Signatures of quantum effects in weak measurements of qubits

Allen Lobo, Carlos Alberto de Lima Ribeiro

Rusko Ruskov, Alexander N. Korotkov, Ari Mizel

With the recent surge of interest in quantum computation, it has become very important to develop clear experimental tests for "quantum behavior" in a system. This issue has been addressed in the past in the form of the inequalities due to Bell and those due to Leggett and Garg. These inequalities concern the results of ideal projective measurements, however, which are experimentally difficult to perform in many proposed qubit designs, especially in many solid-state qubit systems. Here, we show that weak continuous measurements, which are often practical to implement experimentally, can yield particularly clear signatures of quantum coherence, both in the measured correlation functions and in the measured power spectrum.

Darren Pereira, Leonardo Banchi

We present a tensor-network-based method for simulating a weakly-measured quantum circuit. In particular, we use a Markov chain to efficiently sample measurements and contract the tensor network, propagating their effect forward along the spatial direction. Applications of our algorithm include validating quantum computers (capable of mid-circuit measurements) in regimes of easy classical simulability, and studying generative-machine-learning applications, where sampling from complex stochastic processes is the main task. As a demonstration of our algorithm, we consider a (1+1)-dimensional brickwall circuit of Haar-random unitaries, interspersed with generalized single-qubit measurements of variable strength. We simulate the dynamics for tens to hundreds of qubits if the circuit exhibits area-law entanglement (under strong measurements), and tens of qubits if it exhibits volume-law entanglement (under weak measurements). We observe signatures of a measurement-induced phase transition between the two regimes as a function of measurement strength.

Hayato Nakano, Hideaki Takayanagi

Valeria Cimini, Ilaria Gianani, Fabrizio Piacentini +2 more

Abstract Postselection following weak measurements has long been investigated for its peculiar manifestation of quantum signatures. In particular, the postselected events can give rise to anomalous values lying outside the spectrum of the measured quantity, and may provide enhanced Fisher information. Furthermore, the Pusey inequality highlights that, for extremely weak measurements, non-contextual models cannot account for the outcome probabilities. It is then interesting to investigate whether these are linked in a unified framework. Here we discuss on the existence of a possible connection in the case of qubits. We show that when performing generic postselected measurements there exist no one-to-one mapping between them, an instance that leads to drawing more involved considerations.