arXiv subjects

Doyeol Ahn

Publications and source records attributed to Doyeol Ahn.

31 records · Page 2Linked to original sources

arXiv2006

Final state boundary condition of the Schwarzschild black hole

It is shown that the internal stationary state of the Schwarzschild black hole can be represented by a maximally entangled two-mode squeezed state of collapsing matter and infalling Hawking radiation. The final boundary condition at the singularity is then described by the random unitary transformation acting on the collapsing matter field. The outgoing Hawking radiation is obtained by the final state projection on the total wave function, which looks like a quantum teleportation process without the classical information transmitted. The black hole evaporation process as seen by the observer outside the black hole is now a unitary process but non-local physics is required to transmit the information outside the black hole. It is also shown that the final state projection by the evaporation process is strongly affected by the quantum state outside the event horizon, which clearly violates the locality principle.

hep-th↗

arXiv2006

Effects of Hawking radiation and Wigner rotation on fermion entanglement

In this work, we report that the Hawking radiation effect on fermions is fundamentally different from the case of scalar particles. Intrinsic properties of fermions (exclusion principle and spin) affect strongly the interaction of fermions with both Hawking radiation and metric of the spacetime. In particular we have found the following: first, while the fermion vacuum state seen by the Rindler observer is an entangled state in which the right and left Rindler wedge states appear in correlated pairs as in the case of the scalar particles, the entanglement disappears in the excited state due to the exclusion principle; second, the spin of the fermion experiences the Winger rotation under a uniform acceleration; and third, the quantum information of fermions encoded in spin (entangled state is composed of different spin states but with the same mode function) is dissipated not by the Hawking radiation but by the Wigner rotation as the pair approaches the event horizon.

quant-ph↗

arXiv2006

Inter-valley interactions in Si quantum dots

In this paper, we studied the inter-valley interactions between the orbital functions associated with multi-valley of silicon (Si) quantum dots. Numerical calculations show that the inter-valley coupling between orbital functions increases rapidly with an applied electric field. We also considered the potential applications to the quantum bit operation utilizing controlled inter-valley interactions. Quantum bits are the multi-valley symmetric and anti-symmetric orbitals. Evolution of these orbitals would be controlled by an external electric field which turns on and off the inter-valley interactions. Estimates of the decoherence time are made for the longitudinal acoustic phonon process. Elementary single and two qubit gates are also proposed.

quant-ph↗

arXiv2006

Information paradox and black hole final state for fermions

The black hole information paradox is the result of contradiction between Hawking's semi-classical argument, which dictates that the quantum coherence should be lost during the black hole evaporation and the fundamental principles of quantum mechanics, the evolution of pure states to pure states. For over three decades, this contradiction has been one of the major obstacles to the ultimate unification of quantum mechanics and general relativity. Recently, a final-state boundary condition inside the black hole was proposed to resolve this contradiction for bosons. However, no such a remedy exists for fermions yet even though Hawking effect for fermions has been studied for sometime. Here, I report that the black hole information paradox can be resolved for the fermions by imposing a final state boundary condition, which resembles local measurement with post selection. In this scenario, the evaporation can be seen as the post selection determined by random unitary transformation. It is also found that the evaporation processes strongly depends on the boundary condition at the event horizon. This approach may pave the way towards the unified theory for the resolution of information paradox and beyond.

hep-th↗

arXiv2005

The entanglement criterion of multiqubits

We present an entanglement criterion for multiqubits by using the quantum correlation tensors which rely on the expectation values of the Pauli operators for a multiqubit state. Our criterion explains not only the total entanglement of the system but also the partial entanglement in subsystems. It shows that we have to consider the subsystem entanglements in order to obtain the full description for multiqubit entanglements. Furthermore, we offer an extension of the entanglement to multiqudits.

quant-ph↗

arXiv2004

Completely-Positive Non-Markovian Decoherence

We propose an effective Hamiltonian approach to investigate decoherence of a quantum system in a non-Markovian reservoir, naturally imposing the complete positivity on the reduced dynamics of the system. The formalism is based on the notion of an effective reservoir, i.e., certain collective degrees of freedom in the reservoir that are responsible for the decoherence. As examples for completely positive decoherence, we present three typical decoherence processes for a qubit such as dephasing, depolarizing, and amplitude-damping. The effects of the non-Markovian decoherence are compared to the Markovian decoherence.

quant-ph↗

arXiv2003

Entanglement measure for any quantum states

The entanglement measure for multiqudits is proposed. This measure calculates the partial entanglement distributed by subsystems and the complete entanglement of the total system. This shows that we need to measure the subsystem entanglements to explain the full description for multiqudit entanglement. Furthermore, we extend the entanglement measure to mixed multiqubits and the higher dimension Hilbert spaces.

quant-ph↗

arXiv2003

Relativistic entanglement of Bell states with general momentum

In this paper, the Lorentz transformation of the entangled Bell states with momentum, not necessarily orthogonal to the boost direction, and spin, is studied. We extended quantum correlations and Bell's inequality to the relativistic regime by considering normalized relativistic observables. It is shown that quantum information, along the perpendicular direction to the boost, is eventually lost and Bell's inequality is not always violated for entangled states in special relativity. This could impose restrictions to certain quantum information processing such as quantum cryptography using massive particles.

quant-ph↗

arXiv2002

Lorentz covariant reduced-density-operator theory for relativistic quantum information processing

In this paper, we derived Lorentz covariant quantum Liouville equation for the density operator which describes the relativistic quantum information processing from Tomonaga-Schwinger equation and an exact formal solution for the reduced-density-operator is obtained using the projector operator technique and the functional calculus. When all the members of the family of the hypersurfaces become flat hyperplanes, it is shown that our results agree with those of non-relativistic case which is valid only in some specified reference frame. To show that our new formulation can be applied to practical problems, we derived the polarization of the vacuum in quantum electrodynamics up to the second order. The formulation presented in this work is general and might be applied to related fields such as quantum electrodynamics and relativistic statistical mechanics.

quant-ph↗

arXiv2002

Entangled multiplet by angular momentum addition

We present the visible entangled states of 4-qubit system which can be observed easily in physical laboratories. This was motivated from the fact that the entangled state of 2-qubit system comes from singlet and triplet states which are constructed through the angular momentum addition formalism. We show that 4-qubit system has the new entangled states different from GHZ or W types entangled states

quant-ph↗

arXiv2002

Relativistic entanglement and Bell's inequality

In this paper, the Lorentz transformation of entangled Bell states seen by a moving observer is studied. The calculated Bell observable for 4 joint measurements turns out to give a universal value, $<\hat{a}\otimes\vec{b}>+<\hat{a}\otimes\vec{b}'>+\lang le\hat{a}'\otimes\vec{b}> -<\hat{a}'\otimes\vec{b}'>=\frac{2}{\sqrt{2-β^2}}(1+\sqrt{1-\be ta^2})$, where $\hat{a}, \hat{b}$ are the relativistic spin observables derived from the Pauli-Lubanski pseudo vector and $β=\frac{v}{c}$. We found that the degree of violation of the Bell's inequality is decreasing with increasing velocity of the observer and the Bell's inequality is satisfied in the ultra-relativistic limit where the boost speed reaches the speed of light.

quant-ph↗

arXiv2002

Relativistic entanglement of quantum states and nonlocality of Einstein-Podolsky-Rosen(EPR) paradox

Relativistic bipartite entangled quantum states is studied to show that Nature doesn't favor nonlocality for massive particles in the ultra-relativistic limit. We found that to an observer (Bob) in a moving frame S', the entangled Bell state shared by Alice and Bob appears as the superposition of the Bell bases in the frame S' due to the requirement of the special relativity. It is shown that the entangled pair satisfies the Bell's inequality when the boost speed approaches the speed of light, thus providing a counter example for nonlocality of Einstein-Podolsky-Rosen(EPR) paradox.

quant-ph↗

arXiv2001

Self-consistent non-Markovian theory of a quantum state evolution for quantum information processing

It is shown that the operator sum representation for non-Markovian dynamics and the Lindblad master equation in Markovian limit can be derived from a formal solution to quantum Liouville equation for a qubit system in the presence of decoherence processes self-consistently. Our formulation is the first principle theory based on projection-operator formalism to obtain an exact reduced density operator in time-convolutionless form starting from the quantum Liouville equation for a noisy quantum computer. The advantage of our approach is that it is general enough to describe a realistic quantum computer in the presence of decoherence provided details of the Hamiltonians are known.

quant-ph↗