Photon added cat state: phase space structure and statistics

Abstract

The phase space structure and statistics of the photon added cat state are studied in the state’s general form. Photon addition leads to a π phase shift at the origin in the observed phase space interference of the Wigner function, which may serve as an error syndrome detector. The maxima and minima of the sub-Planck tiles in the phase space of the kitten state are interchanged after photon addition, leading to their orthogonality. Interestingly, photon addition to the Yurke–Stoler state characterized by Poissonian statistics leads to a sub-Poissonian distribution, which may find potential use in quantum noise reduction.

Two Mode Photon Added Schrödinger Cat States: Nonclassicality and Entanglement

“…There have been studies showing that oscillations in photon number distribution and negativity of the Mandel parameter indicate nonclassical behavior [1,36]. Also, the phase space structure of cat state [13,37], compass state [16] and squeezing properties of various squeezed states has been studied [23]. If the photon number distribution oscillates then this oscillation is a sure sign of nonclassicality.…”

“…Cat states have intrinsic quantum nature which have been recently experimentally analyzed with the cat code being in reality to use of continuous variable states for quantum information processing. Addition of a single photon to the cat state and its physical manifestation including statistics have been recently investigated [13].…”

“…In a quantum optics research, two-mode cat state is generally used as an entangled tool, which cannot be distilled only by classical communications due to the limitation from the no-go theorem [20]. To suffice the condition of quantum information protocols for long-distance communication, there have been suggestions and realizations for manipulating the quantum states, which are reasonable ways to conditionally operate a nonclassical state [21][22][23] of an optical field by subtracting or adding photons from/to a optical states [2,13,15,24]. Actually, the photon addition and subtraction have been successfully demonstrated experimentally for probing quantum commutation rules by Parigi et al [25].…”

Superpositions of coherent states determined by Gauss sums

“…The first member of this family coincides with the Yurke-Stoler state whose group-theoretical nature was uncovered in [7]. Other members are composed as superpositions of more than two harmonic oscillator coherent states and we call them, following [8], the Schrödinger kittens states. Note that this is different from the terminology suggested in [9], where the term "kittens" was referring to the Schrödinger cat states with small coherence amplitudes.…”

“…The present paper is of a purely theoretical character. However, taking into account wide applications that have been found for the Schrödinger cat states [1,4,5,8,9,15], it is expected that the described superpositions of coherent states, whose interference coefficients are described by regular polygon angle phases, have some interesting experimental implications.…”