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M. Zaimi et al.
an edge state exists. Thus, the qubit can be used to determine whether or not an edge
state exists in this model.
Keywords Open quantum systems · Decoherence · Topological materials ·
Edge states
1 Introduction
The two-level system (TLS) is the simplest nontrivial quantum system. Its simplicity
notwithstanding, many important systems are TLSs. Some familiar examples are: a
spin-1/2 particle (two spin states), a photon (two polarizations), a two-level atom
(the two levels), a quantum dot (empty/full), two-meson systems (K, ¯
K), two-flavor
neutrino oscillations (ν 1,2 ). Some of the above play the role of qubits, the building
blocks of quantum information systems (quantum computers, teleportation, etc.).
An isolated TLS, like any isolated quantum system, will evolve unitarily. This
implies that pure states remain pure; assuming the two basis states are coupled, a
system put in one state will oscillate back and forth between the two.
However, no system is perfectly isolated; in reality, a TLS interacts with its
environment and becomes entangled with it. From the point of view of the TLS,
entanglement with the environment is indistinguishable from a mixed state. We
say that the pure state becomes impure, or it decoheres. In addition, in many TLSs
(including the one we will study here) the interaction can permit a particle to escape
from the system to the environment. In this case, from the point of view of the TLS
probability is not conserved.
Decoherence and nonconservation of probability are almost always undesirable;
in particular, decoherence results in a loss of information and also a loss of
the potential advantage of quantum vs classical computing, quantum vs classical
communication, etc. Thus, understanding (and, usually, minimizing) decoherence is
critically important to the functioning of quantum devices. As an example, in [1] a
tripartite system was studied: a TLS coupled to one end of a finite chain (or channel)
whose other end was coupled to a semi-infinite chain; both chains were described
by tight-binding Hamiltonians. The question addressed was: how can one reduce the
decoherence of the TLS? It was found that adding noise to the channel did the trick,
essentially due to Anderson localization: if excitations in the channel are localized,
it becomes hard for a particle in the TLS to make its way to the far side of the
channel and escape to infinity.
Here, we study a similar system with a very different goal in mind (Fig. 1).
The main difference is that the channel is a Su–Schrieffer–Heeger (SSH) [2]
chain (free of disorder) described by a hopping parameter with alternating hopping
strengths. Such chains have topological edge states (for a review, see [3]), and rather
than trying to minimize the decoherence of the TLS, we imagine measuring its
decoherence rate to determine whether the system to which it is attached has edge
M. Zaimi et al.
an edge state exists. Thus, the qubit can be used to determine whether or not an edge
state exists in this model.
Keywords Open quantum systems · Decoherence · Topological materials ·
Edge states
1 Introduction
The two-level system (TLS) is the simplest nontrivial quantum system. Its simplicity
notwithstanding, many important systems are TLSs. Some familiar examples are: a
spin-1/2 particle (two spin states), a photon (two polarizations), a two-level atom
(the two levels), a quantum dot (empty/full), two-meson systems (K, ¯
K), two-flavor
neutrino oscillations (ν 1,2 ). Some of the above play the role of qubits, the building
blocks of quantum information systems (quantum computers, teleportation, etc.).
An isolated TLS, like any isolated quantum system, will evolve unitarily. This
implies that pure states remain pure; assuming the two basis states are coupled, a
system put in one state will oscillate back and forth between the two.
However, no system is perfectly isolated; in reality, a TLS interacts with its
environment and becomes entangled with it. From the point of view of the TLS,
entanglement with the environment is indistinguishable from a mixed state. We
say that the pure state becomes impure, or it decoheres. In addition, in many TLSs
(including the one we will study here) the interaction can permit a particle to escape
from the system to the environment. In this case, from the point of view of the TLS
probability is not conserved.
Decoherence and nonconservation of probability are almost always undesirable;
in particular, decoherence results in a loss of information and also a loss of
the potential advantage of quantum vs classical computing, quantum vs classical
communication, etc. Thus, understanding (and, usually, minimizing) decoherence is
critically important to the functioning of quantum devices. As an example, in [1] a
tripartite system was studied: a TLS coupled to one end of a finite chain (or channel)
whose other end was coupled to a semi-infinite chain; both chains were described
by tight-binding Hamiltonians. The question addressed was: how can one reduce the
decoherence of the TLS? It was found that adding noise to the channel did the trick,
essentially due to Anderson localization: if excitations in the channel are localized,
it becomes hard for a particle in the TLS to make its way to the far side of the
channel and escape to infinity.
Here, we study a similar system with a very different goal in mind (Fig. 1).
The main difference is that the channel is a Su–Schrieffer–Heeger (SSH) [2]
chain (free of disorder) described by a hopping parameter with alternating hopping
strengths. Such chains have topological edge states (for a review, see [3]), and rather
than trying to minimize the decoherence of the TLS, we imagine measuring its
decoherence rate to determine whether the system to which it is attached has edge