Session U6: Quantum Information Theory

Robust population transfer by non-overlapping pulse trains

We investigate coherent population transfer in a $\Lambda$-type three-level system driven by time delayed pulse trains. We demonstrate that the efficient population transfer can be achieved without partial overlap of the pump and the Stokes sub-pulses of the pulse trains. The mechanism of the population transfer and the robustness of the proposed scheme are discussed.   

Effect of environment on the Berry phase measurements

We study the effect of quantum environment on the Berry phase. The Berry phase was recently measured in interference experiments of a ground and excited states of a qubit. We analyze how the relaxation of the excited state affects measurements of the Berry phase. For this purpose, we first represent the environment by a damped harmonic oscillator and evaluate an error in the Berry phase measurements as a function of the coupling strength between the qubit and the oscillator. Then, we apply the Bloch-Redfield equations for a time dependent Hamiltonian to describe the effect of an Ohmic environment on experimental observation of the Berry phase. We also evaluate non-adiabatic corrections to the Berry arising when the time that takes to close the loop in the Hamiltonian parameter space is finite.   

Strong converse for the classical capacity of all phase-insensitive bosonic Gaussian channels

One of the most fundamental tasks in quantum information theory is to determine the classical capacity for a noisy communication channel. We prove that a strong converse theorem holds for the classical capacity of all phase-insensitive bosonic Gaussian channels, when imposing a maximum photon number constraint on the inputs of the channel. The pure-loss, thermal, additive noise, and amplifier channels are all in this class of channels. The statement of the strong converse theorem is that the probability of correctly decoding a classical message rapidly converges to zero in the limit of many channel uses if the communication rate exceeds the classical capacity. We prove this theorem by relating the success probability of any code with its rate of data transmission, the effective dimension of the channel output space, and the purity of the channel as quantified by the minimum output entropy. Our result bolsters the understanding of the classical capacity of these channels by establishing it as a sharp dividing line between possible and impossible communication rates over them.   

Noise of photons produced by electroluminescence of a double quantum dot connected to high quality resonator

We study the full counting statistics of photons emitted in electroluminescence process, when a current flows through a double quantum dot in the Coulomb blockade regime. In a system without dissipation at the resonant condition between the energy splitting of the DQD and the photon energy, the photon statistics exhibits both a sub-Poissonian distribution and antibunching and the photon noise is reduced below one-half of the noise for the Poisson distribution. In the presence of dissipation, the noise increases, the intensity correlation function approaches that of a thermal black--body radiation and the photon distribution eventually becomes a super-Poissonian.   

Classical stochastic measurement trajectories for a continuously monitored multi-mode quantum system

We formulate computationally efficient classical stochastic measurement trajectories for a multi-mode quantum system under continuous observation. Specifically, we consider the nonlinear dynamics of an atomic condensate contained within an optical cavity subject to continuous detection of the output photons. Analogous to quantum trajectories, these classical trajectories encode the backaction of a continuous quantum measurement process conditioned on a given measurement record. We argue that the dynamics can be unraveled into stochastic classical trajectories that are conditioned on the quantum measurement-induced backaction of the physical photon counting record of the continuously monitored system, and that these trajectories faithfully represent measurement records of individual experimental runs. As continuously monitored observables are expected to behave classically, the method provides a numerically efficient and accurate approach to calculate the measurement record of a large multi-mode quantum system. We show that the measurement backaction on the condensate is represented by a spatially-dependent phase decoherence rate, determined by the cavity mode shape and pump profile.   

Transient quantum fluctuation theorems and generalized measurements

The transient quantum fluctuation theorems of Crooks and Jarzynski restrict and relate the statistics of work performed in forward and backward forcing protocols. So far, these theorems have been obtained under the assumption that the work is determined by two projective energy measurements, one at the end, and the other one at the beginning of each run of the protocol.We found that one can replace these two projective measurements only by special error-free generalized energy measurements with pairs of tailored, protocol-dependent post-measurement states that satisfy detailed balance-like relations. For other generalized measurements, the Crooks relation is typically not satisfied. For the validity of the Jarzynski equality, it is sufficient that the first energy measurements are error-free and the post-measurement states form a complete orthonormal set of elements in the Hilbert space of the considered system. Additionally, the effects of the second energy measurements must have unit trace. We illustrate our results by an example of a two-level system for different generalized measurements.   

Classical Computers Very Likely Can Not Efficiently Simulate Multimode Linear Optical Interferometers with Arbitrary Fock-State Inputs--An Elementary Argument

Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [S. Aaronson and A. Arkhipov, Theory of Computing, 9, 143(2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schr\"odinger and Heisenberg pictures of quantum theory, while mathematically equivalent, are not in general computationally equivalent. Finally, we conclude our argument by comparing the symmetry requirements of multi-particle bosonic to fermionic interferometers and, using simple physical reasoning, connect the non-simulatablity of the bosonic device to the complexity of computing the permanent of a large matrix.   

Atomic Einstein-Podolsky-Rosen entanglement: How much thermal noise can it tolerate?

We examine the prospect of demonstrating EPR entanglement for massive particles using spin-changing collisions in a spinor Bose condensate. Specifically, we address the question of sensitivity of EPR quadrature entanglement to the initial thermal population of the hyperfine states $m_F=\pm1$, for the condensate initially prepared in the $m_F=0$ state. In the photonic analog of this process -- optical parametric downconversion -- this question is irrelevant as at optical frequencies and room temperatures the thermal population of the signal and idler modes is negligible, allowing us to approximate them as vacuum states. These considerations are, however, inapplicable to ultracold atomic gases and motivate our study of the spinor dynamics in the presence of a small thermal population $\bar{n}_{th}$ in the $m_F=\pm1$ states [1]. For condensates containing 150 to 200 atoms in the $m_F=0$ state, we predict an upper bound of $\bar{n}_{th}\simeq 1$ that can be tolerated for observing EPR quadrature entanglement during spin-changing collisions. For $\bar{n}_{th} \agt 1$, EPR entanglement is lost, even though other (less restrictive) entanglement criteria, such as inseparability, can still be satisfied.\\[4pt] [1] R. J. Lewis-Swan \& K. V . Kheruntsyan, PRA 87, 063635 (2013).   

Can the effect of gravity on electromagnetism be measured locally?

Coupling between electromagnetism and gravity, manifested as the distorted Coulomb field of a charge distribution in a gravitational field, has never been observed. Furthermore, it has been suggested that the effect is too small to be accessed experimentally [1]. We propose that an electron in a charged shell could provide measurable, albeit indirect, evidence of the coupling. Both energy and force arguments are used to investigate the electromagnetic interaction between two charged particles in a gravitational field. This dumbbell model [1, 2] is extended to our proposed system. The coupling between gravity and the electric field of the charged shell is shown to affect the acceleration of a charged particle in the shell. A shell voltage of only 1MV leads to a gravitationally induced electric force that can counterbalance the force of gravity on an electron. The experimental feasibility of detecting the effect of gravity on an individual electron will be discussed in its historical context [3]. The effect establishes a relation between Einstein's energy-mass equivalence, gravitational deflection of light, and the coupling between electromagnetism and gravity.\\[4pt] [1] T.Boyer, Am. J. Phys. \textbf{47}, 129 (1979). [2] D.Griffiths {\&} R.Owen, Am. J. Phys. \textbf{51} 1120 (1983). [3] F.Witteborn {\&} W.Fairbank, Nature \textbf{22, }436 (1968).   

Information Processing Structure of Quantum Gravity

The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. Quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of quantum mechanics. In a quantum gravity scenario, the causal structure is indefinite and the processes are causally non-separable. We provide a model for the information processing structure of quantum gravity. We show that the quantum gravity environment is an information resource-pool from which valuable information can be extracted. We analyze the structure of the quantum gravity space and the entanglement of the space-time geometry. We study the information transfer capabilities of quantum gravity space and define the quantum gravity channel. We characterize the information transfer of the gravity space and the correlation measure functions of the gravity channel. We investigate the process of stimulated storage for quantum gravity memories, a phenomenon that exploits the information resource-pool property of quantum gravity. The results confirm that the benefits of the quantum gravity space can be exploited in quantum computations, particularly in the development of quantum computers.