Related papers: A Hierarchy for Replica Quantum Advantage
Learning properties of quantum states from measurement data is a fundamental challenge in quantum information. The sample complexity of such tasks depends crucially on the measurement primitive. While shadow tomography achieves…
It is often argued that entanglement is at the root of the speedup for quantum compared to classical computation, and that one needs a sufficient amount of entanglement for this speedup to be manifest. In measurement-based quantum computing…
We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about number and positions of errors in the noisy ensemble in an explicit and controlled way,…
We consider the quantum memory assisted quantum state verification task, where an adversary prepare independent multipartite entangled states and send to the local verifiers, who then store several copies in the quantum memory and measure…
We produce and holographically measure entangled qudits encoded in transverse spatial modes of single photons. With the novel use of a quantum state tomography method that only requires two-state superpositions, we achieve the most complete…
Fault-tolerant quantum computation can be achieved by creating constant-sized, entangled resource states and performing entangling measurements on subsets of their qubits. Linear optical quantum computers can be designed based on this…
The entanglement entropy of a subsystem $A$ of a quantum system is expressed, in the replica method, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix $\tr\rho_A^n$. We study the…
In multi-parameter quantum metrology, the resource of entanglement can lead to an increase in efficiency of the estimation process. Entanglement can be used in the state preparation stage, or the measurement stage, or both, to harness this…
Suppose you receive a sequence of qubits where each qubit is guaranteed to be in one of two pure states, but you do not know what those states are. Your task is to determine the states. This can be viewed as a kind of quantum state learning…
We consider the problem of private set membership aggregation of $N$ parties by using an entangled quantum state. In this setting, the $N$ parties, which share an entangled state, aim to \emph{privately} know the number of times each…
We consider the problem of learning $N$ identical copies of an unknown $n$-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly $d$ neighboring vertices. Here, we…
There is growing belief that the next decade will see the emergence of sensing devices based on the laws of quantum physics that outperform some of our current sensing devices. For example, in frequency estimation, using a probe prepared in…
The ability of quantum computers to directly manipulate and analyze quantum states stored in quantum memory allows them to learn about aspects of our physical world that would otherwise be invisible given a modest number of measurements.…
This thesis explores the use of entangled states in quantum computation and quantum information science. Entanglement, a quantum phenomenon with no classical counterpart, has been identified as an important and quantifiable resource in many…
Measurements are essential for the processing and protection of information in quantum computers. They can also induce long-range entanglement between unmeasured qubits. However, when post-measurement states depend on many non-deterministic…
In this work, we study the problem of testing properties of the spectrum of a mixed quantum state. Here one is given $n$ copies of a mixed state $\rho\in\mathbb{C}^{d\times d}$ and the goal is to distinguish whether $\rho$'s spectrum…
It is a central fact in quantum mechanics that non-orthogonal states cannot be distinguished perfectly. This property ensures the security of quantum key distribution. It is therefore an important task in quantum communication to design and…
It is shown that (i) all entangled states can be mapped by single-copy measurements into probability distributions containing secret correlations, and (ii) if a probability distribution obtained from a quantum state contains secret…
Unpredictability, or randomness, of the outcomes of measurements made on an entangled state can be certified provided that the statistics violate a Bell inequality. In the standard Bell scenario where each party performs a single…
The entropy of a quantum system is a measure of its randomness, and has applications in measuring quantum entanglement. We study the problem of measuring the von Neumann entropy, $S(\rho)$, and R\'enyi entropy, $S_\alpha(\rho)$ of an…