Investigation of Quantum Roulette

Salimi, S.; Soltanzadeh, M. M.

doi:10.1142/s0219749909004992

Cited by 24 publications

(21 citation statements)

References 20 publications

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“…Salimi et al [6] used permutation matrices and the Fourier matrix as a representation of the symmetric group S n . They viewed quantum roulette as a typical n-state quantum system and developed a methodology that allowed them to solve this quantum game for arbitrary n. As an example, they employed their technique for a quantum roulette with n = 3.…”

Section: Related Workmentioning

confidence: 99%

“…This means that our games take place in the two-dimensional complex Hilbert space H 2 and we shall not be concerned with higher dimensional analogs of the PQ game like those in [6,7].…”

Section: Hypothesis 2 (H2)mentioning

confidence: 99%

“…More formally, the completeness property can be expressed as follows ∀γ ∈ N ∀α ∈ Act : Q(G(|s , γ), α) ⇒λ(α) ∈ L A , and (6) ∀γ ∈ N ∀α ∈ Act :…”

Section: Definition 8 (Complete Automaton For Winning Sequences)mentioning

confidence: 99%

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Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

et al. 2018

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Abstract:The meticulous study of finite automata has produced many important and useful results. Automata are simple yet efficient finite state machines that can be utilized in a plethora of situations. It comes, therefore, as no surprise that they have been used in classic game theory in order to model players and their actions. Game theory has recently been influenced by ideas from the field of quantum computation. As a result, quantum versions of classic games have already been introduced and studied. The PQ penny flip game is a famous quantum game introduced by Meyer in 1999. In this paper, we investigate all possible finite games that can be played between the two players Q and Picard of the original PQ game. For this purpose, we establish a rigorous connection between finite automata and the PQ game along with all its possible variations. Starting from the automaton that corresponds to the original game, we construct more elaborate automata for certain extensions of the game, before finally presenting a semiautomaton that captures the intrinsic behavior of all possible variants of the PQ game. What this means is that, from the semiautomaton in question, by setting appropriate initial and accepting states, one can construct deterministic automata able to capture every possible finite game that can be played between the two players Q and Picard. Moreover, we introduce the new concepts of a winning automaton and complete automaton for either player.

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Section: Related Workmentioning

confidence: 99%

“…This means that our games take place in the two-dimensional complex Hilbert space H 2 and we shall not be concerned with higher dimensional analogs of the PQ game like those in [6,7].…”

Section: Hypothesis 2 (H2)mentioning

confidence: 99%

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Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

et al. 2018

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“…where σ i are the Pauli matrices. The Kraus operators for a single qutrit depolarizing noise are given as [28]…”

Section: Qubit-qutrit System In Depolarizing Noisementioning

confidence: 99%

Generation and sudden death of entanglement in qubit–qutrit systems with depolarising noise

Khan¹

2013

Math. Struct. Comp. Sci.

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In this paper we study the dynamics of entanglement in some hybrid qubit–qutrit systems under the influence of global, collective, local and multilocal depolarising noise. We show that depolarising noise can be used to induce entanglement. A critical point exists under every coupling of the system with the environment at which all the states are equally entangled. Furthermore, we show that no ESD occurs when either only the qubit is coupled to its local environment or the system is coupled to a multilocal or global environment. This is an important result for various quantum information processing tasks and thus merits further investigation.

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“…A study of quantum walks on simple lattice is well known in physics(see [14]). Recent studies of quantum walks on more general graphs were described in [8,7,10,13,15,16,17,18,19,20,21,22]. Some of these works studies the problem in the important context of algorithmic problems on graphs and had suggested that quantum walks is a promising algorithmic technique for designing future quantum algorithms.…”

Section: Introductionmentioning

confidence: 99%

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

Salimi¹,

Jafarizadeh²

2009

Commun. Theor. Phys.

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In this paper we define direct product of graphs and give a recipe for obtained probability of observing particle on vertices in the continuous-time classical and quantum random walk. In the recipe, the probability of observing particle on direct product of graph obtain by multiplication of probability on the corresponding to sub-graphs, where this method is useful to determine probability of walk on complicated graphs. Using this method, we calculate the probability of continuous-time classical and quantum random walks on many of finite direct product cayley graphs ( complete cycle, complete K n , charter and n-cube). Also, we inquire that the classical state the stationary uniform distribution is reached as t −→ ∞ but for quantum state is not always satisfy.

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Investigation of Quantum Roulette

Cited by 24 publications

References 20 publications

Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Finite Automata Capturing Winning Sequences for All Possible Variants of the PQ Penny Flip Game

Generation and sudden death of entanglement in qubit–qutrit systems with depolarising noise

Continuous-Time Classical and Quantum Random Walk on Direct Product of Cayley Graphs

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