Full characterization of polarization states of light via direct measurement

Abstract

Ascertaining the physical state of a system is vital in order to understand and predict its behaviour. However, due to their fragile nature, the direct observation of quantum states has been elusive until recently. Historically, determination of the quantum state has been performed indirectly, through use of tomography. We report on two experiments showing that an alternative approach can be used to determine the polarisation quantum state in a simple, fast, and general manner. The first experiment entails the direct measurement of the probability amplitudes describing pure polarisation states of light, the first such measurement on a two-level system. The second experiment entails the direct measurement of the Dirac distribution (a phase-space quasi-probability distribution informationally equivalent to the density matrix), demonstrating that the direct measurement procedure is applicable to general (i.e., potentially mixed) quantum states. Our work has applications to measurements in foundational quantum mechanics, quantum information, and quantum metrology.Measurement plays a vital role in the practice of science. This is especially so in the case of quantum mechanics, where the measurement process is fundamental to the formulation of the theory. A crucial feature of quantum mechanics is that a measurement of one variable of a system erases information about the corresponding conjugate variable. The classic example is that determining the position of a particle disturbs its momentum, and vice versa. These measurements, known as strong measurements, collapse the wavefunction such that no additional information can be obtained.In order to completely determine a quantum state, which is described in general by complex numbers, one must perform multiple measurements on many identical copies of the system. Quantum tomography 1 is one method of quantum state determination that uses strong measurements 2-6 . Tomographic reconstruction entails estimating the complex numbers that describe the state

Advantages of nonclassical pointer states in postselected weak measurements

“…Weak value has a nature of being a complex number, which lead the weak measurements to provide an ideal method to examine some fundamentals of quantum physics. Quantum paradoxes (Hardy's paradox [17][18][19] and the three-box paradox [20]), quantum correlation and quantum dynamics [21][22][23][24][25][26], quantum state tomography [27][28][29][30][31][32], violation of the generalized Leggett-Garg inequalities [33][34][35][36][37][38] and violation of the initial Heisenberg measurement-disturbance relationship [39,40] are just few examples. In these typ-ical examples, the small effects have been amplified due to the benefit of weak values.…”

Direct Measurement of the Density Matrix of a Quantum System

“…In addition, since QST requires a global reconstruction, it does not provide direct access to coherences (i.e. off-diagonal elements), which are of particular interest in quantum physics.Some recent work has focused on developing a direct approach to measuring quantum states [8][9][10][11][12][13][14][15][16][17][18][19]. Defining features of direct methods are that they can determine the state without complicated computations, and they can do so locally, i.e.…”

“…The weak value is a concept that has proven to be useful in addressing fundamental questions in quantum physics [22][23][24][25][26][27][28][29][30][31], even beyond optics [32]. By foregoing post-selection, previous work [10,11] generalized the direct wave function measurement scheme to measure mixed quantum states. However, their method still does not provide direct access to individual density matrix elements.…”

Fundamental Features of Quantum Dynamics Studied in Matter-Wave Interferometry—Spin Weak Values and the Quantum Cheshire-Cat

“…A review focusing on significant amplification of the pointer deflection is given in [46], where in addition a non-perturbative theory of weak pre-and post-selected measurements is presented. The weak value's property of allowing information to be extracted from a quantum system with minimal disturbance is applied as a new method for estimation of quantum states [47][48][49][50] (see [51] for a recent review). This particular property of the weak value is also utilized in experimental tests of a reformulation of Heisenberg's uncertainty principle [52][53][54][55] (an overview of different viewpoints of that topic can be found in [56]).…”