# Changing Fock matrix elements of two-mode squeezed vacuum state by employing three quantum operations in one-sided lossy channel

## TL;DR

This paper analytically investigates how three quantum operations—one-photon replacement, subtraction, and addition—alter the Fock matrix elements of a two-mode squeezed vacuum state within a lossy channel, revealing their specific effects on state populations.

## Contribution

It derives explicit analytical expressions for the Fock matrix elements of states generated by these operations, expanding understanding of quantum state manipulation in lossy environments.

## Key findings

- OPR adds populations in |10> and |20>
- OPS removes populations in |00> and |11>
- OPA shifts populations to |01> and retains |11>

## Abstract

This paper focuses on changing Fock matrix elements of two-mode squeezed vacuum state (TMSVS) by employing three quantum operations in one-sided lossy channel. These three quantum operations include one-photon replacement (OPR), one-photon substraction (OPS) and one-photon addition (OPA). Indeed, three conditional quantum states have been generated from the original TMSVS. Using the characteristic function (CF) representation of quantum density operator, we derive the analytical expressions of their Fock matrix elements, which are dependent on the interaction parameters, including the squeezing parameter of the input TMSVS, the loss factor and the transmissivity of the variable beam splitter. For convenience of discussion, we only give the Fock matrices in the subspace span {|00>,|01>,|10>,|02>,|11>,|20>} for these two-mode states. Obviously, the TMSVS only has the populations in |00> and |11> in such subspace. By comparing the generated states with the TMSVS, we find that: (1) The generated state after OPR will remain the populations in |00> and |11>, and add the populations in |10> and |20>; (2) The generated state after OPS will lost the populations in |00> and |11>, but add the populations in |10> and |20>; (3) The generated state after OPA will remain the population only in |11> and add the population in |01>.