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The uncertainty of a quantum state is given by the composition of two components. The first is called the quantum component and is given by the probability distribution of an observable relative to the state. The second is the classical…

We can learn (more) about the state a quantum system is in through measurements. We look at how to describe the uncertainty about a quantum system's state conditional on executing such measurements. We show that by exploiting the interplay…

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…

The Heisenberg uncertainty principle shows that no one can specify the values of the non-commuting canonically conjugated variables simultaneously. However, the uncertainty relation is usually applied to two incompatible measurements. We…

The standard postulates of quantum theory can be divided into two groups: the first one characterizes the structure and dynamics of pure states, while the second one specifies the structure of measurements and the corresponding…

A physical experiment comprises along the time trajectory a start, a time evolution (duration), and an end, which is the measurement. In non relativistic quantum mechanics the start of the experiment is defined by the wave function at time…

The dynamics of a single microscopic or mesoscopic non quantum system interacting with a macroscopic environment is generally stochastic. In the same way, the reduced density operator of a single quantum system interacting with a…

Indeterminacy associated with probing of a quantum state is commonly expressed through spectral distances (metric) featured in the outcomes of repeated experiments. Here we express it as an effective amount (measure) of distinct outcomes…

In this work, we show that the quantum mechanical notions of density operator, positive operator-valued measure (POVM), and the Born rule, are all simultaneously encoded in the categorical notion of a natural transformation of functors. In…

I introduce a framework to distinguish two domains of physics - the manifest (i.e. the directly observable empirical records in terms of manifest configurations) and the non-manifest domain of physics (i.e. the things that the manifest…

Do completely unpredictable events exist in nature? Classical theory, being fully deterministic, completely excludes fundamental randomness. On the contrary, quantum theory allows for randomness within its axiomatic structure. Yet, the fact…

The measurement problem is the issue of explaining how the objective classical world emerges from a quantum one. Here we take a different approach. We assume that there is an objective classical system, and then ask that the standard rules…

Heisenberg's uncertainty principle, coherence and Bell nonlocality have been individually examined through many experiments. In this Letter, we systematically characterize all of this quantumness in a unified manner. We first construct…

Wave-particle duality is one of the fundamental properties of matter and at the same time, one of the mysteries of modern physics. In this paper, we propose and analyze a new interpretation of the wave-particle duality, and propose a new…

In a recent paper [1], it has been claimed that the outcomes of a quantum coin toss which is idealized as an infinite binary sequence is 1-random. We also defend the correctness of this claim and assert that the outcomes of quantum…

One unique feature of quantum mechanics is the Heisenberg uncertainty principle, which states that the outcomes of two incompatible measurements cannot simultaneously achieve arbitrary precision. In an information-theoretic context of…

In ordinary situations involving a small part of the universe, Born's rule seems to work well for calculating probabilities of observations in quantum theory. However, there are a number of reasons for believing that it is not adequate for…

The very old problem of the statistical content of quantum mechanics (QM) is studied in a novel framework. The Born's rule (one of the basic postulates of QM) is derived from theory of classical random signals. We present a measurement…

The recently developed framework for quantum theory with no global causal order allows for quantum processes in which operations in local laboratories are neither causally ordered nor in a probabilistic mixture of definite causal orders.…

Indirect measurement can be used to read out the outcome of a quantum system without resorting to a straightforward approach, and it is the foundation of the measurement uncertainty relations that explain the incompatibility of conjugate…