We show that any unitary transformation performed on the quantum state of a closed quantum system, describes an inner, reversible, generalized quantum measurement. We also show that under some specific conditions it is possible to perform a unitary transformation on the state of the closed quantum system by means of a collection of generalized measurement operators. In particular, given a complete set of orthogonal projectors, it is possible to implement a reversible quantum measurement that preserves the probabilities. In this context, we introduce the concept of "Truth-Observable", which is the physical counterpart of an inner logical truth.
We give the logical description of a new kind of quantum measurement that is a reversible operation performed by an hypothetical insider observer, or, which is the same, a quantum measurement made in a quantum space background, like the fuzzy sphere. The result is that the non-contradiction and the excluded middle principles are both invalidated, leading to a paraconsistent, symmetric logic. Our conjecture is that, in this setting, one can develop the adequate logic of quantum computing. The role of standard quantum logic is then confined to describe the projective measurement scheme.
We present a complete classification of all possible sets of classical reversible gates acting on bits, in terms of which reversible transformations they generate, assuming swaps and ancilla bits are available for free. Our classification can be seen as the reversible-computing analogue of Post's lattice, a central result in mathematical logic from the 1940s. It is a step toward the ambitious goal of classifying all possible quantum gate sets acting on qubits. Our theorem implies a linear-time algorithm (which we have implemented), that takes as input the truth tables of reversible gates G and…
I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst" whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von~Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The result…
We prove new inner bounds for several multiterminal channels with classical inputs and quantum outputs. Our inner bounds are all proved in the one-shot setting, and are natural analogues of the best classical inner bounds for the respective channels. For some of these channels, similar quantum inner bounds were unknown even in the asymptotic iid setting. We prove our inner bounds by appealing to a new classical-quantum joint typicality lemma proved in a companion paper ("A one-shot quantum joint typicality lemma", Pranab Sen, arXiv:1806.07278). This lemma allows us to lift to the quantum setti…
A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-local, and it is natural to ask whether there are compelling reasons for rejecting theories in which stronger violations are possible. To shed light on this question, we consider post-quantum theories in which maximally non-local states (non-local boxes) occur. It has previously been conjectured that the set of dynamical transformations possible in such theories is severely limited. We settle the question affirmatively i…
We provide the first inner bounds for sending private classical information over a quantum multiple access channel. We do so by using three powerful information theoretic techniques: rate splitting, quantum simultaneous decoding for multiple access channels, and a novel smoothed distributed covering lemma for classical quantum channels. Our inner bounds are given in the one shot setting and accordingly the three techniques used are all very recent ones specifically designed to work in this setting. The last technique is new to this work and is our main technical advancement. For the asymptotic…
We consider the problem of communication over a classical-quantum broadcast channel with one sender and two receivers. Generalizing the classical inner bounds shown by Marton and the recent quantum asymptotic version shown by Savov and Wilde, we obtain one-shot inner bounds in the quantum setting. Our bounds are stated in terms of smooth min and max Renyi divergences. We obtain these results using a different analysis of the random codebook argument and employ a new one-shot classical mutual covering argument based on rejection sampling. These results give a full justification of the claims of…
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed versio…
The classical (parallel) black pebbling game is a useful abstraction which allows us to analyze the resources (space, space-time, cumulative space) necessary to evaluate a function $f$ with a static data-dependency graph $G$. Of particular interest in the field of cryptography are data-independent memory-hard functions $f_{G,H}$ which are defined by a directed acyclic graph (DAG) $G$ and a cryptographic hash function $H$. The pebbling complexity of the graph $G$ characterizes the amortized cost of evaluating $f_{G,H}$ multiple times as well as the total cost to run a brute-force preimage attac…
As small quantum computers are becoming available on different physical platforms, a benchmarking task known as cross-platform verification has been proposed that aims to estimate the fidelity of states prepared on two quantum computers. This task is fundamentally distributed, as no quantum communication can be performed between the two physical platforms due to hardware constraints, which prohibits a joint SWAP test. In this paper we settle the sample complexity of this task across all measurement and communication settings. The essence of the task, which we call distributed quantum inner pro…
The quantum mechanical description of the evolution of an unstable system defined initially as a state in a Hilbert space at a given time does not provide a semigroup (exponential) decay law. The Wigner-Weisskopf survival amplitude, describing reversible quantum transitions, may be dominated by exponential type decay in pole approximation at times not too short or too long, but, in the two channel case, for example, the pole residues are not orthogonal, and the evolution does not correspond to a semigroup (experiments on the decay of the neutral $K$-meson system strongly support the semigroup …
The concept of inner friction, by which a quantum heat engine is unable to follow adiabatically its strokes and thus dissipates useful energy, is illustrated in an exact physical model where the working substance consists of an ensemble of misaligned spins interacting with a magnetic field and performing the Otto cycle. The effect of this static disorder under a finite-time cycle gives a new perspective of the concept of inner friction under realistic settings. We investigate the efficiency and power of this engine and relate its performance to the amount of friction from misalignment and to t…
