Information Retrieval and Criticality
in Parity-Time-Symmetric Systems
Kohei Kawabata (U. Tokyo)
Collaborators:
Yuto Ashida (U. Tokyo)
Masahito Ueda (U. Tokyo & RIKEN CEMS)

arXiv:1705.04628

Quantum Control Using Dissipation
Loss is usually detrimental to the coherence of a system.
However, loss can be useful in quantum control.
e.g. Dissipative quantum computation and state engineering.
Verstraete et al., Nat. Phys. 5, 633 (2009).

e.g. Topological quantum
computation (Majoranabraiding) with dissipation.
Diehl et al., Nat. Phys. 7, 971 (2011).

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Open System Having PT Symmetry
An open system with balanced gain and loss is effectively
described by a non-Hermitan Hamiltonian with PT symmetry:but

Bender and Boettcher,
PRL 80, 5243 (1998).

Non-unitary dynamics:

Brody and Graefe, PRL
109, 230405 (2012).

PT-unbroken(real spectra)

PT-broken(complex spectra)
gain/loss

PT symmetry breaking

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Experimental Realization
Synthetic photonic lattices
Unidirectional light transport.

Microcavities

Peng et al., Nat. Phys.
10, 394 (2014).

Reciprocal light transmission.

Regensburger et al.,Nature 488, 167 (2012).
テキUltracold atomsStimulated Floquet
dissipative Hamiltonian
with PT symmetry.

Li et al., arXiv: 1608.05061.

Single-photon quantum walks
Robust topologicaledge states due toPT symmetry.
Xiao et al., Nat.
Phys. (in press).

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Non-unitarity in Quantum Measurement
Quantum measurement
Measuringapparatus

System(1) Non-unitary state reduction.
Information acquision of an observer(2) The entire system is Hermitian.
Non-unitary

Unitary
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Questions(1) How does information flow between a PT-symmetricsystem and its environment?

(2) Can a general PT-symmetric system be embedded
into a larger Hermitian system?

Evaluation of Information Flow
Trace distance(distinguishability) Contractive under a CPTP map(=a map without memory)

An increase in

Breuer, Laine, and Piilo,
PRL 103, 210401 (2009).

Information backflow from the environment to the system.
Presence of memory effects! (Non-Markovian)

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Information Retrieval
We study the general behavior of the distinguishability.

PT-unbroken phaseoscillates and always returns to the initial value.
= the system retrieves the information!
= revival of quantum coherence!

PT-broken phase
exponentially decays (NO retrieval):

Phase

Information

MemoryPT-unbroken

Reversible

Non-Markovian

PT-broken

Irreversible

Markovian

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Universal Critical Behavior
Reversible(PT-unbroken)

Irreversible(PT-broken)

Criticality emerges around the transition point!
PT-unbroken: recurrence timePT-broken: relaxation timePT transition: distinguishability itself(: gain/loss parameter): the order of the transition point→ Determines the “PT universality class”
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Example: Two-Level System
Initial states:

and(a) PT-unbroken phase(b) PT-broken phase

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Embedding into a Larger Hermitian SystemPT-unbroken phase
Possible with a finite (two-level) ancilla:
two-level ancilla(measuring apparatus)
Unbroken PT symmetry

The extended system is closed (Hermitian):
is Hermitian.
 Information that has flowed into the environment is
actually stored in the entanglement with a hidden ancilla.

9/10Information Retrieval Revisited
Proof of the information retrieval
The extended finite Hermitian system returns back to the original.
The PT-symmetric system also returns.

PT-broken phase

The above extension in the PT-unbroken phase breaks down,
and information flow is irreversible.
Infinite ancillas are required!
(Irreversibility can emerge in infinite Hermitian systems)

 Physical origin of the information retrieval:
Although the environment is in general infinite,
it is in effect finite as long as PT symmetry is unbroken.

10/10Summary

arXiv: 1705.04628

Studied Information flow between a PT-symmetric system
and its environment.
Information retrieval in the PT-unbroken phase.
Unique criticality at the PT transition point.
Origin of the information retrieval:
Finite-dimensional environment induced by PT symmetry.

Phase

SpectraInfo.

MemoryAncilla

Unbroken

Real

Reversible

Non-Markovian

FiniteBrokenComplex

Irreversible

MarkovianInfinite