Conal representation of quantum states and non-trace-preserving quantum operations
- Computer Laboratory, University of Cambridge, 15 JJ Thomson Avenue, Cambridge CB3 0FD (United Kingdom)
- DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA (United Kingdom)
We represent generalized density matrices of a d-complex dimensional quantum system as a subcone of a real pointed cone of revolution in R{sup d{sup 2}}, or indeed a Minkowskian cone in E{sup 1,d{sup 2}-1}. Generalized pure states correspond to certain future-directed lightlike vectors of E{sup 1,d{sup 2}-1}. This extension of the generalized Bloch sphere enables us to cater for non-trace-preserving quantum operations, and in particular to view the per-outcome effects of generalized measurements. We show that these consist of the product of an orthogonal transform about the axis of the cone of revolution and a positive real linear transform. We give detailed formulas for the one-qubit case and express the post-measurement states in terms of the initial-state vectors and measurement vectors. We apply these results in order to find the information gain versus disturbance trade-off in the case of two equiprobable pure states. Thus we recover Fuchs and Peres's formula in an elegant manner.
- OSTI ID:
- 20640297
- Journal Information:
- Physical Review. A, Vol. 68, Issue 4; Other Information: DOI: 10.1103/PhysRevA.68.042310; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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