Quantum mechanics admits two distinct evolutions: deterministic unitary dynamics governed by the Schrödinger equation and the probabilistic collapse of the wave function. We show that the continuous collapse of a quantum state under measurement can, on a trajectory-by-trajectory basis, be equivalently described as unitary evolution generated by a time- and state-dependent Hermitian Hamiltonian with stochastic parameters. While the ensemble dynamics remains non-unitary, each individual trajectory thus admits a unitary representation. We derive explicit forms of such Hamiltonians for projective measurements on arbitrary n-level systems and for continuous position measurements of a harmonic oscillator, and we propose experimental schemes to test these predictions. Our framework provides a new approach to modeling and controlling continuously monitored quantum systems using only state-dependent unitary resources.
In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the system's initial state, slowing a system's
In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the system's initial state, slowing a system's time evolution.
Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term ha
In quantum mechanics, frequent measurements cause the quantum Zeno effect, a reduction in transitions away from the system's initial state, slowing a system's time evolution.
Sometimes this effect is interpreted as "a system cannot change while you are watching it". One can "freeze" the evolution of the system by measuring it frequently enough in its known initial state. The meaning of the term has since expanded, leading to a more technical definition, in which time evolution can be suppressed not only by measurement: the quantum Zeno effect is the suppression of unitary time evolution in quantum systems provided by a variety of sources: measurement, interactions with the environment, stochastic fields, among other factors. As an outgrowth of study of the quantum Zeno effect, it has become clear that applying a series of sufficiently strong and fast pulses with appropriate symmetry can also decouple a system from its decohering environment.
The name comes by analogy to Zeno's arrow paradox, which states that because an arrow in flight is not seen to move during any single instant, it cannot possibly be moving at all. In the quantum Zeno effect an unstable state seems frozen – to not 'move' – due to a constant series of observations. The comparison is due to a 1977 article by Baidyanath Misra and E. C. George Sudarshan.
According to the reduction postulate, each measurement causes the wavefunction to collapse to an eigenstate of the measurement basis. In the context of this effect, an observation can simply be the absorption of a particle, without the need of an observer in any conventional sense. However, there is controversy over the interpretation of the effect, sometimes referred to as the "measurement problem" in traversing the interface between microscopic and macroscopic objects.
Another crucial problem related to the effect is strictly connected to the time–energy indeterminacy relation (part of the indeterminacy principle). If one wants to make the measurement process more and more frequent, one has to correspondingly decrease the time duration of the measurement itself. But the request that the measurement last only a very short time implies that the…
to the Planck constant. Wave function collapse means that a measurement has forced or converted a quantum (probabilistic or potential) state into a definite
Quantum mechanics is the study of matter and matter's interactions with energy on the scale of atomic and subatomic particles. By contrast, classical physics explains matter and energy only on a scale familiar to human experience, including the behavior of astronomical bodies such as the Moon. Classical physics is still used in much of modern science and technology. However, towards the end of the
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