Geometric description of modular and weak values in discrete quantum systems using the Majorana representation

Abstract

We express modular and weak values of observables of three- and higher-level quantum systems in their polar form. The Majorana representation of N-level systems in terms of symmetric states of N-1 qubits provides us with a description on the Bloch sphere. With this geometric approach, we find that modular and weak values of observables of N-level quantum systems can be factored in N-1 contributions. Their modulus is determined by the product of N-1 ratios involving projection probabilities between qubits, while their argument is deduced from a sum of N-1 solid angles on the Bloch sphere. These theoretical results allow us to study the geometric origin of the quantum phase discontinuity around singularities of weak values in three-level systems. We also analyze the three-box paradox [1] from the point of view of a bipartite quantum system. In the Majorana representation of this paradox, an observer comes to opposite conclusions about the entanglement state of the particles that were successfully pre- and postselected.

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Cited by in corpus (12)

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• Anticoherence measures for pure spin states
• Can Two Quantum Cheshire Cats Exchange Grins?
• Delayed choice of paths selected by grin and snarl of quantum Cheshire Cat
• Geometrical interpretation of the argument of weak values of general observables in N-level quantum systems
• Isolating noise and amplifying signal with quantum Cheshire cat
• On the relevance of weak measurements in dissipative quantum systems
• Revisiting weak values through non-normality
• Exploring weak value arguments and Bargmann invariants in $N$-level quantum systems through the Majorana symmetric representation
• Exploring Weak measurements within the Einstein-Dirac Cosmological framework
• Wick rotation derivation for weak values of the density and time-dependent density functional theory
• A note concerning the modular valued von Neumann interaction operator