I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

I present a series of experimental and theoretical advances in the field of quantum state estimation. Techniques for measuring the quantum state of light that were originally developed for distinguishable photons fail when the particles are indistinguishable. I develop new methods for handling indistinguishability in quantum state estimation. The technique I present provides the first complete description of states of experimentally indistinguishable photons. It allows me to derive the number of parameters needed to describe an arbitrary state and to quantify distinguishability. I demonstrate its use by applying it to the measurement of the quantum polarization state of two and three-photon systems. State characterization is optimal when no redundant information is collected about the state of the system. I present the results of the first optimal characterization of the polarization state of a two-photon system. I show an improved estimation power over the previous state of the art. I also show how the optimal measurements lead to a new description of the quantum state in terms of a discrete Wigner function. It is often desirable to describe the quantum state of a system in terms of properties that are not themselves quantum-mechanical observables. This usually requires a full characterization of the state followed by a calculation of the properties from the parameters characterizing the state. I apply a technique that allows such properties to be determined directly, without a full characterization of the state. This allows one such property, the purity, to be determined in a single measurement, regardless of the size of the system, while the conventional method of determining purity requires a number of measurements that scales exponentially with the system size.

Quantum cryptography is arguably the most successfully applied area of quantum information theory. In this work, We invsetigate the role of quantum indistinguishability in random number generation, quantum temporal correlations, quantum nonlocality and counterfactuality for quantum cryptography. We study quantum protocols for key distribution, and their security in the conventional setting, in the counterfactual paradigm, and finally also in the device-independent scenario as applied to prepare-and-measure schemes. We begin with the interplay of two essential non-classical features like quantum indeterminism and quantum indistinguishability via a process known as bosonic stimulation is discussed. It is observed that the process provides an efficient method for macroscopic extraction of quantum randomness. Next, we propose two counterfactual cryptographic protocols, in which a secret key bit is generated even without the physical transmission of a particle. The first protocol is semicounterfactual in the sense that only one of the key bits is generated using interaction-free measurement. This protocol departs fundamentally from the original counterfactual key distribution protocol in not encoding secret bits in terms of photon polarization. We discuss how the security in the protocol originates from quantum single-particle non-locality. The second protocol is designed for the crypto-task of certificate authorization, where a trusted third party authenticates an entity (e.g., bank) to a client. We analyze the security of both protocols under various general incoherent attack models. The next part of our work includes study of quantum temporal correlations. We consider the use of the Leggett-Garg inequalities for device-independent security appropriate for prepare-and-measure protocols subjected to the higher dimensional attack that would completely undermine standard BB84. In the last part, we introduce the novel concept of nonlocal subspaces constructed using the graph state formalism, and propose their application for quantum information splitting. In particular, we use the stabilizer formalism of graph states to construct degenerate Bell operators, whose eigenspace determines the nonlocal subspace, into which a quantum secret is encoded and shared among an authorized group of agents, or securely transmitted to a designated secret retriever. The security of our scheme arises from the monogamy of quantum correlations. The quantum violation of the Bell-type inequality here is to its algebraic maximum, making this approach inherently suitable for the device-independent scenario.