Related papers: On the distinguishability of random quantum states
Given a quantum state in the finite-dimensional Hilbert space $ \C^n $, the range of possible values of a quantum observable is usually identified with the discrete spectrum of eigenvalues of a corresponding Hermitian matrix. Here any such…
The estimation of high dimensional quantum states is an important statistical problem arising in current quantum technology applications. A key example is the tomography of multiple ions states, employed in the validation of state…
With the advance of quantum information technology, the question of how to most efficiently test quantum circuits is becoming of increasing relevance. Here we introduce the statistics of lengths of measurement sequences that allows one to…
We analyze the properties of entangled random pure states of a quantum system partitioned into two smaller subsystems of dimensions $N$ and $M$. Framing the problem in terms of random matrices with a fixed-trace constraint, we establish,…
It is a fundamental problem to decide how many copies of an unknown mixed quantum state are necessary and sufficient to determine the state. Previously, it was known only that estimating states to error $\epsilon$ in trace distance required…
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 random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the…
The laws of quantum mechanics place fundamental limits on the accuracy of measurements and therefore on the estimation of unknown parameters of a quantum system. In this work, we prove lower bounds on the size of confidence regions reported…
Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another.…
Quantum state tomography via local measurements is an efficient tool for characterizing quantum states. However it requires that the original global state be uniquely determined (UD) by its local reduced density matrices (RDMs). In this…
We study the entanglement generation of operators whose statistical properties approach those of random matrices but are restricted in some way. These include interpolating ensemble matrices, where the interval of the independent random…
In differential privacy (DP), we want to query a database about n users, in a way that "leaks at most eps about any individual user," even conditioned on any outcome of the query. Meanwhile, in gentle measurement, we want to measure n…
We consider two different optimized measurement strategies for the discrimination of nonorthogonal quantum states. The first is conclusive discrimination with a minimum probability of inferring an erroneous result, and the second is…
Standard approaches to quantum statistical inference rely on measurements that induce a collapse of the wave function, effectively consuming the quantum state to extract information. In this work, we investigate the fundamental limits of…
The problem of quantum state classification asks how accurately one can identify an unknown quantum state that is promised to be drawn from a known set of pure states. In this work, we introduce the notion of $k$-learnability, which…
Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin…
This work investigates which sets of quantum states give rise to the highest achievable success probability in minimum-error state discrimination if multiple copies of the unknown state are given. Specifically, we consider uniformly…
We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the…
Entanglement is a cornerstone in quantum information science, yet detecting it efficiently remains a challenging task. Focusing on non-positive partially transposed (NPT) states, we establish a hierarchy among entropy-based, majorization,…
The creation of complex entangled states, resources that enable quantum computation, can be achieved via simple 'probabilistic' operations which are individually likely to fail. However, typical proposals exploiting this idea carry a severe…