Related papers: Trading Quantum Ensembles
Quantum technologies are developing powerful tools to generate and manipulate coherent superpositions of different energy levels. Envisaging a new generation of energy-efficient quantum devices, here we explore how coherence can be…
We discuss counterintuitive aspects of probabilities for systems of identical particles obeying quantum statistics. Quantum coins and children (two level systems) and quantum dice (many level systems) are used as examples. It is emphasized…
Different ensembles of quantum states can have the same average nonpure state. Distinguishing between such constructions, via different mixing procedures of the same nonpure quantum state, is known to entail signaling. In parallel,…
The entropy of a quantum operation, defined as the von Neumann entropy of the corresponding Choi-Jamio{\l}kowski state, characterizes the coupling of the principal system with the environment. For any quantum channel $\Phi$ acting on a…
We introduce and analyze a task that we call symmetrization, in which a state of a quantum system, associated with a symmetry group, is transformed by a random unitary operation to a symmetric state. Each element of the unitary ensemble is…
The class of incoherent operations induces a pre-order on the set of quantum pure states, defined by the possibility of converting one state into the other by transformations within the class. We prove that if two $n$-dimensional pure…
In quantum process tomography, it is possible to express the experimenter's prior information as a sequence of quantum operations, i.e., trace-preserving completely positive maps. In analogy to de Finetti's concept of exchangeability for…
Absolutely maximally entangled (AME) pure states of a system composed of $N$ parties are distinguished by the property that for any splitting at least one partial trace is maximally mixed. Due to maximal possible correlations between any…
Through superposition, a quantum computer is capable of representing an exponentially large set of states, according to the number of qubits available. Quantum machine learning is a subfield of quantum computing that explores the potential…
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
Many appplications in computational science are sufficiently compute-intensive that they depend on the power of parallel computing for viability. For all but the "embarrassingly parallel" problems, the performance depends upon the level of…
The recently established resource theory of quantum coherence allows for a quantitative understanding of the superposition principle, with applications reaching from quantum computing to quantum biology. While different quantifiers of…
We establish a sharp quantum advantage in determining the parity (even/odd) of an unknown permutation applied to any number $n \ge 3$ of particles. Classically, this is impossible with fewer than $n$ labels, being that the success is…
Bounds analogous to entropic uncertainty relations allow one to design practical tests to detect quantum entanglement by a collective measurement performed on several copies of the state analyzed. This approach, initially worked out for…
Two particles are identical if all their intrinsic properties, such as spin and charge, are the same, meaning that no quantum experiment can distinguish them. In addition to the well known principles of quantum mechanics, understanding…
In this paper, we consider a subclass of quantum states in the multipartite system, namely, the supersymmetric states. We investigate the problem whether they admit the symmetrically separable decomposition, i.e., each term in this…
We analyze general aspects of exchangeable quantum stochastic processes, as well as some concrete cases relevant for several applications to Quantum Physics and Probability. We establish that there is a one-to-one correspondence between…
PARITY is the problem of determining the parity of a string $f$ of $n$ bits given access to an oracle that responds to a query $x\in\{0,1,...,n-1\}$ with the $x^{\rm th}$ bit of the string, $f(x)$. Classically, $n$ queries are required to…
We investigate an advantage for information processing of ordering a set of states over making a global quantum processing with a fixed number of copies of coherent states. Suppose Alice has $N$ copies of one of two quantum states…