Entanglement dynamics lies at the heart of nonequilibrium quantum physics. For more than two decades, the standard approach has been remarkably consistent: start from an unentangled product state, let the system evolve unitarily, and study how the entanglement entropy grows over time.
This framework has led to many fundamental discoveries, including our understanding of quantum thermalization and many-body localization (MBL). It also shaped an implicit assumption shared across the field: whenever the half-chain entanglement entropy increases, the system must be creating new quantum entanglement.
Our recent paper, published in Physical Review Letters, argues that this picture is incomplete.
The central observation is surprisingly simple:
An increase in measured entanglement does not necessarily mean new entanglement has been created.
Instead, quantum dynamics possesses two fundamentally different capabilities that have long been mixed together.
Two ways to increase entanglement
A useful way to think about entanglement is to imagine the system as a connected network of water reservoirs.
There are two distinct mechanisms that can raise the water level observed at a particular cut.
Build: Creating new entanglement
The first mechanism genuinely generates new quantum correlations.
This is analogous to pumping fresh water into the entire reservoir system. The total amount of entanglement increases.
Move: Transporting existing entanglement
The second mechanism creates no new entanglement at all.
Instead, quantum evolution simply redistributes the entanglement that already exists inside the system. Water is flowing internally, but no new water enters the reservoirs. Although the total amount remains unchanged, the water level measured at one particular location may still rise.
Exactly the same phenomenon can happen for half-chain entanglement entropy.
This distinction turns out to be much more important than previously appreciated.
The intuitive expectation
Once these two mechanisms are separated, an intuitive principle emerges.
If a system already starts with a large amount of entanglement, there is less room left to generate additional entanglement later.
Indeed, this is exactly what happens in familiar systems such as
- quantum chaotic (thermalizing) systems,
- free-fermion systems,
- random quantum circuits with strong scrambling.
As the initial entanglement increases, the additional entanglement generated during evolution decreases monotonically.
This is precisely what one would expect if entanglement growth were primarily driven by building new entanglement.
MBL breaks the rule
Many-body localized systems tell a completely different story.
Instead of decreasing monotonically, the entanglement growth exhibits a striking bell-shaped dependence on the initial entanglement.
- Starting from nearly product states, the growth is very small.
- Starting from nearly maximally entangled states, the growth is again very small.
- The largest increase occurs at intermediate initial entanglement.
This behavior is difficult to explain if entanglement growth comes solely from generating new entanglement.
Something else must be happening.
A "pure transport" experiment
To isolate the missing ingredient, we designed a particularly simple reference model.
Instead of using an interacting Hamiltonian, we considered a random circuit composed only of SWAP gates.
This circuit has a remarkable property:
- it cannot create any entanglement, and
- it only exchanges the locations of quantum states.
In other words, it performs pure entanglement transport.
Surprisingly, the entanglement-growth curve produced by this SWAP-only circuit closely matches the behavior observed in MBL systems, both qualitatively and even quantitatively.
This comparison reveals the underlying physics.
MBL is not particularly good at generating new entanglement.
Instead, it excels at moving around the entanglement that already exists.
When the system begins with almost no entanglement, there is simply nothing to transport.
When it begins nearly saturated, there is no remaining room for rearrangement.
Only at intermediate entanglement do both ingredients coexist, allowing transport to produce the largest observable increase.
Looking beyond a single bipartition
Most previous studies monitor only one quantity: the entanglement across the middle cut of the system.
While extremely useful, this provides only a partial view of the system's entanglement structure.
In our work, we introduce a more global perspective by considering the Bipartition-Averaged Entanglement Entropy (BAEE), which averages entanglement over all possible bipartitions.
The simulations reveal an interesting phenomenon.
Even in ordinary thermalizing systems, BAEE grows much faster than the half-chain entanglement during the early stages of evolution.
The difference between these two quantities represents a hidden reservoir of entanglement that has already been generated locally but has not yet reached the particular cut being measured.
Returning to our water analogy, thermalization rapidly fills many local reservoirs throughout the system.
Later dynamics can transport this stored entanglement across different partitions.
This picture naturally explains why transport-dominated systems like MBL exhibit their largest observable entanglement growth at intermediate initial entanglement.
A new perspective on entanglement dynamics
The broader message is that entanglement dynamics is not just about creating quantum information.
It is equally about processing, redistributing, and transporting the quantum information that already exists.
The traditional "start from product states" paradigm has taught us a great deal, but it captures only one half of the story.
Distinguishing between entanglement generation and entanglement transport provides a more complete framework for understanding quantum dynamics across thermalizing systems, free fermions, many-body localization, and quantum circuits.
Beyond offering a conceptual picture, this framework makes concrete predictions that can be tested on today's quantum simulation platforms, providing new experimental probes of nonequilibrium quantum dynamics.
Reference
Entanglement growth from entangled states: A unified perspective on entanglement generation and transport
Chun-Yue Zhang, Zi-Xiang Li, and Shi-Xin Zhang
Physical Review Letters 137, 020404 (2026)
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