A quantum version of the Monty Hall problem is proposed inspired by an experimentally-feasible, quantum-optical set-up that resembles the classical game. The expected payoff of the player is studied by analyzing the classical expectation values of the obtained quantum probabilities. Results are examined by considering both entanglement and non-entanglement between player and host, and using two different approaches: random and strategy-based. We also discuss the influence of noise on the game outcome when the parties play through a noisy quantum channel. The experimental set-up can be used to quickly verify the counter-intuitive result of the Monty Hall problem, adding pedagogic value to the proposal.
The purpose of this manuscript is to provide a short pedagogical explanation why "quantum collapse" is not a metaphysical event, by pointing out the analogy with a "classical collapse" which is associated with the Monty Hall Paradox.
The influence of spontaneous emission channel and generalized Pauli channel on quantum Monty Hall Game is analysed. The scheme of Flittney and Abbott is reformulated using the formalism of density matrices. Optimal classical strategies for given quantum strategies are found. The whole presented scheme illustrates how quantum noise may change the odds of a zero-sum game.
This paper presents a quantum version of the Monty Hall problem based upon the quantum inferring acausal structures, which can be identified with generalization of Bayesian networks. Considered structures are expressed in formalism of quantum information theory, where density operators are identified with quantum generalization of probability distributions. Conditional relations between quantum counterpart of random variables are described by quantum conditional operators. Presented quantum inferring structures are used to construct a model inspired by scenario of well-known Monty Hall game, w…
The quantum Pusey--Barrett--Rudolph (PBR) theorem addresses the question of whether the quantum state corresponds to a $ψ$-ontic model (system's physical state) or to a $ψ$-epistemic model (observer's knowledge about the system). We reformulate the PBR theorem as a Monty Hall game, and show that winning probabilities, for switching doors in the game, depend whether it is a $ψ$-ontic or $ψ$-epistemic game. For certain cases of the latter, switching doors provides no advantage. We also apply the concepts involved to quantum teleportation, in particular for improving reliability.
In this work we propose a quantum version of a generalized Monty Hall game, that is, one in which the parameters of the game are left free, and not fixed on its regular values. The developed quantum scheme is then used to study the expected payoff of the player, using both a separable and an entangled initial-state. In the two cases, the classical mixed-strategy payoff is recovered under certain conditions. Lastly, we extend our quantum scheme to include multiple independent players, and use this extension to sketch two possible application of the game mechanics to quantum networks, specifical…
Here, we present the quantum version of a very famous statistical decision problem, whose classical version is counter-intuitive to many. The Monty Hall game can be phrased as a two person game between Alice and Bob. In their pioneering work, Flitney and Abbott [Phys. Rev. A 65, 062318 (2002)] showed that by using a maximally entangled system for Alice and Bob's choices, and using quantum strategies, Bob and Alice can win or lose depending on the strategy chosen by either of the players. Here we develop a new quantum algorithm with quantum circuits for playing the quantum Monty Hall game by a …
We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice's quantum strategy. Where as in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, the Bob's payoffs are found symmetrical with maximum at p=0.5 against his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strat…
A version of the Monty Hall problem is presented where the players are permitted to select quantum strategies. If the initial state involves no entanglement the Nash equilibrium in the quantum game offers the players nothing more than can be obtained with a classical mixed strategy. However, if the initial state involves entanglement of the qubits of the two players, it is advantageous for one player to have access to a quantum strategy while the other does not. Where both players have access to quantum strategies there is no Nash equilibrium in pure strategies, however, there is a Nash equili…
We reformulate the quantum Monty Hall problem in the presence of decoherence. The decoherence destroys the fairness of the game. A new Nash equilibrium for a particular strategy profile in the presence of decoherence emerges. It is shown that in the presence of decoherence under the action of amplitude damping channel, Bob's winning probability is always higher than three-forth, irrespective of Alice's strategy, if he does not switch to the other door and always wins for a fully decohered case of the channel. Depolarizing channel damps up Bob's winning probability and gets better off if he sti…
This work illustrates a possible application of quantum game theory to the area of quantum information, in particular to quantum cryptography. The study proposed two quantum key-distribution (QKD) protocols based on the quantum version of the Monty Hall game devised by Flitney and Abbott. Unlike most QKD protocols, in which the bits from which the key is going to be extracted are encoded in a basis choice (as in BB84), these are encoded in an operation choice. The first proposed protocol uses qutrits to describe the state of the system and the same game operators proposed by Flitney and Abbott…
We consider a quantum version of a well-known statistical decision problem, whose solution is, at first sight, counter-intuitive to many. In the quantum version a continuum of possible choices (rather than a finite set) has to be considered. It can be phrased as a two person game between a player P and a quiz master Q. Then P always has a strategy at least as good as in the classical case, while Q's best strategy results in a game having the same value as the classical game. We investigate the consequences of Q storing his information in classical or quantum ways. It turns out that Q's optimal…
In classical Monty Hall problem, one player can always win with probability 2/3. We generalize the problem to the quantum domain and show that a fair two-party zero-sum game can be carried out if the other player is permitted to adopt quantum measurement strategy.
Spin Hall effect, one of the cornerstones in spintronics refers to the emergence of an imbalance in the spin density transverse to a charge flow in a sample under voltage bias. This study points to a novel way for an ultrafast generation and tuning of a unidirectional nonlinear spin Hall current by means of subpicosecond laser pulses of optical vortices. When interacting with matter, the optical orbital angular momentum (OAM) carried by the vortex and quantified by its topological charge is transferred to the charge carriers. The residual spin-orbital coupling in the sample together with confi…
We present an interferometric scheme producing orbital entanglement in a quantum Hall system upon electron-hole pair emission via tunneling. The proposed setup is an electronic version of the optical interferometer proposed by Cabello et al. [Phys. Rev. Lett. 102, 040401 (2009)], and is feasible with present technology. It requires single-channel propagation and a single primary source. We discuss the creation of entanglement and its detection by the violation of a Bell inequality.
We study the optically pumped nuclear spin polarization in a single GaAs/AlGaAs quantum well in the quantum Hall system. We apply resistive detection via the contact hyperfine interaction, which provides high sensitivity and selectivity, to probe a small amount of polarized nuclear spins in a single well. The properties of the optical nuclear spin polarization are clearly observed. We theoretically discuss the nuclear spin dynamics accompanied with doped electrons to analyze the experimental data. The optical nuclear polarization spectra exhibit electron-spin-resolved lowest Landau level inter…
We propose a scheme to realize bosonic fractional quantum Hall conductance in shaken honeycomb optical lattices. This scheme does not require a very flat band, and the necessary long-range interaction relies on s-wave scattering, which is common in many ultracold-atom experiments. By filling the lattice at 1/4 with identical bosons under Feshbach resonance, two degenerate many-body ground states share one Chern number of 1 and correspond exactly to the fractional quantum Hall conductance of 1/2. Meanwhile, we prove that the fractional quantum Hall state can be prepared by adiabatically turning…
We propose and study various realizations of a Hofstadter-Hubbard model on a cylinder geometry with fermionic cold atoms in optical lattices. The cylindrical optical lattice is created by copropagating Laguerre-Gauss beams, i.e.~light beams carrying orbital angular momentum. By strong focusing of the light beams we create a real space optical lattice in the form of rings, which are offset in energy. A second set of Laguerre-Gauss beams then induces a Raman-hopping between these rings, imprinting phases corresponding to a synthetic magnetic field (artificial gauge field). In addition, by rotati…
We propose an experimental scheme to simulate the many-body dynamical quantum Hall effect with ultra-cold bosonic atoms in a one-dimensional optical lattice. We first show that the required model Hamiltonian of a spin-1/2 Heisenberg chain with an effective magnetic field and tunable parameters can be realized in this system. For dynamical response to ramping the external fields, the quantized plateaus emerge in the Berry curvature of the interacting atomic spin chain as a function of the effective spin-exchange interaction. The quantization of this response in the parameter space with the inte…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. Béri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).
Phenomena associated with topological properties of physical systems are naturally robust against perturbations. This robustness is exemplified by quantized conductance and edge state transport in the quantum Hall and quantum spin Hall effects. Here we show how exploiting topological properties of optical systems can be used to implement robust photonic devices. We demonstrate how quantum spin Hall Hamiltonians can be created with linear optical elements using a network of coupled resonator optical waveguides (CROW) in two dimensions. We find that key features of quantum Hall systems, includin…
We analyze a recently proposed method to create fractional quantum Hall (FQH) states of atoms confined in optical lattices [A. Sørensen {\it et al.}, Phys. Rev. Lett. {\bf 94} 086803 (2005)]. Extending the previous work, we investigate conditions under which the FQH effect can be achieved for bosons on a lattice with an effective magnetic field and finite onsite interaction. Furthermore, we characterize the ground state in such systems by calculating Chern numbers which can provide direct signatures of topological order and explore regimes where the characterization in terms of wavefunction ov…
We study the properties of an ultracold Fermi gas loaded in an optical square lattice and subjected to an external and classical non-Abelian gauge field. We show that this system can be exploited as an optical analogue of relativistic quantum electrodynamics, offering a remarkable route to access the exotic properties of massless Dirac fermions with cold atoms experiments. In particular we show that the underlying Minkowski space-time can also be modified, reaching anisotropic regimes where a remarkable anomalous quantum Hall effect and a squeezed Landau vacuum could be observed.
Local excitations in fractional quantum Hall systems are amongst the most intriguing objects in condensed matter, as they behave like particles of fractional charge and fractional statistics. In order to experimentally reveal these exotic properties and further to use such excitations for quantum computations, microscopic control over the excitations is necessary. Here we discuss different optical strategies to achieve such control. First, we propose that the application of a light field with non-zero orbital angular momentum can pump orbital angular momenta to electrons in a quantum Hall drop…
We propose that a tunable generalized three-dimensional Hofstadter Hamiltonian can be realized by engineering the Raman-assisted hopping of ultracold atoms in a cubic optical lattice. The Hamiltonian describes a periodic lattice system under artificial magnetic fluxes in three dimensions. For certain hopping configurations, the bulk bands can have Weyl points and nodal loops, respectively, allowing the study of both the two nodal semimetal states within this system. Furthermore, we illustrate that with proper rational fluxes and hopping parameters, the system can exhibit the three-dimensional …
