Talks

If two parties have access to entangled parts of a quantum state, the common lore suggests that when measurements are made by one of the parties and its outcomes are classically communicated to the other party, it leaves telltale signatures on the state of the part accessible to the other party. Here we show that this lore is not necessarily true -- in generic scrambling dynamics within a tripartite setting (with the $R$, $S$ and $E$ labelling the three parts), a new kind of dynamical phase emerges, wherein local measurements on $S$ are invisible to one of the remaining two parts, say $R$, despite there existing non-trivial quantum correlations and entanglement between $R$ and $S$. At the heart of this lies the fact that information scrambling transmutes local quantum information into a complex non-local web of spatiotemporal quantum correlations. This non-locality in the information then means that ignorance of the state of part $E$ can leave $R$ and $S$ with sufficient information for them to be quantum correlated or entangled but not enough for measurements on $S$ to have a non-trivial backaction on the state of $R$. This new dynamical phase is sandwiched between two conventionally expected phases where the $R$ and $S$ are either disentangled from each other or are entangled along with non-trivial measurement backaction. This provides a new characterisation of entanglement phases in terms of their response to measurements instead of the more ubiquitous measurement-induced entanglement transitions. Our results have implications for the kind of tasks that can be performed using measurement feedback within the framework of quantum interactive dynamics.

Quantum measurements are described as instantaneous projections in textbooks. They can be stretched out in time using weak measurements, whereby one can observe the evolution of a quantum state towards one of the eigenstates of the measured operator. This evolution is a continuous nonlinear stochastic process, generating an ensemble of quantum trajectories. In particular, the Born rule can be interpreted as a fluctuation-dissipation relation. We experimentally observe the entire quantum trajectory distribution for weak measurements of a superconducting transmon qubit in circuit QED architecture, quantify it, and demonstrate that it agrees very well with the predictions of a single-parameter white-noise stochastic process. This characterisation of quantum trajectories is a powerful clue to unraveling the dynamics of quantum measurement, beyond the conventional axiomatic quantum theory. We emphasise the key quantum features of this framework, and their implications.

Noise in quantum hardware poses the biggest challenge to realizing robust and scalable quantum computing devices. While conventional quantum error correction (QEC) schemes are relatively resource-intensive, approximate QEC (AQEC) promises a comparable degree of protection from specific noise channels using fewer physical qubits [1 ]. However, unlike standard QEC, the AQEC framework faces hurdles in reliable syndrome measurements due to the overlapping syndrome subspaces leading to the violation of the distinguishability criterion of error subspaces. Our work [2 ] provides an algorithm for discriminating overlapping syndrome subspaces based on the Gram-Schmidt-like orthogonalization routine. In the recovery, we map these orthogonal and disjoint subspaces to the code space followed by a recovery like the perfect recovery [1 , 3 ], or the Petz map [4, 5]. We further prove that this evolved recovery utilizing the Petz map (which we call the canonical Petz map ) gives optimal protection on the information regarding the measure of entanglement fidelity. We show that the performance of the canonical Petz map is similar to that of the Fletcher recovery [ 6 ]. 

[1] D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto, Approximate quantum error correction can lead to better codes, Physical Review A 56, 2567 (1997).
[2] D. Biswas and P. Mandayam, Efficient syndrome detection for approximate quantum error correction – road towards the optimal recovery, Manuscript is under preparation (2025).
[3] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, 2000).
[4 ] H. K. Ng and P. Mandayam, Simple approach to approximate quantum error correction based on the transpose channel, Phys. Rev. A 81, 062342 (2010).
[5] H. Barnum and E. Knill, Reversing quantum dynamics with near- optimal quantum and classical fidelity, Journal of Mathematical Physics 43, 2097 (2002).
[6] A. S. Fletcher, P. W. Shor, and M. Z. Win, Channel-adapted quantum error correction for the amplitude damping channel, IEEE Transactions on Information Theory 54, 5705 (2008).

While a generic open quantum system decays to its steady state, continuous time crystals (CTCs) develop spontaneous oscillation and never converge to a stationary state. Just as crystals develop correlations in space, CTCs do so in time. Here, we introduce a Continuous Quasi Time Crystals (CQTC). Despite being characterized by the presence of non-decaying oscillations, this phase does not retain its long-range order, making it the time analogous of quasi-crystal structures. We investigate the emergence of this phase in a system made of two coupled collective spin sub-systems, each developing a CTC phase upon the action of a strong enough drive. The addition of a coupling enables the emergence of different synchronized phases, where both sub-systems oscillate at the same frequency. In the transition between different CTC orders, the system develops chaotic dynamics with aperiodic oscillations. These chaotic features differ from those of closed quantum systems, as the dynamics is not characterized by a unitary evolution. At the same time, the presence of non-decaying oscillations makes this phenomenon distinct from other form of chaos in open quantum system, where the system decays instead. We investigate the connection between chaos and this quasi-crystalline phase using mean-field techniques, and we confirm these results including quantum fluctuations at the lowest order.

We have tried to describe how the interplay between the system environment coupling and external driving frequency shapes the dynamical properties and steady state behavior in a periodically driven transverse field Ising chain subject to measurement. We have analyzed the fate of the steady state entanglement scaling properties as a result of a measurement induced phase transition. We have explained how such steady state entanglement scaling can be computed analytically using asymptotic features of the determinant of associated correlation matrix which turned out to be of block Toeplitz form. We have pointed out the differences from the Hermitian systems in understanding the entanglement scaling behav-ior in regimes where the asymptotic analysis can be performed using Fisher-Hartwig con-jecture. Finally we have discussed how the tuning of the drive frequency controls the do- main of applicability of the Fisher-Hartwig conjecture and the emergence of the long range ordering of the effective Floquet Hamiltonian governing the properties of the system.

What happens when the unitary evolution of a generic closed quantum system is interrupted at random times with non-unitary evolution due to interactions with either the external environment or a measuring apparatus? We adduce a general framework to obtain the average density operator of a generic quantum system experiencing any form of non-unitary interaction. We provide two explicit applications in the context of the tight-binding model for two representative forms of interactions: (i) stochastic resets and (ii) projective measurements at random times. For the resetting case, our exact results show how the particle is localized on the sites at long times, leading to a time-independent mean-squared displacement. For the projective measurement case, repeated projection to the initial state results in an effective suppression of the temporal decay in the probability of the particle being in the initial state. The amount of suppression is comparable to the one in conventional Zeno effect scenarios, where measurements are performed at regular intervals.