In a departure from most work in quantum information utilizing Gaussian states, we use a single such state to represent a qubit and model environmental noise with a class of quadratic dissipative ...equations. A benefit of this single Gaussian representation is that with one deconvolution, we can eliminate noise. In this deconvolution picture, a basis of squeezed states evolves to another basis of such states. One of the limitations of our approach is that noise is eliminated only at a privileged time. We suggest that this limitation may actually be used advantageously to send information securely: the privileged time is only known to the sender and the receiver, and any intruder accessing the information at any other time encounters noisy data.
It is shown that the standard quantum Brownian equation (QBE) can violate positivity not only past the thermal correlation time, but at arbitrarily long times at high system frequencies. In an effort ...to improve the standard QBE, exact operator solutions are provided for a class of non-autonomous master equations. These exact solutions are used to derive sufficient positivity conditions for the coefficients of the master equations.
► Positivity conditions for a standard quantum Brownian equation are stated. ► An operator solution for a class of non-autonomous master equations is formulated. ► Relations are provided that are sufficient to ensure positivity for the class.
For open systems derived from quadratic total Hamiltonians, we derive a dynamic fluctuation–dissipation (FD) inequality valid for any total initial state and without regard to the sign of the ...dissipation. With the added constraint that this state be factorized with the reservoir in thermal equilibrium, an uncertainty relation arises naturally from the FD inequality that can be stronger than the usual uncertainty principle in the form 〈q2〉〈p2〉⩾ℏ2/4. We discuss some of the properties of the uncertainty relation relevant to decoherence.
•I derive a dynamic fluctuation–dissipation inequality for quadratic open quantum systems valid for any total initial state.•I use the fluctuation–dissipation inequality to derive an uncertainty relation for factorized thermal initial states.•The uncertainty relation is related to the ability of the total Hamiltonian to maintain coherence.
For open systems derived from quadratic total Hamiltonians, we derive a dynamic fluctuationadissipation (FD) inequality valid for any total initial state and without regard to the sign of the ...dissipation. With the added constraint that this state be factorized with the reservoir in thermal equilibrium, an uncertainty relation arises naturally from the FD inequality that can be stronger than the usual uncertainty principle in the form aq2aap2aaCO34a2/4aq2aap2aaCO34a2/4. We discuss some of the properties of the uncertainty relation relevant to decoherence.
We utilize a mass independent Klein-Gordon equation that is first order in a variable that plays the role of time, the approach taken in parametric time formulations. Using concepts from semigroup ...evolution, we examine the sign of a noisy Feynman propagator in a quantum field theory, namely, scalar electrodynamics.
For the interacting Feynman propagator \( \Delta_{F,int}(x,y) \) of scalar electrodynamics, we show that the sign property, \( \operatorname{Re} i\Delta_{F,int} \geq 0 \), hinges on the reversibility ...of time evolution. In contrast, \( \operatorname{Im} i\Delta_{F,int} \) is indeterminate. When we switch to reduced dynamics under the weak coupling approximation, the positive semidefinite sign of \( \operatorname{Re} i\Delta_{F,int} \) is generally lost, unless we impose severe restrictions on the Kraus operators that govern time evolution. With another approximation, the rotating wave approximation, we may recover the sign by restricting the test functions to exponentials under certain conditions.
High-temperature and white-noise approximations are frequently invoked when deriving the quantum Brownian equation for an oscillator. Even if this white-noise approximation is avoided, it is shown ...that if the zero-point energies of the environment are neglected, as they often are, the resultant equation will violate not only the basic tenet of quantum mechanics that requires the density operator to be positive, but also the uncertainty principle. When the zero-point energies are included, asymptotic results describing the evolution of the oscillator are obtained that preserve positivity and, therefore, the uncertainty principle.
We use a single squeezed state to represent a qubit, which can be coherently processed in a deconvolution picture (DP) in the presence of noise. We avail ourselves of the fact that when evolution is ...governed by a quadratic dissipative equation, there exists a basis of squeezed states that evolves to another basis of such states in the DP. An operator acts as an impurity filter, restoring the coherence lost from the inexorable interactions of the qubit with its surroundings.
For open systems derived from quadratic total Hamiltonians, we derive a dynamic fluctuation-dissipation (FD) inequality valid for any total initial state and without regard to the sign of the ...dissipation. With the added constraint that this state be factorized with the reservoir in thermal equilibrium, an uncertainty relation arises naturally from the FD inequality that can be stronger than one common form of the uncertainty principle. We discuss some of the properties of the uncertainty relation relevant to decoherence.
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