Abstract Quantum entanglement lies at the heart of quantum mechanics in both fundamental and practical aspects. The entanglement of quantum states has been studied widely both theoretically and experimentally, however, the entanglement of operators has not been studied much experimentally in spite of its importance. Here, we propose a scheme to realize arbitrary entangled operations based on a coherent superposition of local operations with a non-zero probability of failure. Then, we experimentally implement several intriguing two-qubit entangled operations in photonic systems. We also discuss the generalization of our scheme to extend the number of superposed operations and the number of qubits. Due to the simplicity of our scheme, we believe that it can reduce the complexity or required resources of the quantum circuits and provide insights to investigate properties of entangled operations.
There has recently been much discussion regarding entanglement transformations in terms of local filtering operations and whether the optimal entanglement for an arbitrary two-qubit state could be realized. We introduce an experimentally realizable scheme for manipulating the entanglement of an arbitrary state of two polarization-entangled qubits. This scheme is then used to provide some perspective to the mathematical concepts inherent in this field with respect to a laboratory environment. Specifically, we look at how to extract enhanced entanglement from systems with a fixed rank, and, in the case where the rank of the density operator for the state can be reduced, show how the state can be made arbitrarily close to a maximally entangled pure state. In this context we also discuss bounds on entanglement in mixed states.
In this thesis, we report the theoretical and experimental investigations towards the creation, characterization, and manipulation of quantum entanglement in a photonic system. We examine two different aspects of quantum entanglement: In the first part, we discuss the experimental method for the preparation and characterization of SPDC-based polarization-entangled photon source. We provide a review study comparing different Entanglement Measures for non-maximally entangled two-qubit pure states and extend this analysis to higher-dimensional systems. In the second part, we study the entanglement dynamics of a two-qubit system in the presence of an Amplitude Damping Channel and present a scheme based on local unitary operations to protect entanglement from undergoing Entanglement Sudden Death. We extend the decoherence study to qubit-qutrit and qutrit-qutrit entangled systems and propose an entanglement protection scheme for the higher dimensional system.
Although quantum computers promise significant advantages, the complexity of quantum algorithms remains a major technological obstacle. We have developed and demonstrated an architecture-independent technique that simplifies adding control qubits to arbitrary quantum operations—a requirement in many quantum algorithms, simulations and metrology. The technique, which is independent of how the operation is done, does not require knowledge of what the operation is, and largely separates the problems of how to implement a quantum operation in the laboratory and how to add a control. Here, we demonstrate an entanglement-based version in a photonic system, realizing a range of different two-qubit gates with high fidelity. Quantum computing has advantages over conventional computing, but the complexity of quantum algorithms creates technological challenges. Here, an architecture-independent technique, that simplifies adding control qubits to arbitrary quantum operations, is developed and demonstrated.
A crucial subroutine in quantum computing is to load the classical data of
N complex numbers into the amplitude of a superposed $n=\ensuremath{\lceil}{log}_{2}N\ensuremath{\rceil}$-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least
O(N) constant weight operations. However, the proof assumes that only
n qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with
O(n2) circuit depth to encode any
N complex numbers using only single- and two-qubit gates, and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with
O(N2) ancillary qubits,
O(n2) circuit depth, and
O(n2) average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits, and at most
O(n) qubits are entangled. We also prove a fundamental lower bound $\mathrm{\ensuremath{\Omega}}(n)$ for the minimum circuit depth and runtime with an arbitrary number of ancillary qubits, aligning with our scheme with
O(n2). The algorithms are expected to have wide applications in both near-term and universal quantum computing.
A crucial subroutine in quantum computing is to load the classical data of
N complex numbers into the amplitude of a superposed
n=⌈log2N⌉-qubit state. It has been proven that any algorithm universally implementing this subroutine would need at least
O(N) constant weight operations. However, the proof assumes that only
n qubits are used, whereas the circuit depth could be reduced by extending the space and allowing ancillary qubits. Here we investigate this space-time tradeoff in quantum state preparation with classical data. We propose quantum algorithms with
O(n2) circuit depth to encode any
N complex numbers using only single-, two-qubit gates and local measurements with ancillary qubits. Different variances of the algorithm are proposed with different space and runtime. In particular, we present a scheme with
O(N2) ancillary qubits,
O(n2) circuit depth, and
O(n2) average runtime, which exponentially improves the conventional bound. While the algorithm requires more ancillary qubits, it consists of quantum circuit blocks that only simultaneously act on a constant number of qubits and at most
O(n) qubits are entangled. We also prove a fundamental lower bound $\mitΩ(n)$ for the minimum circuit depth and runtime with arbitrary number of ancillary qubits, aligning with our scheme with
O(n2). The algorithms are expected to have wide applications in both near-term and universal quantum computing.