Related papers: Subsystem Trace-Distances of Two Random States
We consider a fixed quantum measurement performed over $n$ identical copies of quantum states. Using a rigorous notion of distinguishability We consider a fixed quantum measurement performed over $n$ identical copies of quantum states.…
While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this work, we introduce an alternative…
We show that the quantum measurement known as the pretty good measurement can be used to identify an unknown quantum state picked from any set of $n$ mixed states that have pairwise fidelities upper-bounded by a constant below 1, given…
Distances between quantum states are reviewed within the framework of the tomographic-probability representation. Tomographic approach is based on observed probabilities and is straightforward for data processing. Different states are…
Measuring the closest distance between two states is an alternative and significant approach in the resource quantification, which is the core task in the resource theory. Quite limited progress has been made for this approach even in…
The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when…
In recent years, several measures have been proposed for characterizing the coherence of a given quantum state. We derive several results that illuminate how these measures behave when restricted to pure states. Notably, we present an…
The partial trace operation is usually considered in composite quantum systems, to reduce the state on a single subsystem. This operation has a key role in the decoherence effect and quantum measurements. However, partial trace operations…
We investigate the quantum state discrimination task for sets of linear independent pure states with an intrinsic ordering. This structured discrimination problems allow for a novel scheme that provides a certified level of error, that is,…
Quantum state designs, by enabling an efficient sampling of random quantum states, play a quintessential role in devising and benchmarking various quantum protocols with broad applications ranging from circuit designs to black hole physics.…
We study a coarse-graining map arising from incomplete and imperfect addressing of particles in a multipartite quantum system. In its simplest form, corresponding to a two-qubit state, the resulting channel produces a convex mixture of the…
We study the properties of the random quantum states induced from the uniformly random pure states on a bipartite quantum system by taking the partial trace over the larger subsystem. Most of the previous studies have adopted a viewpoint of…
The average subsystem trace distance has been proposed as an indicator of quantum many-body chaos and integrability. In integrable systems, evaluating the trace distance faces two challenges: the computational cost for large systems and…
We show that there is genuine quantum chaos despite that quantum dynamics is linear. This is revealed by introducing a physical distance between two quantum states. Qualitatively different from existing distances for quantum states, for…
We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the optimal strategy that minimizes the total probability of error. This leads to the identification of the…
We show it is possible to obtain quantum pseudorandomness and pseudoentanglement from random subset states -- i.e. quantum states which are equal superpositions over (pseudo)random subsets of strings. This answers an open question of…
The success of quantum information processing applications relies on accurate and efficient characterization of quantum states, especially nearly-pure states. In this work, we investigate a procedure for adaptive qubit state tomography…
We investigate the generic aspects of quantum coherence guided by the concentration of measure phenomenon. We find the average relative entropy of coherence of pure quantum states sampled randomly from the uniform Haar measure and show that…
We study the estimation of the overlap between two unknown pure quantum states of a finite dimensional system, given $M$ and $N$ copies of each type. This is a fundamental primitive in quantum information processing that is commonly…
We present exact results on a novel kind of emergent random matrix universality that quantum many-body systems at infinite temperature can exhibit. Specifically, we consider an ensemble of pure states supported on a small subsystem,…