantum discord, which we show can be interpreted as the difference in superdense coding capacity between a quantum state and a classical state.Comment: Thesis, 109 page

Quantum two player game in thermal environment

A two-player quantum game is considered in the presence of thermal decoherence. It is shown how the thermal environment modeled in terms of rigorous Davies approach affects payoffs of the players. The conditions for either beneficial or pernicious effect of decoherence are identified. The general considerations are exemplified by the quantum version of Prisoner Dilemm